CONGRESS SCHEDULE OVERVIEW

CONGRESS SCHEDULE OVERVIEW

SUN MON TUE WED THU FRI

08:00 Registration 08:00

08:45Opening

08:45

09:00 09:00

09:30 Special Sessions and Contributed Talks 09:30

10:00 10:00

10:30 MORNING TEA 10:30

11:00 11:00

11:30 Special Sessions and Contributed Talks 11:30

12:00 12:00

12:30 12:30

1:00 LUNCH 1:00

1:30 1:30

2:00Plenary 3 Plenary 6 Plenary 11

2:00

2:30Plenary 1 Plenary 9

2:30


AFT TEA 3:00

3:30 Registration AFT TEA AFT TEAPlenary 12

3:30

4:00Plenary 2

AFTERNOON TEAPlenary 10

4:00


Closing 4:30

5:00 Welcome 5:00

5:30 Reception Buses to 5:30

6:00 and King St 6:00

6:30 Registration Wharf 6:30

7:00 7:00

7:30 7:30

8:00 Harbour 8:00

8:30 Cruise 8:30

9:00 9:00

9:30 9:30

10:00 10:00

10:30 Buses to 10:30

11:00 UNSW 11:00

1st PRIMA Congress

The inaugural Pacific Rim Mathematical Association (PRIMA) Congress will be held at theUniversity of New South Wales, Sydney, Australia, on July 6–10, 2009.

PRIMA is an association of mathematical sciences institutes, departments and societies fromaround the Pacific Rim, established in 2005 with the aim of promoting and facilitating thedevelopment of the mathematical sciences throughout the Pacific Rim region.

2 1st PRIMA Congress

Contents

1st PRIMA Congress 1

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Welcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Sponsors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Congress Planning Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Scientific Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Local Arrangements Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Plenary Speakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Special Sessions Organizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Thanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Related Conferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Information 11

Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Dining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Congress Venue and Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Registration and Information Desk . . . . . . . . . . . . . . . . . . . . . . . . . 15

Welcome Reception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Opening Ceremony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Plenary Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Special Sessions and Contributed Talks . . . . . . . . . . . . . . . . . . . . . . . 15

Morning and Afternoon Tea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Lunch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Sydney Harbour Dinner Cruise . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Closing Ceremony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Breakout Rooms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Book Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Contents 3

Useful Contacts and Services on Campus . . . . . . . . . . . . . . . . . . . . . . 17

Information Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Equipment in Seminar Rooms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Wireless Internet Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Computer Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Printing and Photocopying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Program 19

Plenary Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Special Sessions and Contributed Talks . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Timetable by Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Timetable by Day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Abstracts 35

Plenary Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Algebraic Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Commutative Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Computational Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Dynamical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Geometric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Industrial Applications of Mathematics: Multiscale Mechanics . . . . . . . . . . . . . 71

Industrial Applications of Mathematics: Mathematical Finance . . . . . . . . . . . . 75

Inverse Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Mathematics of Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Mathematical Finance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Mathematical Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Scientific Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Stringy Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Symplectic Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Contributed Papers 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118




List of Delegates 145

Welcome 5

Welcome

The Pacific Rim Mathematical Association (PRIMA) has as its goal to promote and facilitatethe development of the mathematical sciences in the Pacific Rim region, broadly defined. Themotivation for forming it was a recognition that this region would play an increasingly importantrole in world mathematics in the years to come.

PRIMA was begun at a meeting in Banff in 2005 convened by the Pacific Institute of the Math-ematical Sciences in Vancouver and the Mathematical Sciences Research Institute in Berkeley.Delegates from a large number of institutes and universities around the Rim attended. Theinternational character of mathematics and science, so often remarked on, was clearly displayed,and it proved easy to agree on the goals of the the new organization, including activities to en-courage communication, to train the next generations of researchers, and to promote the impactof mathematics on society and the global economy by pooling resources.

One of the many concrete steps proposed was to hold international congresses. The meeting inSydney that is about to take place is the first of these events. It has been very gratifying to seehow well and quickly it has come together through the cooperative work of many scientific andorganizational committees! We are particularly grateful to the Local Arrangements Committeemembers, both at the University of New South Wales here in Sydney, and internationally, whohave done an outstanding job with the local organization of the congress.

Now the work is done, and it’s time to enjoy the fruits. We very much look forward not onlyto the scientific addresses and sessions, but also the great diversity of participants. We hopeyou’ll enjoy them too, and that you’ll make many productive new contacts, both scientific andpersonal. If so, this first PRIMA Congress will have been a success.

Alejandro AdemChair of the Congress Planning Committee

David EisenbudChair of the Scientific Committee

Gary FroylandChair of the Local Arrangements Committee


Organization

Sponsors

Australian Mathematical Sciences Institute (AMSI)http://www.amsi.org.au

Australian Mathematical Society (AustMS)http://www.austms.org.au

Australian and New Zealand Industrial and Applied Mathematics (ANZIAM)http://www.anziam.org.au

Australian Research Council: Centre of Excellence for Mathematics and Statistics of ComplexSystems (MASCOS)http://www.complex.org.au

Mathematical Sciences Research Institute (MSRI)http://www.msri.org

National Sciences Foundation (NSF)http://www.nsf.gov

Pacific Institute for the Mathematical Sciences (PIMS)http://pims.maths.ca

School of Mathematics and Statistics, University of New South Waleshttp://www.maths.unsw.edu.au

Organization 7

Congress Planning Committee

ChairAlejandro Adem (Pacific Institute for the Mathematical Sciences, Canada)

Nassif Ghoussoub (University of British Columbia, Canada)

Tony Guttmann (University of Melbourne, Australia)

Toshitake Kohno (University of Tokyo, Japan)

Doug Lind (University of Washington, USA)

Yiming Long (Chern Institute of Mathematics, China)

Jong Hae Keum (Korea Institute for Advanced Study, Korea)

Scientific Committee

ChairDavid Eisenbud (University of California Berkeley, USA)

Rafael Benguria (Catholic University, Chile)

Phil Broadbridge (Australian Mathematical Sciences Institute, Australia)

Kung-Ching Chang (Peking University, China)

Jose Antonio de la Pena (UNAM & CONACYT, Mexico)

Ivar Ekeland (University of British Columbia, Canada)

Yasha Eliashberg (Stanford University, USA)

Masaki Kashiwara (Research Institute for Mathematical Sciences, Kyoto University, Japan)

Hyo Chul Myung (Korean Institute for Advanced Study, Korea)

Ian Sloan (University of New South Wales, Australia)

Tatiana Toro (University of Washington, USA)

Local Arrangements Committee

ChairGary Froyland (University of New South Wales, Australia)

Alejandro Adem (Pacific Institute for the Mathematical Sciences, Canada)

Adelle Coster (University of New South Wales, Australia)

Josef Dick (University of New South Wales, Australia)

Tony Dooley (University of New South Wales, Australia)


Mark Gotay (Pacific Institute for the Mathematical Sciences, Canada)

Catherine Greenhill (University of New South Wales, Australia)

Tony Guttmann (University of Melbourne, Australia)

Jonathan Kress (University of New South Wales, Australia)

Frances Kuo (University of New South Wales, Australia)

Doug Lind (University of Washington, USA)

Chi Mak (University of New South Wales, Australia)

Ian Sloan (University of New South Wales, Australia)

Amber Tye (University of New South Wales, Australia)

Plenary Speakers

Myles Allen (University of Oxford, UK)

Federico Ardila (San Francisco State University, USA)

Kenji Fukaya (Kyoto University, Japan)

Nassif Ghoussoub (University of British Columbia, Canada)

Seok-Jin Kang (Seoul National University, Korea)

Yujiro Kawamata (University of Tokyo, Japan)

Shige Peng (Shandong University, China)

Linda Petzold (University of California Santa Barbara, USA)

Cheryl Praeger (University of Western Australia, Australia)

Stanislav Smirnov (University of Geneva, Switzerland)

Gang Tian (Princeton University, USA and Peking University, China)

Gunther Uhlmann (University of Washington, USA)

Special Sessions Organizers

Algebraic GeometryJ. Keum (KIAS), L. Ein (UIC), K. Oguiso (Keio U.)

Commutative AlgebraD. Eisenbud (UC Berkeley), A. K. Singh (U. Utah), K. Watanabe (Nihon)

Computational AlgebraJ. Cannon (U. Sydney), K. Geddes (U. Waterloo)

Organization 9

Dynamical SystemsD. Lind (U. Washington), T. Dooley (UNSW), G. Froyland (UNSW)

Geometric AnalysisG. Tian (Princeton), J. Chen (UBC), W. Ding (Peking U.)

Industrial Applications of Mathematics: Multiscale MechanicsA. Tordesillas (U. Melbourne)

Industrial Applications of Mathematics: Mathematical FinanceR. Kuske (UBC)

Inverse ProblemsG. Uhlmann (U. Washington), G. Bal (Columbia)

Mathematics of Climate ChangeM. England (UNSW), C. Jones (U. North Carolina)

Mathematical FinanceS. Peng (Shandong U.), I. Ekeland (UBC)

Mathematical PhysicsR. Benguria (U. Catolica de Chile), T. Guttmann (U. Melbourne)

Partial Differential EquationsN. Ghoussoub (UBC), Y. Long (Nankai U.)

Scientific ComputingL. Petzold (UC Santa Barbara), I. Sloan (UNSW)

Stringy TopologyA. Adem (UBC), Y. Ruan (U. Michigan), C. Westerland (U. Melbourne)

Symplectic GeometryK. Fukaya (Kyoto U.), Y. Eliashberg (Stanford)

Thanks

Main Website and Front Cover:Adam Wojtowicz <[email protected]>

PRIMA Sydney 2009 Logo Creator:Andrew Bramble <[email protected]>

PRIMA Sydney 2009 Logo Creative Input:Bruce Henry <[email protected]>


Related Conferences

IMACS / MODSIM09

The 18th World IMACS Congress and MODSIM09 InternationalCongress on Modelling and Simulation will be held in Cairns, Aus-tralia from the 13–17th July 2009.

Interfacing Modelling and Simulation with Mathematical andComputational Sciences MSSANZ and IMACS bring together abroad spectrum of scientists who apply various mathematical mod-elling, simulation, statistical, engineering, spatial and computerscience methodologies and skills in solving practical problems com-ing from a wide range of endeavours including environmental andglobal change modelling, water resources management, health care,biological simulation and engineering.

For them, the practical matter under investigation and the available data are the driving forcesbehind the methodology chosen for the task, or in developing techniques required to analyse newmodels.

The Congress is the first time MSSANZ and IMACS have combined their meetings and it is sureto provide a rich forum for the exchange of knowledge about modelling and simulation.

The running of the The 18th World IMACS and MODSIM09 International Congress and thePRIMA Congress in consecutive weeks provide an excellent opportunity for international visitorsto participate in two world-class scientific events in iconic Australian cities.

CEF09

Computing in Economics and Finance (CEF09) is the annual meet-ing of the Society for Computational Economics, bringing togetherresearchers in economics, finance and decision-making whose workhas a strong computational focus. CEF09 will be held at the Uni-versity of Technology, Sydney (UTS) in the week following PRIMA2009.

FMEWM09

AMSI / MASCOS / UNESCO Industry workshop and shortcourse: Future Models for Energy and Water Management undera Regulated Environment will be held at Queensland Universityof Technology from 20–22 July 2009.

Information

12 Information

Location

The conference venue is the Kensington Campus of the University of New South Wales. TheUniversity, one of Australia’s largest, is located seven kilometres from the heart of Sydney. It iswithin walking distance of shopping facilities, banks and a variety of places to eat.

The University of New South Wales is a short bus ride away from Coogee Beach. Although it iswinter in Australia in July, there are still lots of reasons to visit Coogee: beautiful views of theocean, a coastal path stretching north to Bondi Beach, many great cafes and restaurants.

There are also buses from the University of New South Wales to take visitors right into thecentre of Sydney: either to Central Station or to Circular Quay, home of the Sydney OperaHouse and the Sydney Harbour Bridge.

The weather in Sydney in July can vary from quite cool (maximum 16 degrees Celsius) to verycomfortable (maximum 20 degrees Celsius). Even when the weather is cool, there is a goodchance of blue skies: the mean number of sunshine hours in Sydney in July is 6.4 per day.

Sydney is within easy distance of several great holiday destinations within the state of New SouthWales. These include the Blue Mountains, the Hunter Valley wine region and the snowfields ofthe Snowy Mountains, near Mt Kosciuszko (Australia’s highest peak).

Information about the University of New South Waleshttp://www.unsw.edu.au/about/pad/about.html

Public transport to and from the University of New South Waleshttp://prima2009.maths.unsw.edu.au/publictransport.html

Coogee Beachhttp://en.wikipedia.org/wiki/Coogee,_New_South_Wales

More information about Sydney including Sydney eventshttp://www.sydneyaustralia.com/

Climate statistics for Sydneyhttp://www.bom.gov.au/climate/averages/tables/cw_066062.shtml

Weather forecast for Sydneyhttp://www.bom.gov.au/products/IDN10064.shtml

Tourism New South Waleshttp://www.visitnsw.com/

Tourism Australiahttp://www.australia.com/

Location 13

Transport

Travel to and from the airport

Taxi: The journey from either the City or the University of New South Wales to the airporttakes 15 to 20 minutes and costs around AUD $35. All taxis are licenced and all journeys aremetered. Tipping is not necessary, but people often round the fare up.

Bus: The route 400 bus will take you from the University of New South Wales to the airport.The bus takes about 40 minutes and costs AUD $4.20.

(Warning: not every 400 bus goes to the airport. Please check the timetable carefully and if indoubt, ask the driver before you get on. This is quite a slow journey and the buses are oftencrowded.)

Train: If you are staying in the City near Central Station or one of the City Circle stations, theeasiest and fastest way to get to the airport is by train. The Airport Link train runs regularlyand takes about 15 minutes to reach the airport from Central Station. The fare is approximatelyAUD $15.

Travel around Sydney

Sydney has an extensive public transport network involving trains, buses and ferries. There is alot of information on the Transport Infoline webpage http://www.131500.info/.

If travelling with a group of people, a taxi could be an affordable alternative. These can behailed on the street or ordered by telephone.

Travelling to the University of New South Wales on public transport will involve getting on abus. (The University of New South Wales does not lie on a rail line.) For general informationabout Sydney’s buses including timetables and maps, visit the Sydney Buses “Getting Around”site http://www.sydneybuses.info/getting-around/timetables.htm.

Below we give some details about how to catch buses to the University of New South Wales.

If you will be catching buses regularly while in Sydney you should consider buying a TravelTen card. A brown Travel Ten card covers the journey from Central Station to the Universityof New South Wales and a red Travel Ten card covers the journey from Circular Quay to theUniversity of New South Wales. Alternatively, a Blue Weekly Travelpass will provide unlimitedtravel between the University of New South Wales and the City and throughout the Blue TravelZone. Travel Ten and Weekly Travelpass cards as well as single trip prepaid tickets are availablefrom shops displaying the purple PREPAID symbol, including ARC shops on campus.

Note that you must purchase a prepaid ticket before boarding any express or limited stop busservice (e.g. bus numbers 891 and 10) and bus in the City (e.g., Eddy Ave, George St, etc.)between 7am and 7pm on weekdays.

14 Information

Travel to the University of New South Wales

The University of New South Wales is situated on several bus lines. From Central Station catchthe 891 Express bus or routes 391, 393, and 395. These depart from Eddy Ave and stop atthe University of New South Wales Kensington Campus. The journey takes around 15 minuteson the express and around 25 minutes on the other routes, depending on traffic. The route 10metrobus is a limited stop service that passes the University of New South Wales. Catch it fromRailway Square, and a number of stops on George, Park and Elizabeth Streets.

From Circular Quay catch the 392, 394, X94 (express), L94 or 396 to the University of NewSouth Wales Kensington Campus. The journey should take about 30 minutes. From BondiJunction take the 400 which passes the University of New South Wales on its way to the airport.

The PRIMA2009 Local Information website

http://prima2009.maths.unsw.edu.au/publictransport.html

has more detailed information on getting to and from the University of New South Wales bybus.

Parking is restricted on the University of New South Wales campus, with only a limited numberof Pay and Display parking spaces available for those without a permit.

Dining

Sydney has many restaurant districts, only a few of which are mentioned below. Tipping is notexpected, but often something between a few dollars and 10% is left for good service.

Restaurants near the University of New South Wales

ANZAC Parade: Walk South along ANZAC Parade from the University of New South Walesto find a number of inexpensive Asian restaurants.

Randwick Shops: Walk East up High Street past the Prince of Wales Hospital and left intoBelmore Rd. There are number of restaurants along Belmore and Alison Roads.

The Spot: A village setting with Cafes, Bar, Restaurants and a cinema.

Restaurants at Coogee

There are many restaurants around the bay and along Coogee Bay Road heading away from thebeach.

Restaurants in the City

Many restaurants are scattered around the City Centre. The Chinatown area between RailwaySquare and Darling Harbour has a high density of Asian Restaurants.

Congress Venue and Schedule 15

Congress Venue and Schedule

An outline of the congress schedule is shown on the inside of the front cover of this book. Acampus map with the congress venue highlighted can be found on the back cover. There is alsoa venue schematic map on the inside of the back cover.

Registration and Information Desk

Registration will take place from 2:30pm to 7pm on Sunday 5 July and from 8am to 4pm onMonday 6 July at the back counter of Sir John Clancy Auditorium (map reference C24).

From Tuesday to Friday the registration and information desk will be located in the MathewsPavilions (map reference E24) each day from 10am until the end of afternoon tea (see Page 16).

Welcome Reception

The welcome reception will take place in the Scientia Foyer (map reference G19) from 5pm to7pm on Sunday 5 July. This reception is free to all delegates. Drinks and finger food will beprovided. Come along and meet some of your fellow Pacific Rim mathematicians.

Opening Ceremony

The opening ceremony will be held in Sir John Clancy Auditorium from 8:45am to 9:15am onMonday 6 July.

Plenary Lectures

Plenary lectures will be held in Sir John Clancy Auditorium in the afternoons from either 2pmor 2:30pm each day. For the precise times each day see the schedule outline on the inside of thefront cover.

Plenary lectures are 45 minutes long plus 10 minutes for questions and discussions.

Special Sessions and Contributed Talks

Special sessions and contributed talks will be held from 9:30am to 1pm in the Mathews TheatresB, C and D (map reference D23), and various seminar rooms in the Mathews Building (mapreference F23).

Talks in special sessions are either 45 minutes long plus 10 minutes for questions and discussionsor 20 minutes long plus 5 minutes for questions and discussions. All contributed talks are 20minutes long plus 5 minutes for questions and discussions.

16 Information

There is a 5-minute window after each talk for delegates to move between parallel sessions.Due to the tight congress schedule, we kindly ask the chair of each session to observe the timeconstraints.

Morning and Afternoon Tea

Half-hour morning and afternoon teas will be provided in the Mathews Pavilions from 10:30amevery morning, and in the afternoons from 3:30pm on Monday and Thursday, from 4pm onTuesday and Wednesday, and from 3pm on Friday; see the schedule outline on the inside of thefront cover.

Lunch

Lunch break starts at 1pm daily and ends at 2:30pm on Monday and Thursday, and at 2pm onTuesday, Wednesday and Friday. There are many cafes, restaurants and foodcourts on campus.Locations are marked in yellow on the campus map and venue map.

Sydney Harbour Dinner Cruise

On Thursday 9 July there will be a harbour dinner cruise on the “Sydney Harbour Ballroom”.The cruise will depart at 7pm from King St Wharf, Darling Harbour, in the centre of Sydney.We will cruise the beautiful Sydney Harbour and enjoy a three course dinner.

Buses will be provided to transport delegates between the University of New South Wales andDarling Harbour. Or if you prefer, you can meet us there. Buses will depart from the Universityof New South Wales at 5:30pm and return from Darling Harbour at 10:30pm.

Closing Ceremony

The closing ceremony will be held in Sir John Clancy Auditorium from 4:30pm on Friday 6 July,immediately after the final plenary lecture.

Breakout Rooms

Seminar rooms 302 and 303 in the Mathews Building will be available as breakout rooms from9am to 5pm daily.

Book Display

There will be a book display at the Mathews Pavilions from 9:30am to 4:30pm daily.

Congress Venue and Schedule 17

Useful Contacts and Services on Campus

The Police, Ambulance and Fire emergency phone number is 000.

To contact the University of New South Wales Campus security dial 56666 from an internalphone or 9385 6666 from an off-campus phone.

The University Health Service is located in the East Quadrangle Building (map reference E17).Visit in person or call 9385 5425 for an appointment to see a doctor.

Taxis can be hailed on the street or booked online at http://www.taxiscombined.com.au orby calling 133 300.

The Commonwealth Bank and an Australia Post office are located at F22 on the campus map.

18 Information

Information Technology

Equipment in Seminar Rooms

Each seminar room is equipped with a desktop computer running Windows, with USB portaccess and internet connection, a data projector, an overhead projector, a projection screen, anda blackboard or a whiteboard.

We strongly encourage you to bring your talk in the form of a PDF document on a USB storagedevice. Please make sure that your talk is copied onto the desktop computer during the breakprior to your talk. The seminar rooms will be open from 9am each day.

The desktop computers in the seminar rooms can display Powerpoint documents but we cannotguarantee that all fonts will be available. Note that postscript files cannot be displayed.

If you require access to other software packages or other audio-visual equipments, please com-municate with the organizers well ahead of time to see if it can be arranged. It is possible toconnect your personal laptop to the data projector, but we prefer that you avoid this option dueto the tight congress schedule. If you need to use your own laptop, please make sure you testthe connection well before your talk.

Wireless Internet Access

Wireless internet access is available for all delegates through the UNIWIDE network. A per-sonal login and password together with instructions for configuration will be provided with theregistration pack.

Computer Access

Delegates can also access the computer lab M020 on the Mezzanine level of the Red Center (mapreference H15). The lab is open from 8am to 9pm daily. A login and password will be providedwith the registration pack.

Printing and Photocopying

Delegates will not be able to print documents in the computer lab. Print Post Plus (P3) canprint documents on a USB memory key for a small fee. This shop is located on level 1 of theMathews building (map reference F23) near the Commonwealth Bank.

A photocopy card for use in the library (map reference E21) can be purchased from the printingand copying counter on the entry level of the library.

Program

20 Program

Plenary Lectures

AFT

ER

NO

ON

PLE

NA

RY

LE

CT

UR

ES

Sir

Joh

nC

lancy

Audit

oriu

m

MO

NT

UE

WE

DT

HU

FR

I

2:0 0

K.Fuka

yap37

L.Pet

zold

p38

C.E

.P

raeg

erp41

2:3 0

G.U

hlm

ann

p36

chai

r:Y

.Elias

hber

gch

air:

I.Sloan

N.G

hou

ssou

bp39

chai

r:J.Can

non

3:0 0

chai

r:D

.Lin

dF.A

rdila

p37

M.A

llen

p38

chai

r:Y

.Lon

gA

FT

ER

NO

ON

TE

A

3:30

AFT

ER

NO

ON

TE

Ach

air:

L.Ein

chai

r:C.Jon

esA

FT

ER

NO

ON

TE

AS.-J.K

ang

p41

4:00

S.Sm

irnov

p36

AFT

ER

NO

ON

TE

AS.Pen

gp39

chai

r:H

.C.M

yung

4:30

chai

r:J.de

Gie

rY

.K

awam

ata

p37

G.T

ian

p39

chai

r:R

.Ellio

ttC

losi

ng

5:00

chai

r:D

.Eisen

bud

chai

r:J.Che

n

Special Sessions and Contributed Talks 21

Special Sessions and Contributed TalksM

OR

NIN

GSE

SSIO

NS

OU

TLIN

E

MO

NT

UE

WE

DT

HU

FR

I

Mathew

s-B

Inve

rse

Pro

blem

sIn

vers

ePro

blem

sIn

vers

ePro

blem

sStr

ingy

Top

olog

yStr

ingy

Top

olog

y

Mathew

s-C

Dyn

amic

alSys

tem

sD

ynam

ical

Sys

tem

sPar

tial

Diff

eren

tial

Equ

atio

ns

Par

tial

Diff

eren

tial

Equ

atio

ns

Par

tial

Diff

eren

tial

Equ

atio

ns

Mathew

s-D

Indu

stri

alA

pplica

tion

sof

Mat

hem

atic

s:M

ultis

cale

Mec

hanic

s

Indu

stri

alA

pplica

tion

sof

Mat

hem

atic

s:M

ultis

cale

Mec

hanic

s

Sci

entific

Com

puting

Sci

entific

Com

puting

Sci

entific

Com

puting

Mathew

s-102

Com

muta

tive

Alg

ebra

Com

muta

tive

Alg

ebra

Com

muta

tive

Alg

ebra

Mat

hem

atic

alFin

ance

Mat

hem

atic

alFin

ance

Mathew

s-107

Alg

ebra

icG

eom

etry

Alg

ebra

icG

eom

etry

Com

puta

tion

alA

lgeb

raC

ompu

tation

alA

lgeb

raC

ompu

tation

alA

lgeb

ra

Mathew

s-309

Mat

hem

atic

alFin

ance

Indu

stri

alA

pplica

tion

sof

Mat

hem

atic

s:M

athe

mat

ical

Fin

ance

Mat

hem

atic

sof

Clim

ate

Cha

nge

Mat

hem

atic

sof

Clim

ate

Cha

nge

Mat

hem

atic

sof

Clim

ate

Cha

nge

Mathew

s-310

Sym

plec

tic

Geo

met

rySym

plec

tic

Geo

met

ryM

athe

mat

ical

Phy

sics

Mat

hem

atic

alPhy

sics

Mat

hem

atic

alPhy

sics

Mathew

s-312

Str

ingy

Top

olog

yG

eom

etri

cA

nal

ysis

Geo

met

ric

Anal

ysis

Geo

met

ric

Anal

ysis

Dyn

amic

alSys

tem

s

Mathew

s-307

Con

trib

ute

dPap

ers

1C

ontr

ibute

dPap

ers

1Sym

plec

tic

Geo

met

ryC

ontr

ibute

dPap

ers

1A

lgeb

raic

Geo

met

ry

Mathew

s-308

Con

trib

ute

dPap

ers

2C

ontr

ibute

dPap

ers

2C

ontr

ibute

dPap

ers

2C

ontr

ibute

dPap

ers

2C

ontr

ibute

dPap

ers

1

Mathew

s-104

Con

trib

ute

dPap

ers

3C

ontr

ibute

dPap

ers

3C

ontr

ibute

dPap

ers

3C

ontr

ibute

dPap

ers

3

22 Program

Timetable by Session

Algebraic Geometry

DAY MON TUE WED THU FRI

room Mathews-107 Mathews-107 Mathews-307

chair J. Keum L. Ein K. Oguiso

9:30S. Kovacs p42 Y. Lee p43 M. Kawakita p43

10:00

MORNING TEA

11:00Y. Namikawa p42 D.-Q. Zhang p43 M. Popa p44

11:30

12:00T. Terasoma p42 I. Coskun p43

S. Kawaguchi p44

12:30 J. Sawon p44

Commutative Algebra



chair D. Eisenbud K. Watanabe A. K. Singh

9:30 S. Goto p45 A. K. Singh p48 A. Neeman p50

10:00 H. Dao p46 A. Dickenstein p48 R. Takahashi p50

MORNING TEA

11:00 K. Kurano p46 D. Maclagan p48 G. Lyubeznik p50

11:30 K. Yoshida p46 K. Yanagawa p49 D. Eisenbud p51

12:00 M. Velasco p47 S. Petrovic p49 K. Watanabe p51

12:30 G. G. Smith p47 J. Weyman p49


Computational Algebra



chair M. Newman J. Cannon N. Bruin

9:30 N. Bruin p52 H. Hong p55 M. Watkins

10:00 T. Satoh p52 E. Schost p55 TBA

MORNING TEA

11:00 M. Conder p53 M. Noro p56 C. Fieker p58

11:30 V. Gebhardt p53 A. Steel p57 M. Kida p58

12:00 P. Brooksbank p53 G. G. Smith p57 T. Sasaki p58

12:30 B. Unger p54 D. Eisenbud p57 A. Ghitza p60

Dynamical Systems


room Mathews-C Mathews-C Mathews-312

chair D. Lind G. Froyland T. Dooley

9:30 J. Hawkins p61 M. Dellnitz p63 J. Kiwi p66

10:00 M. I. Cortez p61 S. Lloyd p64 J. A. G. Roberts p66

MORNING TEA

11:00 M. Hochmann p62 M. Demers p64 L. DeMarco p67

11:30 R. Pavlov p62 E. Mihailescu p64 A. Fish p67

12:00 K. Park p63 R. Murray p65 P. Shmerkin p67

12:30 D. Ralston p63 C. Bose p65

Geometric Analysis



chair G. Tian G. Tian J. Chen

9:30T. Mabuchi p68 J.-M. Hwang p68 D. Pollack p69

10:00

MORNING TEA

11:00M.-C.Hong p68 A. Chau p69 E. Carberry p70

11:30

12:00S. Yamada p68 M. Ishida p69 X. Zhang p70

12:30

24 Program

Industrial Applications of Mathematics: Multiscale Mechanics


room Mathews-D Mathews-D

chair D. Walker D. Walker

9:30P. Broadbridge p71 A. Ord p72

10:00

MORNING TEA

11:00I. Einav p71 N. Thamwattana p73

11:30

12:00D. Walker p72 G. W. Delaney p73

12:30

Industrial Applications of Mathematics: Mathematical Finance


room Mathews-309

chair J. Wang

9:30

10:00

MORNING TEA

11:00J. Wang p75

11:30

12:00C. Chiarella p75

12:30

Inverse Problems


room Mathews-B Mathews-B Mathews-B

chair G. Uhlmann G. Uhlmann G. Uhlmann

9:30 G. Milton p77 P. Stefanov p80 G. Bao p82

10:00 N.-A. P. Nicorovicip77

M. Salo p80 A. Osses p82

MORNING TEA

11:00 H. Smith p78 A. Vasy p80 C. Fox p83

11:30 M. V. de Hoop p78 G. Nakamura p81 L. Stoyanov p83

12:00 H. Kang p79 A. D. Kim p81 H. Gao p83

12:30 J.-N. Wang p79 E. Chung p82


Mathematics of Climate Change



chair M. England C. Jones C. Jones

9:30C. Franzke p85 J. Li p87 J. Duan p89

10:00

MORNING TEA

11:00 W. Duan p85 G. Froyland p88K. Golden p90

11:30 C. D. Camp p86 S. Sisson p88

12:00K. Itoh p87 A. Monahan p89 P. Sardeshmukh p90

12:30

Mathematical Finance



chair E. Platen E. Platen S. Peng

9:30R. Elliott p92 E. Platen p92 J. Sung p94

10:00

MORNING TEA

11:00S. Peng p93 S. Tang p94

11:30

12:00H. Nagai p92 Y. Sun p93

12:30

Mathematical Physics



chair T. Guttmann T. Guttmann J. de Gier

9:30P. Bouwknegt p95 P. J. Forrester p96 A. Kuniba p97

10:00

MORNING TEA

11:00G. Raykov p95 V. Mangazeev p96 B. Nienhuis p97

11:30

12:00J. Links p95 J. H. H. Perk p96 B. Nachtergaele p97

12:30

26 Program

Partial Differential Equations


room Mathews-C Mathews-C Mathews-C

chair N. Ghoussoub Y. Long N. Ghoussoub

9:30E. N. Dancer p98 S. Chen p99 Z.-Q. Wang p101

10:00

MORNING TEA

11:00 C. Zeng p98Y. Du p100

M.-C. Hong p101

11:30 J. Byeon p98 R. Illner p101

12:00 S. Sun p99 Z. Liu p100 D. Daners p102

12:30 T. Li p99 G. Auchmuty p101 L. Tzou p102

Scientific Computing


room Mathews-D Mathews-D Mathews-D

chair L. Petzold I. Sloan L. Petzold

9:30 J. A. Sethian p103 J. Borwein p105 I. Turner p108

10:00 B. Anderssen p103 S. Hawkins p106 W. McLean p108

MORNING TEA

11:00 F. de Hoog p104 F. Y. Kuo p106 R. Beatson p108

11:30 J. C. Butcher p105 D. Nuyens p106 T. Tran p109

12:00 H. Brunner p105 I. Sloan p107

12:30 Discussion J. Sun p107

Stringy Topology


room Mathews-312 Mathews-B Mathews-B

chair A. Adem Y. Ruan C. Westerland

9:30 M. Guest p110 A. Adem p111 R. Lu p113

10:00 B. Chen p110 J. M. Gomez p112 D. Kneezel p113

MORNING TEA

11:00H. Fan p110 S. Galatius p112 M. Varghese p114

11:30

12:00 M. Krawitz p111 P. Norbury p112 C. Westerland p114

12:30 E. Luperico p111 V. Godin p113 J. Zhou p114


Symplectic Geometry



chair K. Fukaya Y. Eliashberg K. Fukaya

9:30C.-H. Cho p115 M. Tsukamoto p116 L. Macarini p116

10:00

MORNING TEA

11:00Y. Long p115 L. Polterovich p116 K. Honda p117

11:30

12:00B. Parker p115 K. Ono p116 Discussion

12:30

Contributed Papers 1


room Mathews-307 Mathews-307 Mathews-307 Mathews-308

theme Combinatorics &Algebra

Number Theory Analysis FunctionalAnalysis

chair D. Combe J. Dick I. Doust T. Bates

9:30 D. Combe p118 H. Ito p120 E. Kikianty p124

10:00 K. Pula p118 I. Jensen p120 S.-C. Ong p124

MORNING TEA

11:00 R. Haas p118 R. K. Das p121 E. Martin p122 A. Skripka p125

11:30 A. Helminckp119

K. C. Prasadp121

S.-K. Chua p122 M. Tacy p125

12:00 A. Hendersonp119

B. Bhavnagrip122

L. A. Raphaelp123

I. Sihwaningrump126

12:30 R. Vozzo p120 A. Weston p123

28 Program




theme ScientificComputing

MathematicalPhysics

DynamicalSystems

DynamicalSystems

chair D. Nuyens J. Kress G. Froyland J. Roberts

9:30 P. Renaud p128 R. Tudoran p131

10:00 J. Doukas p127 S. Post p129 S. Yildirim p131

MORNING TEA

11:00 T. Garoni p127 W.-H. Chenp129

P. Oprocha p131 R. Peng p133

11:30 H. Li p127 A.Alvarez-Parrillap130

M. Leite p132 V. Manukianp133

12:00 R. Tappendenp128

N. Saito p130 N.Santitissadeekornp132

B.-S. Kim p134

12:30 Y. Habib p128 R. Green p130 O. Stancevicp133

A. Ghazaryanp134




theme MathematicalModelling

MathematicalModelling

Stochastic Mod.& Education

DynamicalSystems &Control

chair B. Henry B. Henry S. Sisson N. Santitis-sadeekorn

9:30 C. Burt p136 M. Small p141

10:00 G. Iliev p137 A. Prasad p141

MORNING TEA

11:00 A. Chertockp135

I. Loladze p137 B. Kang p139 B. Sharma p142

11:30 A. Kurganovp135

W. Ong p137 S. Cohen p139 U. Chand p142

12:00 S. F. Woon p136 D. Triadis p138 H. Pratiwi p140 M. Minchevap142

12:30 P. D. Smith p138 M. J. Orig p140


Timetable by DayM

onday

room

Mathew

s-B

Mathew

s-C

Mathew

s-D

Mathew

s-102

Mathew

s-107

Mathew

s-309

sess

ion

Inve

rse

Pro

blem

sD

ynam

ical

Sys

tem

sIn

du.

App

l.:

Multis

cale

Mec

hanic

s

Com

muta

tive

Alg

ebra

Alg

ebra

icG

eom

etry

Mat

hem

atic

alFin

ance

chai

rG

.U

hlm

ann

D.Lin

dD

.W

alke

rD

.Eis

enbu

dJ.K

eum

E.Pla

ten

9:30

G.M

ilto

np77

J.H

awkin

sp61

P.B

road

bri

dge

p71

S.G

oto

p45

S.K

ovac

sp42

R.E

llio

ttp92

10:0

0N

.-A

.P.N

icor

ovic

ip77

M.I.

Cor

tez

p61

H.D

aop46

MO

RN

ING

TE

A

11:0

0H

.Sm

ith

p78

M.H

och

man

np62

I.E

inav

p71

K.K

ura

no

p46

Y.N

amik

awa

p42

11:3

0M

.V

.de

Hoop

p78

R.Pav

lov

p62

K.Y

oshid

ap46

12:0

0H

.K

ang

p79

K.Par

kp63

D.W

alke

rp72

M.V

elas

cop47

T.Ter

asom

ap42

H.N

agai

p92

12:3

0J.-N

.W

ang

p79

D.R

alst

onp63

G.G

.Sm

ith

p47

room

Mathew

s-310

Mathew

s-312

Mathew

s-307

Mathew

s-308

Mathew

s-104

sess

ion

Sym

plec

tic

Geo

met

ryStr

ingy

Top

olog

y〈C

ontr

ib.〉

Com

binat

oric

s&

Alg

ebra

〈Con

trib

.〉Sci

entific

Com

puting

〈Con

trib

.〉M

athe

mat

ical

Mod

elling

chai

rK

.Fuka

yaA

.Ade

mD

.C

ombe

D.N

uye

ns

B.H

enry

9:30

C.-H

.C

ho

p11

5M

.G

ues

tp11

0D

.C

ombe

p11

8

10:0

0B

.C

hen

p11

0K

.P

ula

p11

8J.D

ouka

sp12

7

MO

RN

ING

TE

A

11:0

0Y

.Lon

gp11

5H

.Fan

p11

0R

.H

aas

p11

8T

.G

aron

ip12

7A

.C

her

tock

p13

5

11:3

0A

.H

elm

inck

p11

9H

.Lip12

7A

.K

urg

anov

p13

5

12:0

0B

.Par

ker

p11

5M

.K

raw

itz

p11

1A

.H

ender

son

p11

9R

.Tap

pend

enp12

8S.F.W

oon

p13

6

12:3

0E

.Luper

ico

p11

1R

.V

ozzo

p12

0Y

.H

abib

p12

8

30 ProgramTues

day

room

Mathew

s-B

Mathew

s-C

Mathew

s-D

Mathew

s-102

Mathew

s-107

Mathew

s-309

sess

ion

Inve

rse

Pro

blem

sD

ynam

ical

Sys

tem

sIn

du.

App

l.:

Multis

cale

Mec

hanic

s

Com

muta

tive

Alg

ebra

Alg

ebra

icG

eom

etry

Indu

.A

ppl.:

Mat

hem

atic

alFin

ance

chai

rG

.U

hlm

ann

G.Fro

ylan

dD

.W

alke

rK

.W

atan

abe

L.Ein

J.W

ang

9:30

P.Ste

fanov

p80

M.D

elln

itz

p63

A.O

rdp72

A.K

.Sin

ghp48

Y.Lee

p43

10:0

0M

.Sal

op80

S.Llo

yd

p64

A.D

icke

nst

ein

p48

MO

RN

ING

TE

A

11:0

0A

.V

asy

p80

M.D

emer

sp64

N.T

ham

wat

tana

p73

D.M

acla

gan

p48

D.-Q

.Zhan

gp43

J.W

ang

p75

11:3

0G

.N

akam

ura

p81

E.M

ihai

lesc

up64

K.Y

anag

awa

p49

12:0

0A

.D

.K

imp81

R.M

urr

ayp65

G.W

.D

elan

eyp73

S.Pet

rovic

p49

I.C

oskun

p43

C.C

hia

rella

p75

12:3

0E

.C

hung

p82

C.B

ose

p65

J.W

eym

anp49

room

Mathew

s-310

Mathew

s-312

Mathew

s-307

Mathew

s-308

Mathew

s-104

sess

ion

Sym

plec

tic

Geo

met

ryG

eom

etri

cA

nal

ysis

〈Con

trib

.〉N

um

ber

The

ory

〈Con

trib

.〉M

athe

mat

ical

Phy

sics

〈Con

trib

.〉M

athe

mat

ical

Mod

elling

chai

rY

.Elias

hber

gG

.T

ian

J.D

ick

J.K

ress

B.H

enry

9:30

M.T

suka

mot

op11

6T

.M

abuch

ip68

H.It

op12

0P.R

enau

dp12

8C

.B

urt

p13

6

10:0

0I.

Jen

sen

p12

0S.Pos

tp12

9G

.Ilie

vp13

7

MO

RN

ING

TE

A

11:0

0L.Pol

tero

vic

hp11

6M

.-C

.Hon

gp68

R.K

.D

asp12

1W

.-H

.C

hen

p12

9I.

Lol

adze

p13

7

11:3

0K

.C

.P

rasa

dp12

1A

.A

lvar

ez-P

arri

lla

p13

0W

.O

ng

p13

7

12:0

0K

.O

no

p11

6S.Y

amad

ap68

B.B

hav

nag

rip12

2N

.Sai

top13

0D

.Tri

adis

p13

8

12:3

0R

.G

reen

p13

0P.D

.Sm

ith

p13

8


Wed

nes

day

room

Mathew

s-B

Mathew

s-C

Mathew

s-D

Mathew

s-102

Mathew

s-107

Mathew

s-309

sess

ion

Inve

rse

Pro

blem

sPar

tial

Diff

eren

tial

Equ

atio

ns

Sci

entific

Com

puting

Com

muta

tive

Alg

ebra

Com

puta

tion

alA

lgeb

raM

athe

mat

ics

ofC

lim

ate

Cha

nge

chai

rG

.U

hlm

ann

N.G

houss

oub

L.Pet

zold

A.K

.Sin

ghM

.N

ewm

anM

.Engl

and

9:30

G.B

aop82

E.N

.D

ance

rp98

J.A

.Set

hia

np10

3A

.N

eem

anp50

N.B

ruin

p52

C.Fra

nzk

ep85

10:0

0A

.O

sses

p82

B.A

nder

ssen

p10

3R

.Tak

ahas

hip50

T.Sat

ohp52

MO

RN

ING

TE

A

11:0

0C

.Fox

p83

C.Zen

gp98

F.de

Hoog

p10

4G

.Lyubez

nik

p50

M.C

onder

p53

W.D

uan

p85

11:3

0L.Sto

yanov

p83

J.B

yeon

p98

J.C

.B

utc

her

p10

5D

.E

isen

bud

p51

V.G

ebhar

dt

p53

C.D

.C

amp

p86

12:0

0H

.G

aop83

S.Sun

p99

H.B

runner

p10

5K

.W

atan

abe

p51

P.B

rook

sban

kp53

K.It

ohp87

12:3

0T

.Lip99

Dis

cuss

ion

B.U

nge

rp54

room

Mathew

s-310

Mathew

s-312

Mathew

s-307

Mathew

s-308

Mathew

s-104

sess

ion

Mat

hem

atic

alPhy

sics

Geo

met

ric

Anal

ysis

Sym

plec

tic

Geo

met

ry〈C

ontr

ib.〉

Dyn

amic

alSys

tem

s

〈Con

trib

.〉Sto

chas

tic

Mod

.&

Edu

cation

chai

rT

.G

uttm

ann

G.T

ian

K.Fuka

yaG

.Fro

ylan

dS.Sis

son

9:30

P.B

ouw

kneg

tp95

J.-M

.H

wan

gp68

L.M

acar

inip11

6R

.Tudor

anp13

1

10:0

0S.Y

ildir

imp13

1

MO

RN

ING

TE

A

11:0

0G

.R

ayko

vp95

A.C

hau

p69

K.H

onda

p11

7P.O

pro

cha

p13

1B

.K

ang

p13

9

11:3

0M

.Lei

tep13

2S.C

ohen

p13

9

12:0

0J.Lin

ks

p95

M.Is

hid

ap69

Dis

cuss

ion

N.Sa

ntit

issa

deek

orn

p13

2H

.P

rati

wip14

0

12:3

0O

.Sta

nce

vic

p13

3M

.J.O

rig

p14

0

32 ProgramT

hurs

day

room

Mathew

s-B

Mathew

s-C

Mathew

s-D

Mathew

s-102

Mathew

s-107

Mathew

s-309

sess

ion

Str

ingy

Top

olog

yPar

tial

Diff

eren

tial

Equ

atio

ns

Sci

entific

Com

puting

Mat

hem

atic

alFin

ance

Com

puta

tion

alA

lgeb

raM

athe

mat

ics

ofC

lim

ate

Cha

nge

chai

rY

.Ruan

Y.Lon

gI.

Slo

anE.Pla

ten

J.C

annon

C.Jon

es

9:30

A.A

dem

p11

1S.C

hen

p99

J.B

orw

ein

p10

5E

.P

late

np92

H.H

ong

p55

J.Lip87

10:0

0J.M

.G

omez

p11

2S.H

awkin

sp10

6E

.Sch

ost

p55

MO

RN

ING

TE

A

11:0

0S.G

alat

ius

p11

2Y

.D

up10

0F.Y

.K

uo

p10

6S.Pen

gp93

M.N

oro

p56

G.Fro

yla

nd

p88

11:3

0D

.N

uye

ns

p10

6A

.Ste

elp57

S.Sis

son

p88

12:0

0P.N

orbury

p11

2Z.Liu

p10

0I.

Slo

anp10

7Y

.Sun

p93

G.G

.Sm

ith

p57

A.M

onah

anp89

12:3

0V

.G

odin

p11

3G

.A

uch

muty

p10

1J.Sun

p10

7D

.E

isen

bud

p57

room

Mathew

s-310

Mathew

s-312

Mathew

s-307

Mathew

s-308

Mathew

s-104

sess

ion

Mat

hem

atic

alPhy

sics

Geo

met

ric

Anal

ysis

〈Con

trib

.〉A

nal

ysis

〈Con

trib

.〉D

ynam

ical

Sys

tem

s

〈Con

trib

.〉D

ynam

ical

Sys

tem

s&

Con

trol

chai

rT

.G

uttm

ann

J.C

hen

I.D

oust

J.Rob

erts

N.Sa

ntitis

sade

ekor

n

9:30

P.J.For

rest

erp96

D.Pol

lack

p69

M.Sm

allp14

1

10:0

0A

.P

rasa

dp14

1

MO

RN

ING

TE

A

11:0

0V

.M

anga

zeev

p96

E.C

arber

ryp70

E.M

arti

np12

2R

.Pen

gp13

3B

.Shar

ma

p14

2

11:3

0S.-K

.C

hua

p12

2V

.M

anukia

np13

3U

.C

han

dp14

2

12:0

0J.H

.H

.Per

kp96

X.Zhan

gp70

L.A

.R

aphae

lp12

3B

.-S.K

imp13

4M

.M

inch

eva

p14

2

12:3

0A

.W

esto

np12

3A

.G

haza

ryan

p13

4


Fri

day

room

Mathew

s-B

Mathew

s-C

Mathew

s-D

Mathew

s-102

Mathew

s-107

Mathew

s-309

sess

ion

Str

ingy

Top

olog

yPar

tial

Diff

eren

tial

Equ

atio

ns

Sci

entific

Com

puting

Mat

hem

atic

alFin

ance

Com

puta

tion

alA

lgeb

raM

athe

mat

ics

ofC

lim

ate

Cha

nge

chai

rC

.W

este

rlan

dN

.G

houss

oub

L.Pet

zold

S.Pen

gN

.Bru

inC

.Jon

es

9:30

R.Lu

p11

3Z.-Q

.W

ang

p10

1I.

Turn

erp10

8J.Sung

p94

M.W

atkin

sJ.D

uan

p89

10:0

0D

.K

nee

zelp11

3W

.M

cLea

np10

8T

BA

MO

RN

ING

TE

A

11:0

0M

.V

argh

ese

p11

4M

.-C

.H

ong

p10

1R

.B

eats

onp10

8S.Tan

gp94

C.Fie

ker

p58

K.G

olden

p90

11:3

0R

.Illn

erp10

1T

.Tra

np10

9M

.K

ida

p58

12:0

0C

.W

este

rlan

dp11

4D

.D

aner

sp10

2T

.Sas

akip58

P.Sa

rdes

hmuk

hp90

12:3

0J.Zhou

p11

4L.T

zou

p10

2A

.G

hit

zap60

room

Mathew

s-310

Mathew

s-312

Mathew

s-307

Mathew

s-308

Mathew

s-104

sess

ion

Mat

hem

atic

alPhy

sics

Dyn

amic

alSys

tem

sA

lgeb

raic

Geo

met

ry〈C

ontr

ib.〉

Funct

ional

Anal

ysis

chai

rJ.de

Gie

rT

.D

oole

yK

.O

guis

oT

.Bat

es

9:30

A.K

unib

ap97

J.K

iwip66

M.K

awak

ita

p43

E.K

ikia

nty

p12

4

10:0

0J.A

.G

.R

ober

tsp66

S.-C

.O

ng

p12

4

MO

RN

ING

TE

A

11:0

0B

.N

ienhuis

p97

L.D

eMar

cop67

M.Pop

ap44

A.Skri

pka

p12

5

11:3

0A

.Fis

hp67

M.Tac

yp12

5

12:0

0B

.N

acht

erga

ele

p97

P.Shm

erkin

p67

S.K

awag

uch

ip44

I.Sih

wan

ingr

um

p12

6

12:3

0J.Saw

onp44

Abstracts

36 Abstracts

Plenary Lectures

Monday 2:30 – 3:15, Clancy

Cloaking and transformation opticsGunther UhlmannUniversity of [email protected]

We describe recent theoretical and experimental progress on making objects invisible to detec-tion by electromagnetic waves, acoustic waves and quantum waves. Maxwell’s equations havetransformation laws that allow for design of electromagnetic materials that steer light arounda hidden region, returning it to its original path on the far side. Not only would observers beunaware of the contents of the hidden region, they would not even be aware that something wasbeing hidden. The object, which would have no shadow, is said to be cloaked. We recount therecent history of the subject and discuss some of the mathematical and physical issues involved,especially the use of singular transformations.

Monday 4:00 – 4:45, Clancy

Conformal invariance and universality in the 2D Ising modelStanislav SmirnovGeneva [email protected]

It is conjectured that many 2D lattice models of physical phenomena (percolation, Ising model ofa ferromagnet, self avoiding polymers, ...) become invariant under rotations and even conformalmaps in the scaling limit (i.e. when “viewed from far away”). A well-known example is theRandom Walk (invariant only under rotations preserving the lattice) which in the scaling limitconverges to the conformally invariant Brownian Motion.

Assuming the conformal invariance conjecture, physicists were able to make a number of strikingbut unrigorous predictions: e.g. dimension of a critical percolation cluster is almost surely 91/48;the number of simple length N trajectories of a Random Walk is about N11/32 · µN , with µdepending on a lattice, and so on.

We will discuss the recent progress in mathematical understanding of this area, in particular forthe Ising model. Much of the progress is based on combining ideas from probability, complexanalysis, combinatorics.

Plenary Lectures 37

Tuesday 2:00 – 2:45, Clancy

Lagrangian Floer homology and mirror symmetryKenji FukayaKyoto [email protected]

This is a survey of Lagrangian Floer homology which I developed together with Y.G.-Oh, HiroshiOhta, and Kaoru Ono. I will focus on its relation to (homological) mirror symmetry. The topicdiscussed include

1. Definition of filtered A infinity algebra associated to a Lagrangian submanifold and itscategorification.

2. Its family version and how it is related to mirror symmetry.

3. Some example including toric manifold. Calculation in that case and how mirror symmetryis observed from calculation.


Linearity in the tropicsFederico ArdilaMathematics Department, San Francisco State [email protected]

Tropical geometry studies an algebraic variety X by ‘tropicalizing’ it into a polyhedral complexTrop(X) which retains much of the information about X. This technique has been appliedsuccessfully in numerous contexts in pure and applied mathematics.

Tropical varieties may be simpler than algebraic varieties, but they are by no means well un-derstood. In fact, tropical linear spaces already feature a surprisingly rich and beautiful combi-natorial structure, and interesting connections to geometry, topology, and phylogenetics. I willdiscuss what we currently know about them.


Categorical crepant resolutions of simple singularitiesYujiro KawamataUniversity of [email protected]

Simple singularities in dimension 2 have crepant resolutions and satisfy the McKay correspon-dence. But higher dimensional generalizations do not. We propose the categorical crepantresolutions of such singularities in the sense that the Serre functors act as fractional shifts onthe added objects.

38 Abstracts

Wednesday 2:00 – 2:45, Clancy

Discrete stochastic simulation of spatially inhomogeneous biochemical systemsLinda PetzoldUniversity of California Santa [email protected]

In microscopic systems formed by living cells, the small numbers of some reactant moleculescan result in dynamical behavior that is discrete and stochastic rather than continuous anddeterministic. An analysis tool that respects these dynamical characteristics is the stochasticsimulation algorithm (SSA), which applies to well-stirred chemically reacting systems. However,cells are hardly homogeneous! Spatio-temporal gradients and patterns play an important rolein many biochemical processes. In this lecture we report on recent progress in the developmentof methods for spatial stochastic and multiscale simulation, and outline some of the many in-teresting complications that arise in the modeling and simulation of spatially inhomogeneousbiochemical systems.


Impact of cumulative emissions of carbon dioxide: the trillionth tonneMyles R. AllenDepartment of Physics, University of [email protected]

Coauthors: David J. Frame, Chris Huntingford, Chris D. Jones, Jason A. Lowe, M. Meinshausen,and N. Meinshausen

The eventual equilibrium global mean temperature associated with a given stabilization level ofatmospheric greenhouse gas concentrations remains uncertain, complicating the setting of stabi-lization targets to avoid potentially dangerous levels of global warming. Similar problems applyto the carbon cycle: observations currently provide only a weak constraint on the response tofuture emissions. These present fundamental challenges for the statistical community, since thenon-linear relationship between quantities we can observe and the response to a stabilizationscenario makes estimates of the risks associated with any stabilization target acutely sensitiveto the details of the analysis, prior selection etc. Here we use ensemble simulations of simpleclimate-carbon-cycle models constrained by observations and projections from more comprehen-sive models to simulate the temperature response to a broad range of carbon dioxide emissionpathways. We find that the peak warming caused by a given cumulative carbon dioxide emis-sion is better constrained than the warming response to a stabilization scenario and hence lesssensitive to underdetermined aspects of the analysis. Furthermore, the relationship between cu-mulative emissions and peak warming is remarkably insensitive to the emission pathway (timingof emissions or peak emission rate). Hence policy targets based on limiting cumulative emis-sions of carbon dioxide are likely to be more robust to scientific uncertainty than emission-rateor concentration targets. Total anthropogenic emissions of one trillion tonnes of carbon (3.67trillion tonnes of CO2), about half of which has already been emitted since industrializationbegan, results in a most likely peak carbon-dioxide induced warming of 2C above pre-industrialtemperatures, with a 5–95% confidence interval of 1.3–3.9C.

Plenary Lectures 39


Geometry and analysis of low dimensional manifoldsGang TianPrinceton University and Peking [email protected]

In this talk, I will start with a brief tour on geometrization of 3-manifolds. Then I will discussrecent progresses on geometry and analysis of 4-manifolds.

Thursday 2:30 – 3:15, Clancy

On fourth order PDEs modeling electrostatic Micro-ElectroMechanical SystemsNassif GhoussoubDepartment of Mathematics, University of British Columbia, Vancouver, [email protected]

Micro-ElectroMechanical Systems (MEMS) and Nano-ElectroMechanical Systems (NEMS) arenow a well established sector of contemporary technology. A key component of such systems isthe simple idealized electrostatic device consisting of a thin and deformable plate that is heldfixed along its boundary ∂Ω, where Ω is a bounded domain in R2. The plate, which lies belowanother parallel rigid grounded plate (say at level z = 1) has its upper surface coated witha negligibly thin metallic conducting film, in such a way that if a voltage λ is applied to theconducting film, it deflects towards the top plate, and if the applied voltage is increased beyonda certain critical value λ∗, it then proceeds to touch the grounded plate. The steady-state isthen lost, and we have a snap-through at a finite time creating the so-called pull-in instability.A proposed model for the deflection is given by the evolution equation

∂u

∂t−∆u + δ∆2u =

λf(x)

(1− u)2for x ∈ Ω, t > 0;

u(x, t) = δ∂u

∂η(x, t) = 0 for x ∈ ∂Ω, t > 0;

u(x, 0) = 0 for x ∈ Ω.

Now unlike the model involving only the second order Laplacian (i.e., δ = 0), very little is knownabout this equation. We shall explain how, besides the above practical considerations, the modelis an extremely rich source of interesting mathematical phenomena.

Thursday 4:00 – 4:45, Clancy

Law of large number and central limit theorem under uncertainty, the related newIto’s calculus and applications to risk measuresShige PengInstitute of Mathematics, Shandong [email protected]

Let Sn =∑n

i=1 Xi where Xi∞i=1 is a sequence of independent and identically distributed (i.i.d.)of random variables with E[X1] = µ. According to the classical law of large number (LLN),

40 Abstracts

the sum Sn/n converges strongly to µ. Moreover, the well-known central limit theorem (CLT)tells us that, with µ = 0 and σ2 = E[X2

1 ], for each bounded and continuous function ϕ we havelimn E[ϕ(Sn/

√n))] = E[ϕ(X)] with X ∼ N(0, σ2).

These two fundamentally important results are widely used in probability, statistics, data anal-ysis as well as in many practical situation such as financial pricing and risk controls. Theyprovide a strong argument to explain why in practice normal distributions are so widely used.But a serious problem is that the i.i.d. condition is very difficult to be satisfied in practice forthe most real-time processes for which the classical trials and samplings becomes impossible andthe uncertainty of probabilities and/or distributions cannot be neglected.

In this talk we present a systematical generalization of the above LLN and CLT. Instead of fixinga probability measure P , we only assume that there exists a uncertain subset of probabilitymeasures Pθ : θ ∈ Θ. In this case a robust way to calculate the expectation of a financialloss X is its upper expectation: E[X] = supθ∈Θ Eθ[X] where Eθ is the expectation under theprobability Pθ. The corresponding distribution uncertainty of X is given by Fθ(x) = Pθ(X ≤ x),θ ∈ Θ. Our main assumptions are:

1. The distributions of Xi are within an abstract subset of distributions Fθ(x) : θ ∈ Θ,called the distribution uncertainty of Xi, with µ = E[Xi] = supθ

∫∞−∞ xFθ(dx) and µ =

−E[−Xi] = infθ

∫∞−∞ xFθ(dx).

2. Any realization of X1, · · · , Xn does not change the distributional uncertainty of Xn+1 (anew type of ‘independence’ ).

Our new LLN is: for each linear growth continuous function ϕ we have

limn→∞

E[ϕ(Sn/n)] = supµ≤v≤µ

ϕ(v).

Namely, the distribution uncertainty of Sn/n is, approximately, δv : µ ≤ v ≤ µ.In particular, if µ = µ = 0, then Sn/n converges strongly to 0. In this case, if we assume

furthermore that σ2 = E[X2i ] and σ2 = −E[−X2

i ], i = 1, 2, · · · . Then we have the followinggeneralization of the CLT:

limn→∞

[ϕ(Sn/√

n)] = E[ϕ(X)], L(X) ∈ N(0, [σ2, σ2]).

Here N(0, [σ2, σ2]) stands for a distribution uncertainty subset and E[ϕ(X)] its the correspondingupper expectation. The number E[ϕ(X)] can be calculated by defining u(t, x) := E[ϕ(x+

√tX)]

which solves the following PDE ∂tu = G(uxx), with G(a) := 12(σ2a+ − σ2a−).

An interesting situation is when ϕ is a convex function, E[ϕ(X)] = E[ϕ(X0)] with X0 ∼ N(0, σ2).But if ϕ is a concave function, then the above σ2 has to be replaced by σ2. This coincidencecan be used to explain a well-known puzzle: many practitioners, particularly in finance, usenormal distributions with ‘dirty’ data, and often with successes. In fact, this is also a high riskyoperation if the reasoning is not fully understood. If σ = σ = σ, then N(0, [σ2, σ2]) = N(0, σ2)which is a classical normal distribution. The method of the proof is very different from theclassical one and a very deep regularity estimate of fully nonlinear PDE plays a crucial role.

A type of combination of LLN and CLT which converges in law to a more general N([µ, µ], [σ2, σ2])-distributions have been obtained. We also present our systematical research on the continuous-time counterpart of the above ‘G-normal distribution’, called G-Brownian motion and the cor-responding stochastic calculus of Ito’s type as well as its applications.

Plenary Lectures 41

Friday 2:00 – 2:45, Clancy

Regular permutation groups and Cayley graphsCheryl E. PraegerUniversity of Western [email protected]

Coauthors: Martin Liebeck and Jan Saxl

Regular permutation groups are the ‘smallest’ transitive groups of permutations, and have beenstudied for more than a century. They occur, in particular, as subgroups of automorphismsof Cayley graphs, and their applications range from obvious graph theoretic ones through tostudying word growth in groups and modeling random selection for group computation. Recentwork, using the finite simple group classification, has focused on the problem of classifying thefinite primitive permutation groups that contain regular permutation groups as subgroups, andclassifying various classes of vertex-primitive Cayley graphs. Both old and very recent work onregular permutation groups will be discussed.

Friday 3:30 – 4:15, Clancy

Perfect crystals for quantum affine algebras and combinatorics of Young wallsSeok-Jin KangSeoul National [email protected]

In this talk, we will give a detailed exposition of theory of perfect crystals, which has brought usa lot of significant applications. On the other hand, we will also discuss the strong connectionbetween the theory of perfect crystals and combinatorics of Young walls. We will be able toderive LLT algorithm of computing global bases using affine paths. The interesting problem ishow to construct affine Hecke algebras out of affine paths.

42 Abstracts

Algebraic Geometry

Monday 9:30 – 10:15, Mathews-107

Log canonical implies Du BoisSandor KovacsUniversity of [email protected]

Coauthors: Janos Kollar

In joint work with Janos Kollar, we show that log canonical singularities are Du Bois. Theaim of the talk is to explain the main ideas of the proof and its consequences for the moduli ofvarieties of general type.

Monday 11:00 – 11:45, Mathews-107

Symplectic varieties and Poisson deformationsYoshinori NamikawaDepartment of Mathematics, Kyoto University, [email protected]

We study the universal Poisson deformation of an affine symplectic variety. A typical exampleis the normalization X of the closure of a nilpotent orbit in a complex simple Lie algebra. WhenX has a crepant resolution, we can construct the universal Poisson deformation of X in a veryexplicit way.

Monday 12:00 – 12:45, Mathews-107

Motivic relative completionTomohide TerasomaUniversity of [email protected]

Coauthors: R. Hain, M. Matsumoto, and G. Perlstein

In this talk, we introduce a motivic construction of relative completion with respect to a rep-resentation of fundamental group arising from polarized variation of Hodge structure whoseZariski closure of the image is reductive group. As a consequence, we prove an exact sequenceof Tannaka fundamental groups which is an analogue for exact sequence for fundamental groupsfor arithmetic varieties.

Algebraic Geometry 43

Tuesday 9:30 – 10:15, Mathews-107

Construction of surfaces of general type via Q-Gorenstein smoothingsYongnam LeeSogang [email protected]

In this talk, I will present several effective methods for the construction of sufaces of generaltype via Q-Gorenstein smoothings.


Rationality of rationally connected varieties with endomorphismsDe-Qi ZhangNational University of [email protected]

We consider endomorphisms f of degree > 1 on normal projective varieties X. When X isnon-uniruled and f is polarized, X is shown to be of Kodaira dimension zero and with onlycanonical singularities and torsion canonical divisor. We try to run an equivariant MMP for thepair (X, f) and give some sufficient condition for a rationally connected variety X to be rational.In particular, we show that every three-dimensional Fano manifold with an endomorphism ofdegree > 1, is rational.


The geometry of homogeneous varietiesIzzet CoskunUniversity of Illinois at [email protected]

In this talk I will discuss positive, geometric algorithms for computing the cohomology of homo-geneous varieties.

Friday 9:30 – 10:15, Mathews-307

Towards boundedness of minimal log discrepanciesMasayuki KawakitaRIMS, Kyoto [email protected]

The minimal model program works at present with provision of termination of flips, whereasthe termination is reduced to two conjectures on minimal log discrepancy, a numerical invariantattached to a singularity. Each of the two conjectures leads as its corollary another more ac-cessible conjecture, the boundedness of minimal log discrepancies. I shall introduce my attempttowards boundedness of minimal log discrepancies.

44 Abstracts

Friday 11:00 – 11:45, Mathews-307

Bernstein-Gel’fand-Gel’fand correspondence and the cohomology of compact KaehlermanifoldsMihnea PopaUniversity of Illinois at [email protected]

Coauthors: Robert Lazarsfeld

The cohomology algebra of the sheaf of holomorphic functions on a compact Kaehler manifoldcan be naturally viewed as a module over the exterior algebra of a vector space. A well-knownresult of Bernstein-Gel’fand-Gel’fand gives a correspondence between such “exterior” modulesand linear complexes of modules over the symmetric algebra, i. e. the polynomial ring. I willexplain how one can use a modern view on this correspondence, together with the GenericVanishing theory developed by Green and Lazarsfeld via Hodge-theoretic methods, in order tounderstand subtle algebraic structures of the cohomology algebra. As a bonus, homological andcommutative algebra tools can be applied on the polynomial ring side to obtain new inequalitiesfor the holomorphic Euler characteristic and the Hodge numbers of compact Kaehler manifolds.

Friday 12:00 – 12:20, Mathews-307

The elliptic J-function and the Borcherds Phi-functionShu KawaguchiOsaka [email protected]

Coauthors: Ken-Ichi Yoshikawa

We relate the difference of the elliptic J-functions and the Borcherds Phi-function, using involu-tions on Kummer surfaces of product type.

Friday 12:30 – 12:50, Mathews-307

Holomorphic coisotropic reductionJustin SawonColorado State [email protected]

Let Y be a hypersurface in a 2n-dimensional holomorphic symplectic manifold X. The restrictionσ|Y of the holomorphic symplectic form induces a rank one foliation on Y . If this “characteristicfoliation” has compact leaves, then the space of leaves Y/F is a holomorphic symplectic manifoldof dimension 2n−2. This construction also works when Y is a coisotropic submanifold of highercodimension, and is known as “coisotropic reduction”. In this talk we will consider when thecharacteristic foliation has compact leaves, and look at some applications of coisotropic reduction.

Commutative Algebra 45

Commutative Algebra


Cohen-Macaulayness versus vanishing of e1Q(A)

Shiro GotoMeiji [email protected]

My talk is based on a joint work [1] with Ghezzi, Hong, Ozeki, Phuong, and Vasconcelos. Tostate the results, let (A,m) be a Noetherian local ring with d = dim A > 0. Let `A(M) denote,for an A-module M , the length of M . Then, for each m-primary ideal I in A, we have theintegers ei

I(A)0≤i≤d such that the equality

`A(A/In+1) = e0I(A)

(n + d

d

)− e1

I(A)

(n + d− 1

d− 1

)+ · · ·+ (−1)ded

I(A)

holds true for all n À 0, which we call the Hilbert coefficients of A with respect to I. We saythat A is unmixed, if dim A/p = d for every p ∈ Ass A, where A denotes the m-adic completionof A. With this notation Wolmer V. Vasconcelos posed, exploring the vanishing of e1

Q(A) forparameter ideals Q, in his lecture at the conference in Yokohama of March, 2008 the followingconjecture.

Conjecture [2, 3]. Assume that A is unmixed. Then A is a Cohen-Macaulay local ring, oncee1Q(A) = 0 for some parameter ideal Q of A.

In my talk I shall settele this conjecture affirmatively. As a direct consequence of the result, onegets that, for a given Noetherian local ring (A,m) with d = dim A > 0, e1

Q(A) = 0 for everyparameter ideal Q in A, once e1

Q(A) = 0 for some parameter ideal Q. The next question is,naturally, when the set Λ(A) = e1

Q(A) | Q is a parameter ideal inA is finite, or a singleton.I shall show that the local cohomology modules Hi

m(A)0≤i≤d−1 of A with respect to m areall finitely generated, if Λ(A) is finite, and eventually that A is a Buchsbaum local ring if andonly if Λ(A) is a singleton, that is the value e1

Q(A) is constant and independent of the choice ofparameter ideals Q in A, provided A is unmixed.

[1] L. Ghezzi, S. Goto, J.-Y. Hong, K. Ozeki, T. T. Phuong, and W. V. Vasconcelos, Cohen-Macaulayness versus vanishing of e1

Q(A).

[2] L. Ghezzi, J.-Y. Hong and W. V. Vasconcelos, The signature of the Chern coefficients oflocal rings, Preprint 2008.

[3] W. V. Vasconcelos, The Chern coefficients of local rings, Michigan Math. J. 57 (2008),725–743.

46 Abstracts

Monday 10:00 – 10:20, Mathews-102

Homological properties of modules over complete intersectionsHailong DaoUniversity of [email protected]

There is a well known phenomenon that a hyperplane section of a smooth complex variety Xretains some topological invariants of X. One could translate such properties into purely alge-braic statements and study them using techniques of commutative algebra. Most of time thesestatements involve asymptotic homological properties of modules over complete intersections.In this talk I will describe some recent results and open questions.

Monday 11:00 – 11:20, Mathews-102

Nagata conjecture and the symbolic Rees rings of space monomial curvesKazuhiko KuranoMeiji [email protected]

We introduce a relation between the rings of Nagata-type and the symbolic Rees rings of spacemonomial curves. As a corollary, we show that, if there exists an example of infinitely generatedsymbolic Rees rings of space monomial curves in positive characteristic, then Nagata conjectureis true in a case.

Monday 11:30 – 11:50, Mathews-102

On Cowsik-Nori theorem for Stanley-Reisner ideals and edge idealsKen-ichi YoshidaNagoya [email protected]

Coauthors: Naoki Terai and Giancarlo Rinaldo

In my talk, we discuss about a generalization or a refinement of the Cowsik-Nori theorem forsome classes of monomial ideals.

First, in the case of Stanley-Reisner ideals we show that if S/In is Buchsbaum for infinitely manyn then I is complete intersection. In the proof, we use a structure theorem for locally completeintersection Stanley-Reisner ideals (with N. Terai), and a lower bound theorem for multiplicitiesof Buchsbaum homogeneous algebras (with S. Goto).

Secondly, in the case of edge ideals I(G), we show that S/I(G)n is Cohen-Macaulay for some(every) n at least 3 then I(G) is complete intersection. For the proof, we characterize anygraph G whose symbolic power I(G)(n) is Cohen-Macaulay for some n at least 3 (with M. Crupi,G. Rinaldo, N. Terai).


Monday 12:00 – 12:20, Mathews-102

Two results on the Cox rings of rational varietiesMauricio VelascoUC [email protected]

Coauthors: B. Sturmfels, D. Testa, and A. Varilly-Alvarado

The Cox ring of an algebraic variety X fits in the following analogy: Cox(X) is to X as the ringof polynomials k[x0, .., xn] is to projective space P n. It is known that the Cox ring of X is apolynomial ring if and only if X is Toric and that there is a large class of varieties, the so calledMori Dream Spaces, whose Cox rings are finitely generated algebras.

I am interested in the following two questions:

1. Which algebraic varieties are Mori dream spaces?

2. How to construct presentations for the Cox rings of Mori Dream Spaces?

In this talk I will describe recent progress in these two questions for some rational varieties:a Theorem stating that every rational surface with Big anticanonical divisor is a Mori DreamSpace (with D. Testa and A. Varilly-Alvarado) and some in progress work (with B. Sturmfels) onthe defining ideals of the Cox rings of blow-ups of P n at n+3 general points and its relationshipwith spinor varieties.

Monday 12:30 – 12:50, Mathews-102

Eulerian numbers and Laurent polynomialsGregory G. SmithQueen’s [email protected]

Coauthors: Daniel Erman and Anthony Varilly-Alvarado

Duistermaat and van der Kallen prove, using complex analysis, that there are no nontrivialLaurent polynomials all of whose powers have a zero constant term. Motivated by this result,Sturmfels proposed an effective version: compute the dimension and degree of a specific familyof ideals. In this talk, we’ll show that the degrees are given by Eulerian numbers. The proofinvolves reinterpreting the problem in terms of toric geometry.

48 Abstracts


A computation of local cohomologyAnurag K. SinghUniversity of [email protected]

We will describe the computation of a local cohomology module, and use this to deduce avanishing theorem.


Implicitization of rational (hyper)surfacesAlicia DickensteinDto. de Matematica, FCEN, Universidad de Buenos [email protected]

We shall present some advances on two different approaches for the basic problem of turning aparametrization of a rational projective hypersurface H into an implicit equation, based on thestructure of the polynomials defining the parametrization.

The first approach is to compute a representation matrix for H, that is, a matrix M of fullrank with polynomial entries, and such that a given point p lies in H if and only if the rank ofM evaluated at p is not maximum (as suggested by L. Buse and M. Dohm). In common workwith N. Botbol and M. Dohm, we show that a surface in P3 parametrized over a 2-dimensionaltoric variety can be represented by a matrix of linear syzygies, if the base points are finite innumber and form locally a complete intersection. This constitutes a direct generalization of thecorresponding results over P2 established by L. Buse, M. Chardin and J.-P. Jouanolou (basedon the approximation complexes introduced by A. Simis and W. Vasconcelos). By exploitingthe sparse structure of the parametrization, we obtain significantly smaller matrices than inthe homogeneous case and the method becomes applicable to parametrizations for which itpreviously failed.

The second approach, following common work with B. Mourrain, extends methods from tropicalimplicitization developed by B. Sturmfels, J. Tevelev and J. Yu, to predict the Newton polytopeof an implicit equation of H.


The T -graph of the Hilbert scheme of pointsDiane MaclaganUniversity of [email protected]

The torus T = (C∗)2 acts on the Hilbert scheme Hilbd(A2) of d points in the plane. Algebraicallythe Hilbert scheme parameterizes ideals in S = C[x, y] with dimCS/I = d, and the fixed pointsare monomial ideals. The one-dimensional T -orbits whose closure contains a pair of monomialideals (a T -edge) can be computed using combinatorial commutative algebra/Grobner bases, but


a combinatorial characterization of the resulting graph does not yet exist. I will describe jointwork with Milena Hering where we give necessary conditions for the existence of such a T -edge.


Dualizing complex of a toric face ringKohji YanagawaDepartment of Mathematics, Kansai [email protected]

Coauthors: Ryota Okazaki

A toric face ring, which generalizes both Stanley-Reisner rings and affine semigroup rings, isstudied by Bruns, Romer and their coauthors recently. In this talk, we describe a dualizingcomplex of a toric face ring R. In the (cone-wise) normal case, the description is very concise.Since R is not a graded ring in general, the proof is quite technical. In the normal case, we alsodevelop the squarefree module theory over R, and show that the Cohen-Macaulay, Buchsbaum,and Gorenstein properties of R are topological properties of its associated cell complex.


Cut ideals of ring graphs: a family of surprisingly nice toric idealsSonja PetrovicUniversity of Illinois at [email protected]

Coauthors: Uwe Nagel

Cut ideals record the relations among the cuts of a graph. They are a natural generalizationof ideals arising in phylogenetics. For a family of cut ideals associated to ring graphs we derivea quadratic squarefree Grobner basis, settling a large part of the Sturmfels-Sullivant conjectureclassifying Cohen-Macaulay cut varieties. In addition, for subfamilies of ring graphs, we canshow that the lattice basis ideal is, surprisingly, a complete intersection binomial ideal. Thistalk will survey recent results and open problems in the area.


Some results on syzygies of Plucker and Veronese idealsJerzy WeymanNortheastern [email protected]

In this talk I will present some results and conjectures on the lengths of linear strands of minimalresolutions of Plucker and Veronese ideals.

50 Abstracts

Wednesday 9:30 – 9:50, Mathews-102

Brown representability via flat modulesAmnon NeemanAustralian National [email protected]

We describe a string of new results given some novel characterizations of dualizing complexes.One consequence of the theory is that it is possible, on an arbitrary scheme, to have a reasonableanalog of the homotopy category of projective modules, even when there are no projectivequasicoherent sheaves.


Thick subcategories of stable categories of Cohen-Macaulay modulesRyo TakahashiShinshu [email protected]

In 1997 Benson, Carlson and Rickard gave a description of the thick subcategories of the stablecategory of finitely generated representations of a finite p-group. In this talk, we will considerclassifying, by using certain sets of prime ideals, thick subcategories of the stable category ofmaximal Cohen-Macaulay modules over a Gorenstein local ring.


A property of the ring of polynomials over a perfect field of characteristic p > 0Gennady LyubeznikUniversity of [email protected]

Coauthors: Wenliang Zhang and Yi Zhang

Let R be the ring of polynomials in a finite number of variables over a perfect field of charac-teristic p > 0. We describe a class of Rp-bilinear R-valued forms on R, use it to establish aone-to-one correspondence between the saturated Rp-submodules of R of complementary rank,and use this correspondence to prove an adjointness property between Frobenius pullback andpushforward. This is potentially important for algorithmic questions involving computationswith the Frobenius.



Interesting sets of deformationsDavid EisenbudUniversity of California, [email protected]

I’ll talk about two invariants of a ring that are connected with deformations. These come fromrecent work of mine with Roya Beheshti, and I’ll also describe our reasons for being interestedin them, and our attempts to understand them in some special cases.


The a invariants of normal graded Gorenstein rings and varieties with even canonicalclassKei-ichi WatanabeNihon [email protected]

Given a normal projective variety X, we want to know the existence of normal Gorenstein ringswith Proj(R) = X and what is the set AX of a-invariants of such R. In particular, we showthat if there exists a normal graded Gorenstein ring R with Proj(R) = X with even a invariant,then X has even canonical class, even if the ring is not standard graded nor determined by anample divisor. We determine the shape of the set AX under certain condition.

52 Abstracts

Computational Algebra


Deciding the existence of rational points on curvesNils BruinSimon Fraser [email protected]

Coauthors: Michael Stoll

It is unknown whether there exists an algorithm to decide if a curve has any rational points.There are several practical methods that often succeed in making that decision, though. Infact, there is a heuristic argument that one of these methods, now commonly referred to asMordell-Weil sieving, should always succeed.

I will describe the method and briefly sketch the heuristic argument. I will also describe acomputational experiment in which we determined the existence of rational points on all genus2 curves admitting a model of the form

y2 = a6x6 + · · ·+ a0

where the coefficients ai are integers satisfying −3 ≤ ai ≤ 3.


Simple but not absolutely simple Jacobians in cryptographyTakakazu SatohDepartment of Mathematics, Tokyo Institute of [email protected]

Simpleness is one of important properties on the Abelian varieties. However, its cryptographicimplication does not seem to be considered well. I would like to talk about a use of certainFp-simple but (2,2)-split Jacobians of genus two hyperelliptic curves. We discuss the followingtopics:

1. generating verifiably random curves suitable for cryptographic systems;

2. generating pairing friendly curves;

3. difficulties of the discrete log problems on such curves.

Computational Algebra 53


Some unexpected theoretical consequences of computations involving groupsMarston ConderUniversity of [email protected]

In this talk I will give some instances of experimental computations involving groups (in thecontext of their actions on graphs and maps) that have led to unexpected theoretical discoveries.These include new presentations for 3-dimensional special linear groups, a closed-form definitionfor the binary reflected Gray codes, a new theorem on groups expressible as a product of anabelian group and a cyclic group, and revealing observations about the genus spectra of particularclasses of regular maps on surfaces. Such examples highlight the value of computational algebraas a tool for experimental work, that can have surprising outcomes.


The conjugacy problem in braid groups and Garside groupsVolker GebhardtUniversity of Western [email protected]

Braid groups have applications in a wide range of areas reaching from cryptography to knot the-ory. Of particular importance is the ability to decide whether two given elements are conjugate,respectively to find a conjugating element; over the last 5 years, significant progress on thesequestions has been made.

The methods which have been developed to address these problems extend to a more generalclass of groups, called Garside groups, which includes all Artin groups of spherical type, amongothers. The most fundamental characteristics of Garside groups, which is crucial for effectivecomputations, is the existence of the so-called greedy normal form of an element.

After giving some background on braid /Garside groups and on the conjugacy problem, I willdiscuss the recent advances and the current state of the art regarding this question.


Intersections of classical groupsPeter BrooksbankBucknell University, United [email protected]

Coauthors: James Wilson

Let G1, . . . , Gn be a set of finite classical groups defined naturally on a common vector space.In this talk I will describe an efficient algorithm to construct generators for the group

⋂ni=1 Gi.

The main idea is to define this intersection as a subgroup of the group of norm 1 elementsof a certain ring equipped with an involutory anti-automorphism (a ∗-ring). To facilitate thisapproach we develop a polynomial-time theory of ∗-rings, analogous to the better known theory

54 Abstracts

of ordinary (associative) matrix algebras. Algorithms for ∗-rings are of independent interest; forexample they can be used to investigate properties of group algebras. The algorithms for ∗-ringsand classical group intersections have been implemented in Magma. This is a report on jointwork with James Wilson (Ohio State University).


New algorithms for character tables and Schur indices based on Brauer/Witt theo-remsBill UngerUniversity of [email protected]

Around 1950, R. Brauer and E. Witt both proved that many properties of the ordinary charactersof a finite group are controlled by certain supersoluble subgroups of the group, specifically, theelementary and quasi-elementary subgroups. I will describe a new algorithm for computingthe character table of a finite group based on Brauer’s theorem on characters induced fromelementary subgroups. The new algorithm is applicable to a far wider range of groups thanthe Dixon-Schneider algorithm, and played an important role in the recent proof of the Oreconjecture by Liebeck, O’Brien, Shalev, and Tiep.

The Schur index of a character is the minimum degree field extension over the character fieldneeded to realise a representation affording the character. I will describe the first practicalalgorithm for computing the Schur Index of an irreducible character over both local fields andnumber fields. The problem is reduced to working with quasi-elementary sections of the group.The Brauer-Witt Theorem assures us that it is always possible to reduce to quasi-elementarysubgroups.

Implementations of both algorithms are part of the current version of Magma.


Thursday 9:30 – 9:50, Mathews-107

Connectivity in semi-algebraic setsHoon HongNorth Carolina State [email protected]

Coauthors: Robert Quinn

A semialgebraic set is a subset of real space defined by polynomial equations and inequalities.A semialgebraic set is a union of finitely many maximally connected components.

In this talk, we consider the problem of deciding whether two given points in a semialgebraic setare connected, that is, whether the two points lie in a same connected component. In particular,we consider the semialgebraic set defined by f not equal 0 where f is a given bivariate polynomial.

The motivation comes from the observation that many important/non-trivial problems in scienceand engineering can be often reduced to that of connectivity. Due to it importance, there hasbeen intense research effort on the problem.

We will describe a method based on gradient fields and provide a sketch of the proof of correctnessbased Morse complex. The method seems to be more efficient than the previous methods inpractice.


Computing roadmaps of compact smooth hypersurfacesEric SchostUniversity of Western [email protected]

Coauthors: Mohab Safey el Din

We consider the problem of constructing roadmaps of real algebraic sets.

The problem was introduced by Canny (Proc. 28th IEEE Symp. FOCS, 1987, 39-48) to answerconnectivity questions and solve motion planning problems. Given s polynomial equations withrational coefficients, of degree D in n variables, Canny’s algorithm has a probabilistic complexityof snDO(n2) operations in Q; a deterministic version runs in time snDO(n4).

The next improvement was due to Basu, Pollack and Roy (Proc. 28th ACM STOC, 1996, 168-173), where an algorithm of deterministic cost sd+1DO(n2) is given for the more general problemof computing roadmaps of semi-algebraic sets (d ≤ n is the dimension of an associated object).

We give a probabilistic algorithm of complexity (nD)O(n1.5) ⊂ DO(n1.5log(n)) for the problem ofcomputing a roadmap of a compact hypersurface V of degree D in n variables; we also have toassume that V has a finite number of singular points. Even under these extra assumptions, noprevious algorithm featured a cost better than DO(n2).

56 Abstracts


Algorithms for computing b-functions and their efficient implementationMasayuki NoroDemartment of Mathematics, Graduate School of Science, Kobe [email protected]

Computational algebraic analysis developed by N. Takayama, T. Oaku et al. provides algo-rithms for computing various invariants of systems of linear partial differential equations givenby D-module theory. Its fundamental tools are basic operations in Weyl algebra that is a ringof differential operators over a polynomial ring, and Groebner basis computations in Weyl al-gebra. Theoretically these Groebner bases can be computed by the Buchberger algorithm andhigher level algorithms are constructed by combining these fundamental facilities. But they areusually harder than the computation over commutative polynomial rings because of the non-commutativity. In this talk we focus on the computation of the b-functions and show severaltechniques for computing b-function efficiently.

The local b-function is interesting because it is an invariant of hypersurface singularity. Theglobal b-function is practically important because cohomology computations are reduced tocomputations in finite dimensional vector spaces by using the roots of the global b-function.The b-function is the monic generator of an elimination ideal, but the Buchberger algorithmwith respect to an elimination order is often inefficient in this case. We proposed a methodfor computing the global b-function as the minimal polynomial of an operator by the methodof indeterminate coefficients. Also, we proposed modular Groebner basis computation in Weylalgebra in order to get rid of coefficient explosions. We notice that modular method is widelyused in commutative polynomial computation, but not in Weyl algebra.

Recently we found a new algorithm for computing a stratification of Cn associated with the localb-function of a polynomial. The first algorithm for computing the same stratification was givenby Oaku, but it needs a primary ideal decomposition. Our new algorithm only requires radicalmembership tests and ideal quotient computations. Modular techniques are efficiently used alsoin this algorithm.



Computing Groebner bases in general algebras via linear algebraAllan SteelUniversity of [email protected]

Groebner bases are fundamental to Computational Commutative Algebra. A Groebner basis(GB) is a canonical generating set for an ideal of a multivariate polynomial ring. This allowsmany structural properties of the ideal to be effectively computed. One can also use GB tech-niques to solve a system of simultaneous multivariate equations: this has been greatly exploitedin recent years in Cryptanalysis.

The Buchberger algorithm has been the basic method to compute a GB. However, in the late1990s, Jean-Charles Faugere introduced a new general method for computing GBs via sparse lin-ear algebra techniques, and this is generally much faster than the original Buchberger approach.

I will describe how I have extended Faugere’s sparse linear algebra approach to computing GBsfor a wide range of finitely presented algebras, both associative and non-associative, includingexterior algebras and finitely presented Lie algebras.


Computations on toric varietiesGregory G. SmithQueen’s [email protected]

Following the ideas of David Cox, one may represent a coherent sheaf on a toric variety X by afinitely generated module over the Cox ring of X. We’ll discuss various algorithms that use thisrepresentation to compute cohomological invariants. These methods have been implemented inMacaulay 2.


The worst fibers of a finite morphismDavid EisenbudUniversity of California, [email protected]

Any variety in projective space, over a field of characteristic zero, can be projected to a hypersur-face by a finite birational map; this is no more than the theorem that every finite field extensionhas a primitive element. I will explain a method of finding how “bad” the worst fiber of sucha projection is, without actually finding that fiber, and I’ll discuss some of the conjectures andpotential applications surrounding this problem. The work I will present is part of joint projectswith Roya Beheshti, Joe Harris, and Bernd Ulrich.

58 Abstracts

Friday 11:00 – 11:20, Mathews-107

Computation of Galois groups and applications: degree 24 and moreClaus FiekerUniversity of Sydney, [email protected]

Coauthors: Jurgen Kluners

The computation of Galois groups is one of the oldest tasks in computational algebra. Originallydeveloped to decide solvability of polynomial equations, it quickly matured into an independentbranch of research. While a trivial argument shows that Galois groups can be computed in finitetime, a practical algorithm in the genral case was still missing. Since Stauduhars thesis in 78,the problem has been solved degree by degree and thesis by thesis, until it reached 23 by 2004.Over the last 2 years, we managed to remove the degree limitation from the algorithm, resultingin an unlimited practical method.

In this talk I will explain how we succeeded to remove the degree limitation. Furthermore,applications, such as solvability be radicals, will be discussed.

Friday 11:30 – 11:50, Mathews-107

Constructing metacyclic extensionsMasanari KidaUniversity of [email protected]

A group G is called metacyclic if it contains a normal cyclic subgroup N such that G/N isalso cyclic. Dihedral groups and Frobenius groups are examples of metacyclic groups. A Galoisextension L over k is called a metacyclic extension if the Galois group Gal(L/k) is isomorphicto a metacyclic group. In this talk, we use a Kummer theory arising from an endomorphismof certain algebraic tori to construct metacyclic extensions. The extensions constructed by thismethod enjoy nice arithmetic properties. For example, we know the decomposition law in theextensions when the base field is a number field. Explicit defining equations of the extensionsalso can be computed. Our work relates to a former result due to Nakano and Sase (Tokyo J.Math. (2002)).

Friday 12:00 – 12:20, Mathews-107

Series expansion of multivariate algebraic functions at singular pointsTateaki SasakiInstitute of Mathematics, University of [email protected]

Let F (x, u1, . . . , u`), with ` ≥ 2, be a given irreducible multivariate polynomial and χ(u1, . . . , u`)be an algebraic function defined to be a root ofF (x, u1, . . . , u`) w.r.t. x. In this talk, we introduce a rather new method of expanding χ(u1, . . . , u`)into a series at a singular point, explain characteristic features of the resulting series, and showseveral remarkable applications.


In the case of ` = 1, univariate algebraic function can be expanded into a fractional-power series,or Puiseux series, at a singular point. This expansion method can be generalized to the case of` ≥ 2, giving multivariate Puiseux series which are of fractional powers w.r.t. each variable [5].The multivariate Puiseux series is, however, not useful because we are very difficult to know itsbehavior. On the other hand, Sasaki and Kako devised another expansion method in 1993 [9, 7].The resulting series was named Hensel series because it is computed by the Hensel construction.

The Hensel series has the following very characteristic features [2, 8]:

1. Hensel series is a series in the total-degree variable with coefficients of homogeneous rationalfunctions and a simple algebraic function θ (θ may be 1 in simple cases).

2. Mutually conjugate algebraic functions intersect one another near the zero-points of thedenominators of the coefficients.

3. The Hensel series converges quite well in the convergence domain, even if the evaluationpoint is far from the expansion point (a general formula for the convergence domain wasconjectured).

4. In any neighborhood of the expansion point, the convergence and the divergence domainsco-exist.

5. The ratio [divergence area]/[convergence area] decreases to 0 as we approach the expansionpoint.

The Hensel series has been applied to the following topics so far: solving the so-called nonzerosubstitution problem in multivariate polynomial factorization [1], analytic factorization of mul-tivariate polynomials [3, 4], and so on [6]. We are looking for applications in symbolic-numericcomputation.

[1] D. Inaba. Factorization of multivariate polynomials by extended Hensel construction. ACMSIGSAM Bulletin 39 (2005), 142-154.

[2] D. Inaba and T. Sasaki. A numerical study of extended Hensel series. Proc. SNC’2007(Symbolic-Numeric Computation), J. Verchelde and S. Watt (Eds.), ACM, 103-109, 2007.

[3] M. Iwami. Analytic factorization of the multivariate polynomial. Proc. CASC 2003 (Com-puter Algebra in Scientific Computing), V.G. Ganzha, E.W. Mayr and E.V. Vorozhtsov(Eds.), Technishe Universitat Munchen Press, 213-225, 2003.

[4] M. Iwami. Extension of expansion base algorithm to multivariate analytic factorization.Proc. CASC 2004 (Computer Algebra in Scientific Computing), V.G. Ganzha, E.W. Mayrand E.V. Vorozhtsov (Eds.), Technishe Universitat Munchen Press, 269-282, 2004.

[5] J. McDonald. Fiber polytopes and fractional power series. J. Pure Appl. Algebra 104 (1995),213-233.

[6] T. Sasaki. Approximately singular multivariate polynomials. Proc. CASC 2004 (ComputerAlgebra in Scientific Computing), V.G. Ganzha, E.W. Mayr and E.V. Vorozhtsov (Eds.),Technishe Universitat Munchen Press, 399-408, 2004.

[7] T. Sasaki and D. Inaba. Hensel construction of F (x, u1, . . . , u`), ` ≥ 2, at a singular pointand its applications. ACM SIGSAM Bulletin 34 (2000), 9-17.

[8] T. Sasaki and D. Inaba. Extended Hensel construction and multivariate algebraic functions.Preprint of Univ. Tsukuba (18 pages), 2007, submitted.

60 Abstracts

[9] T. Sasaki and F. Kako. Solving multivariate algebraic equation by Hensel construction.Japan J. Indust. Appl. Math. 16 (1999), 257-285. (This paper was submitted in 1993; thepublication was delayed by a very slow refereeing procedure.)

Friday 12:30 – 12:50, Mathews-107

Enumerating Galois representations (mod p)Alex GhitzaUniversity of [email protected]

Coauthors: Craig Citro

Serre’s conjecture (now a theorem of Khare and Wintenberger) opens the door to studyingGalois representations (mod p) via the associated Hecke eigenforms. In this talk, we use thiscorrespondence to enumerate the set of Galois representations (mod p) with a given ramificationbehaviour. I will describe the algorithm and some implementation details.

Dynamical Systems 61

Dynamical Systems

Monday 9:30 – 9:50, Mathews-C

Stochastic and deterministic cellular automata: theory and an applicationJane HawkinsUniversity of North Carolina at Chapel [email protected]

Coauthors: Emily Burkhead and Donna Molinek

Beginning with a finite state space A and any integer dimension d ≥ 1 we consider the latticeZd, consisting of vectors ~i = (i1, i2, . . . , id), ij ∈ Z for each j = 1, . . . , d. The space on which

a cellular automaton is defined is X = AZd; for each x ∈ X and ~i ∈ Zd, by x~i = x(i1,...,id) we

denote the coordinate of x at ~i.

We define the shift action on X by: ∀~i ∈ Zd, σ~i(x)(j1,...,jd) = x(j1+i1,...,jd+id). A d-dimensional

cellular automaton (CA) is a continuous map F on X such that for every~i ∈ Zd, F σ~i = σ~i F .By work of Curtis, Hedlund, and Lyndon we characterize F by a local rule (often called a blockcode).

If we have several CA’s defined on X, F1, . . . Fm, then at each x~i we can choose randomly one ofthe local rules for the CA’s to obtain a stochastic CA. We discuss some measure theoretic anddynamical properties of CA’s and stochastic CA’s, and briefly discuss an application to virology.


Choquet simplices as the set of invariant probability measures of a postcritical setMaria Isabel CortezUniversidad de Santiago de [email protected]

Coauthors: Juan Rivera-Letelier

A well-known consequence of the ergodic decomposition theorem is that the space of invariantprobability measures of a topological dynamical system, endowed with the weak∗ topology, isa non-empty metrizable Choquet simplex. We show that every non-empty metrizable Choquetsimplex arises as the space of invariant probability measures of the post-critical set of a logisticmap. In fact we show the logistic map f can be taken in such a way that its post-critical set is aCantor set where f is minimal, and such that each invariant probability measure supported bythe post-critical set has zero Lyapunov exponent, and is an equilibrium state for the potential− ln |f ′|.

62 Abstracts


Non-expansive directions for Z2 actionsMichael HochmanPrinceton [email protected]

A line L in the plane is expansive for a symbolic Z2 action if, for some r > 0, any two con-figurations which agree on an r-neighborhood of L must agree everywhere. When L containsa rational point, this is equivalent to expansiveness in the classical sense of the action by thecorresponding group element.

In a paper from 1995 Lind and Boyle studied the set of non-expansive directions, showing that itis closed and, for infinite subshifts, non-empty. They also showed that any closed set of directionscontaining at least 2 points occurs in this way.

I will discuss a recent construction which realizes an arbitrary singleton as the set of non-expansive directions.


Estimating the entropy of a Z2 shift of finite type with probabilistic methodsRonnie PavlovUniversity of British [email protected]

In symbolic dynamics, a Zd shift of finite type (or SFT) is the set of all ways to assign elementsfrom a finite alphabet A to all sites of Zd, subject to local rules about which elements of A areallowed to appear next to each other.

The (topological) entropy of any Z SFT is easily computable (it is the log of an algebraicnumber). However, for d > 1, the situation becomes more complex. There are in fact only a fewnontrivial examples of Z2 SFTs whose entropies have explicit closed forms.

For the Z2 golden mean shift (for which no explicit closed form for the entropy is known), wegive a sequence of approximations to the entropy which converge at an exponential rate. Thisimplies that this entropy is computable in polynomial time.



Complexity of non chaotic systemsKyewon ParkAjou [email protected]

We investigate the complexity of entropy zero systems. We introduce the notions like entropygenerating sequence, positive entropy sequence and define the complexity via the dimensions ofthe sequences. We also consider the examples exhibiting the above properties.


On the frequency of balanced times in cylinder flowsDavid RalstonDepartment of Mathematics, The Ohio State [email protected]

Building a cylinder flow over an irrational circle rotation, it follows that the times when a givenstarting position returns to its starting level almost surely form an infinite but density zerosubset of the natural numbers. In joint work with J. Chaika, we investigate the size of thisset through summation of reciprocals. Our principal results are that for almost every irrationalrotation, almost every position gives rise to divergent sums, but certain exceptional rotationsgive rise to convergent sums for almost every position.

Tuesday 9:30 – 9:50, Mathews-C

Set oriented numerical methods in space mission designMichael DellnitzDepartment of Mathematics, University of [email protected]

Over the last years new techniques for the design of energetically efficient trajectories for spacemissions have been proposed which are based on the circular restricted three body problemas the underlying mathematical model. These techniques exploit the structure and geometry ofcertain invariant sets and associated invariant manifolds in phase space in order to systematicallyconstruct efficient flight paths.

In this talk numerical methods will be presented that enable an implementation of this approach.Using a set oriented framework it is shown how to compute approximations to invariant mani-folds, how to detect connecting orbits as well as pseudo-trajectories that serve as initial guessesfor the solution of corresponding optimal control problems.

64 Abstracts


Isolated Lyapunov spectrum for Perron-Frobenius cocyclesSimon LloydUniversity of New South [email protected]

Coauthors: Gary Froyland, Anthony Quas, and Naratip Santitissadeekorn

We consider compositions of expanding interval maps and the rates of decay for functions ofbounded variation under the action of the associated Perron-Frobenius cocycles. We provethat for piecewise affine maps sharing a common Markov partition, the Lyapunov spectrum ofthe Perron-Frobenius cocycle has at most finitely many isolated points. Moreover, we presenta strengthened version of the Multiplicative Ergodic Theorem for non-invertible matrices andconstruct an invariant splitting into Oseledets subspaces.


Billiards with holesMark DemersFairfield [email protected]

Coauthors: Paul Wright and Lai-Sang Young

Introducing a small hole into the phase space of an ergodic dynamical system causes almostevery trajectory to eventually escape. Despite this, such systems can have rich dynamics. Fordispersing billiards with holes, we construct physically relevant invariant and conditionally in-variant measures with properties analogous to those of SRB measures for closed systems. Wealso prove that the conditionally invariant measures converge to the smooth invariant measurein the small hole limit. This is joint work with Lai-Sang Young and Paul Wright.


Equilibrium states on repellors for endomorphismsEugen MihailescuInstitute of Mathematics of the Romanian [email protected]

Attractors for hyperbolic diffeomorphisms are known to possess unique SRB measures havingthe property that their conditional measures on unstable manifolds are absolutely continuous. Inthis talk we will investigate the case of non-invertible transformations (endomorphisms) whichhave repellors, or more general basic invariant sets. The situation proves to be different thanthe one for diffeomorphisms, due to possible overlaps and lack of a nice foliating structurefor unstable manifolds. We give methods to form invariant measures by using local inverseiterates. In certain cases we obtain the asymptotic distribution of preimages with the helpof equilibrium measures for Holder potentials; they are proved to have absolutely continuousconditional measures induced on stable manifolds. In particular this applies to hyperbolic toralendomorphisms.



Ulam’s method without a spectral gapRua MurrayDepartment of Mathematics and Statistics, University of [email protected]

Most convergence proofs for Ulam’s discretisation of Frobenius-Perron (transfer) operators relymore or less explicitly on the existence of a spectral gap for the transfer operator. In non-uniformly expanding scenarios, there is no spectral gap.

This talk will describe two aspects of Ulam’s method applied to the transfer operators for afamily of 1d maps with a single indifferent fixed point: first, convergence for approximationsof the absolutely continuous invariant measure; second, numerical evidence for a “discretisationinduced spectral gap” exhibiting interesting scaling.


Intermittent baker’s mapsChris BoseDepartment of Mathematics and Statistics, University of Victoria, [email protected]

Coauthors: Rua Murray

The baker’s map is a standard example in any introductory ergodic theory course. It exhibits themost regular properties that can be expected from a m.p system. (In fact, a standard exercise isto establish isomorphism between the baker’s map and a Bernoulli shift.) The generalized baker’smap construction allows one to build a much wider class of transformations, with the potentialfor more delicate statistical behavior while maintaining a geometrically simple, Lebesgue measurepreserving system.

In joint work with Rua Murray, we have constructed a family of baker’s maps in the non-uniformly hyperbolic category. In this talk we will approach these examples from three relateddirections: maps with ‘some hyperbolicity’ in the spirit of L.S. Young with analysis via Markovtower extensions, 1-D nonuniformly expanding maps with analysis of the first hyperbolic timein the spirit of Alves et al, and finally, as nonuniformly hyperbolic maps with singularities in thespirit of Katok and Strelcyn.

All of our maps have sharp polynomial mixing rates for Holder data and all are isomorphic toBernoulli shifts (as invertible m.p. transformations)

66 Abstracts


Complex quadratic rational maps and Puiseux series dynamicsJan KiwiPontificia Universidad Catlica de [email protected]

The moduli space of complex quadratic rational maps (as dynamical systems) is isomorphic toC2. We will show that the structure of moduli space near infinity may be studied with the aid ofnon-Archimedean dynamics. More precisely, we consider the non-Archimedean field L obtainedas the completion of an algebraic closure (Puiseux series) of the field of formal Laurent seriesin one variable. We study iterations of quadratic rational maps with coefficients in L over thecorresponding projective line. We obtain a complete description of the dynamical space and ofthe parameter space of these maps.

We are able to use this description to obtain some results which are the natural analogue forcomplex quadratic rational maps of part of Branner and Hubbard’s picture of the parameterspace of complex cubic polynomials near infinity. In particular, we will show that objects suchas solenoids and Mandelbrot tori parametrize dynamically relevant subsets of the moduli spaceof complex quadratic rational maps near infinity.

Friday 10:00 – 10:20, Mathews-312

Aspects of planar mappings that preserve biquadratic curvesJohn A. G. RobertsSchool of Mathematics and Statistics, University of New South [email protected]

Coauthors: Danesh Jogia and Jim Pettigrew

Birational planar maps that send a family of biquadratic curves that foliate the plane to anothersuch family are considered (some well-studied integrable planar maps being a special case). Usingalgebraic geometry, we characterise such maps. In the phase portraits of integrable maps, thesingular curves are important as they act as separatrices for the dynamics. We show how thesingular curves in parametrized families of biquadratic curves can be found and characterised.


Friday 11:00 – 11:20, Mathews-312

Polynomial dynamics and combinatorial invariantsLaura DeMarcoUniversity of Illinois at [email protected]

Coauthors: Kevin Pilgrim

I will discuss certain combinatorial methods for studying the basins of infinity of 1-dimensionalcomplex polynomials. We can use these invariants to study dynamical decompositions of themoduli space of polynomials; in particular, we obtain a new proof that the Mandelbrot set (orconnectedness locus in any degree) is connected.

Friday 11:30 – 11:50, Mathews-312

Sumset phenomenon in countable amenable groupsAlexander FishThe Ohio State [email protected]

Coauthors: Mathias Beiglbock and Vitaly Bergelson

We extend the result of Bergelson, Furstenberg and Weiss about piecewise Bohrness of a sumsetof two sets of positive upper Banach density in integers to general countable amenable groups.In abelian case this result implies that sumset of two sets of positive upper Banach densitycontains a sumset of three sets of upper Banach density.

Friday 12:00 – 12:20, Mathews-312

The dimension of projections via local entropy averagesPablo ShmerkinUniversity of [email protected]

Coauthors: Michael Hochman

A classical theorem of Marstrand asserts that if X is a set in the plane, then the Hausdorffdimension of the orthogonal projection of X in almost every direction has Hausdorff dimensionmin(1, d), where d is the Hausdorff dimension of X. The exceptional set of directions can ingeneral be very complicated. However, if X is dynamically defined, one may hope to determinethe set of exceptions explicitly.

I will discuss a new framework to tackle this kind of problem, which involves averaging localentropies as a mean of calculating dimension. I will then focus on the following application:if A, B are subsets of the circle invariant under ×2 and ×3 mod 1 respectively, then for theproduct set X = A × B, the only exceptional directions in Marstrand’s Theorem are the twotrivial ones (projections onto the coordinate axes). This generalizes a recent result of Y. Peresand P. Shmerkin, which deals with the case in which A and B are modeled by a full shift, andanswers a question of H. Furstenberg.

68 Abstracts

Geometric Analysis


Stability and extremal metrics for projective bundlesToshiki MabuchiDepartment of Mathematics, Osaka [email protected]

I would like to review a recent result of V. Apostolov, P. Gauduchon and D. Calderbank on thestability and extremal metrics for projective bundles over curves. In this talk, the method ofapproach is quite different from the original one.


Global existence for the Seiberg-Witten flowMin-Chun HongDepartment of Mathematics, University of [email protected]

Coauthors: Lorenz Schabrun

We introduce the gradient flow of the Seiberg-Witten functional on a compact, orientable Rie-mannian 4-manifold and show the global existence of a unique smooth solution to the flow.


On a new symmetric structure of moduli spaces of Riemann surfacesSumio YamadaMathematical Institute, Tohoku [email protected]

A new symmetric structure involving the Teichmuller space is presented. In particular, anisometric group action with respect to the Weil-Petersson distance function will be introduced,and a similarity to the theory of Bruhat-Tits building will be pointed out. This symmetry shedsome new light on further understanding of the surface mapping class groups.


Injectivity radius and gonality of a compact Riemann surfaceJun-Muk HwangKorea Institute for Advanced [email protected]

Coauthors: Wing-Keung To

This work is about the relation between the hyperbolic geometry of a compact Riemann surface

Geometric Analysis 69

of genus at least 2 and the algebraic geometry of the corresponding complex algebraic curve.More precisely, we show that the hyperbolic injectivity radius is bounded by the gonality, i.e.the minimal degree of holomorphic maps to the Riemann sphere.


Lagrangian mean curvature flow for entire Lipschitz graphsAlbert ChauUniversity of British [email protected]

Coauthors: Jingyi Chen and Weiyong He

We prove existence of longtime smooth solutions to mean curvature flow of entire LipschitzLagrangian graphs. As an application of the estimates for the solution, we establish a Bernsteintype result for translating solitons. The results are from joint work with Jingyi Chen andWeiyong He.


The Ricci flow and exotic smooth structures in dimension fourMasashi IshidaDepartment of Mathematics, Sophia University, [email protected]

In this talk, we will discuss the relationship between the existence or non-existence of non-singular solutions to the normalized Ricci flow and smooth structures on closed 4-manifolds,where non-singular solutions to the normalized Ricci flow are solutions which exist for all timewith uniformly bounded sectional curvature. In dimension 4, there exist infinitely many compacttopological manifolds admitting distinct smooth structures, i.e., exotic smooth structures. Wewould like to point out that the difference between existence and non-existence of such solutionsstrictly depends on the choice of smooth structure.


Initial data for vacuum spacetimes with a positive cosmological constantDaniel PollackUniversity of [email protected]

The time-symmetric vacuum constraint equations for the Einstein field equations are preciselythe condition that a Riemannian metric has constant scalar curvature, with the sign of the scalarcurvature corresponding to the sign of the cosmological constant. In the positive case, we willshow how this leads to the recognition that known results for the singular Yamabe problemmay be reinterpreted as results on the existence of spacetimes with asymptotically Kottler-Schwarzschild-de Sitter ends. Joint work with Piotr Chrusciel and Frank Pacard shows howone can go further to construct spacetimes with exactly Kottler-Schwarzschild-de Sitter ends.

70 Abstracts

This will be compared with analogous results for zero and negative choices of the cosmologicalconstant.


Almost-complex tori in the 6-sphereEmma CarberryUniversity of [email protected]

Coauthors: Erxiao Wang

Octonionic multiplication defines a natural almost-complex structure on S6 ⊂ Im O and almost-complex curves M2 → S6 are rather pleasant examples of minimal surfaces. In particular, thecone over such a curve is associative and hence absolutely volume minimising. These almost-complex curves come in two types: they are either isotropic (in which case Bryant has shownthey can be algebraically constructed from holomorphic maps) or they are superconformal. Ishall describe a spectral curve approach to superconformal almost-complex tori; the main pointof which is to also obtain an algebraic characterisation of these surfaces and hence study theirmoduli. An interesting feature is that the relevant abelian variety in this case is the intersectionof two Prymians.


Positive mass theorems for asymptotically de Sitter spacetimesXiao ZhangInstitute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy [email protected]

Coauthors: M. Luo and N. Xie

We use planar coordinates as well as hyperbolic coordinates to separate the de Sitter spacetimeinto two parts. These two ways of cutting the de Sitter give rise to two different spatial infinities.For spacetimes which are asymptotic to either half of the de Sitter spacetime, we are able toprovide definitions of the total energy, the total linear momentum, the total angular momentum,respectively. And we prove two positive mass theorems, corresponding to these two sorts ofspatial infinities, for spacelike hypersurfaces whose mean curvatures are bounded by certainconstant from above.

Industrial Applications of Mathematics: Multiscale Mechanics 71

Industrial Applications of Mathematics: Multiscale Mechanics

Monday 9:30 – 10:15, Mathews-D

Nonlinear boundary value problems for porous media and metal surface evolution:use of canonical coordinates of an approximate symmetryPhilip BroadbridgeLa Trobe [email protected]

From the mid 1980s, integrable nonlinear convection-diffusion equations were adapted to obtainsolutions for transient flow in unsaturated soil subject to constant-flux boundary conditions.However, the solution with Dirichlet boundary conditions has been more difficult. This problemcan be transformed to a modified Stefan problem, with latent heat release, linear heat conductionand additional steady heat extraction occurring at the free boundary. The standard scale-invariant Neumann solution is the leading term of the early-time solution, which neglects thesteady heat extraction. If we choose independent coordinates to be canonical coordinates ofthe approximate scaling symmetry, then separation of variables is admissible at all levels ofcorrection for the non-invariant problem. The formal solution is a power series in square roottime, involving generalized hypergeometric functions. Similar methods apply to fourth ordersurface diffusion near a grain boundary on a metal surface.


Confined comminution: discrete models and breakage mechanicsItai EinavSchool of Civil Engineering, University of [email protected]

Coauthors: Oded Ben-Nun

Comminution, the process of grain size reduction, is pivotal to many operations in variousindustries, including mineral processing, agriculture, pharmaceutics, and in geoscience. This isbecause the size and shape of particles critically affect the chemical and physical characteristicsof industrial products. For example, in pharmaceutics, controlled comminution is required foroptimising the properties of tablets, including the chemical absorption and the overall strengthof tablets. Direct compression in confined conditions is often the preferred method for thepreparation of tablets. Traditional comminution theories (often more than 100 years old) arecontinuously employed to study the connection between the energy spent in the operation andthe product size distribution of the particles. The problem is that these models do not explicitlyaccount for the boundary conditions, which defines the loading conditions, and therefore alteringthese conditions requires refitting models parameters. This in effect prevents from adequatelyoptimising the conditions. In my talk I will present numerical and theoretical advances. Thenumerical advance involves the development of a crushable discrete element method [1]. Usingthis we explore the connections between several aspects, including: self-similarity, attractors,energy scaling and evolution of gsd. The theoretical advance enables to explain many of theseaspects through a new theory called breakage mechanics [2, 3], which resolves the problems ofchanges in boundary conditions. The theory is based on principles of continuum mechanics,

72 Abstracts

but its predictions are supported by experiments and the complimentary discrete observations.Examples will be driven from the world of pharmaceutics and geosciences. In particular, we willlook at the problem of tablets compaction and their strengths as a function of phase contentsand the applied compression loads. This will be achieved by applying the breakage mechanicstheory to mixtures [4].

[1] Ben-Nun O., Einav I. Phil. Trans. Roy. Soc. A. Invited to Theme Issue “Patterns in ourPlanet”.

[2] Einav I. 2007. Proc. Roy. Soc. A. 463, 2087, 3021–3035.

[3] Einav I. 2007. J. Mech. Phys. Solids. 55(6), 1274–1297.

[4] Einav I., Valdes J. 2008. J. Mech. Phys. Solids. 56(6), 2136–2148.


A complex network approach to dense granular rheologyD. WalkerDepartment of Mathematics and Statistics, University of [email protected]

Coauthors: T. Tshaikiwsky and A. Tordesillas

The rheological behaviour of dense granular materials under stress is of importance to a widerange of industries. Studies of such materials reveal complexity, self-organization and behaviourakin to phase transitions and criticality. Simulations of deforming dense granular assembliesusing the discrete element method produce rich data sets of contact network and force chainstructures. We consider if such data can usefully be investigated with methods from complexnetwork theory. Throughout the loading history we study evolving network statistics to probethe behaviour of the crossover from solid-like to liquid-like properties and towards and withinthe critical state.

Tuesday 9:30 – 10:15, Mathews-D

Gold in, gold out: mathematics for exploration and miningAlison OrdCSIRO Exploration and Mining, Perth, Western [email protected]

Exploration and mining both require us to understand how a particular element, be it gold orcopper, lead or zinc, arrived exactly where it did, when it did, and in such huge quantities as itdid. If we understand the critical mineralising processes, then we can improve our predictions ofwhere the ore is, thus improving our targeting efficiency for finding it; and we can also improvethe manner in which we dig it out of the ground and process it.

All relevant formation processes depend on the Darcy velocity of incoming fluids and upon theporosity of the rock mass being mineralised as well as upon gradients in temperature, pressure

Industrial Applications of Mathematics: Multiscale Mechanics 73

and chemical composition. Without an additional proposition that defines the way in whichthe porosity evolves as mineralisation proceeds, so that the concentration of mineralisation cancontinuously increase and so that the flow of fluids to the mineralising site can be maintained, themineralising process is unsustainable and self destroying since the porosity progressively clogs up.In order to generate a giant ore body, a self enhancing process, or coupled set of processes, thatinvolves porosity generation must operate. This porosity evolution is presumably accomplishedby a combination of mechanical and chemical processes. The processes involved must be self-enhancing in order to generate factors of 10e6 in enhancement of mineral concentration overbackground values. It appears that the processes involved must all be part of a system governedby reaction-diffusion equations of one kind or another.

We describe two approaches presently under discussion for how one might generate a giant orebody, one based on non-equilibrium thermodynamics and other on related analysis of particle-based simulations.


Mathematical modelling in nanotechnologyNgamta ThamwattanaNanomechanics Group, School of Mathematics and Applied Statistics, University of [email protected]

The prefix nano means one billionth, so that a nanometer is one billionth of a meter. To empha-size how small a nanometer is, a human hair measures 50,000–100,000 nanometers in diameter,and the smallest objects which might be seen by the unaided human eye are approximately10,000 nanometers. Nanotechnology is the term used to describe technology performed on thenanoscale, typically less than a 1000 nm, and which has practical applications. Nanostructuressuch as carbon nanotubes, fullerenes and graphene sheets are potentially applicable to a widevariety of novel devices in nanotechnology and nanotherapeutics, because of their small size,their special mechanical and electronic properties and their biocompatibility. Examples of suchdevices include memory devices for nanocomputing, gigahertz oscillators for ultra-sensitive andultra-fast signaling nanodevices, nanocontainers for targeted drug and gene delivery and biode-tection of pathogens and proteins. However, in such complex physical areas, while there is oftenan abundance of numerical information and data, there tends to be a lack of well-formed con-ceptual ideas and applied mathematical models. This talk reviews some applications of carbonnanostructures in nanotechnology and discusses some applied mathematical models that areuseful in order to understand and to gain insights into the interactions of nanostructures.


Understanding dense granular packings and their applicationsGary W. DelaneyCSIRO Mathematical and Information [email protected]

Random granular packings are found in a wide range of biological, physical and industrial sys-tems. Improving our understanding of such packings has wide spread applicability, from simpleissues of grain transportation, to large geological events such as landslides. We investigate how

74 Abstracts

the shape of the individual particles affects the macroscopic properties of granular packings. Weconsider systems with a range of size distributions, from monodisperse random granular pack-ings to Apollonian type packings where the particles have very large power-law variations in size[1]. We demonstrate the different behaviors observed as we transition from spherical particlespossessing only translational degrees of freedom to large aspect ratio non-spherical grains whererotational degrees of freedom are highly important.

[1] “Relation Between Grain Shape and Fractal Properties in Random Apollonian Packingwith Grain Rotation”, G.W. Delaney, S. Hutzler and T. Aste, Physical Review Letters,101, 120602, (2008).

Industrial Applications of Mathematics: Mathematical Finance 75

Industrial Applications of Mathematics: Mathematical Finance


Pairs trading with robust correlationJieren WangUniversity of British [email protected]

Coauthors: Holger H. Hoos, Camilo Rostoker, and Alan S. Wagner

This paper compares the performance of two types of correlation measures in triggering trades ina pairs trading application in the presence of high-frequency stock data. One correlation measureis the commonly-used Pearson correlation and the other is a robust correlation measure calledMaronna correlation. These correlation measures are used to define three methods of initiatingtrades – called trigger mechanisms. We test the relative performance of trading strategy usingthree types of triggering mechanisms on historical data and perform statistical tests based onthese results. We find that strategies based on trigger mechanisms which employ robust measuresof correlation yield consistently lower returns but more favorable risk characteristics. Finally,we used ParamILS, an automated parameter optimization tool based on stochastic local search,to assist in exploring the large strategy parameter space.


The evaluation of American compound option prices under stochastic volatilityCarl ChiarellaSchool of Finance and Economics, University of Technology, [email protected]

Coauthors: Boda Kang

We consider the problem of evaluating numerically American compound option prices whenthe dynamics of the underlying are driven by stochastic volatility, in particular following thesquare root process of Heston (1993). A compound option (called the mother option) gives theholder the right, but not obligation to buy (long) or sell (short) the underlying option (calledthe daughter option). Geske (1979) developed the first closed-form solution for the price of avanilla European call on a European call.

The incorporation of stochastic volatility into the price of compound options was first attemptedby Han (2003), while Fouque and Han (2004) introduce a fast, efficient and robust approxima-tion to compute the prices of compound options such as call-on-call options within the contextof multi-scale stochastic volatility models. However, they only consider the case of Europeanoptions on European options. Also their method relies on certain expansions so the range ofvalidity of their approach is not entirely clear. In this paper, we set up the partial differentialequation (PDE) approach to pricing European and American-type compound options. We as-sume that both the mother and the daughter options may be American-type. The compoundoption prices are modelled as a solution of a two-pass free boundary PDE problem.

It seems computationally demanding to solve those two nested PDEs, however, we have applied amodified sparse grid combination approach which was developed by Reisinger (2004) to solve high

76 Abstracts

dimensional PDEs in a fast and accurate manner. Since the underlying share price has differentscale characteristics compared with the levels of the volatility, it is difficult to implement thetechniques in Reisinger’s work directly. Instead, we have found that by modifying their approachslightly, namely by adding some fixed number of points to the volatility direction in each ofthe subspaces results in a relative “balance” in both direction and this modification producesaccurate and efficient results.

We have implemented the modified sparse grid combination technique to solve the free boundaryPDE followed by the price of the daughter option and obtained the desired prices and freeboundaries by further interpolation and extrapolation. In this way we obtain the initial andboundary conditions for the mother option. Next, we apply this technique again to solve thefree boundary PDE followed by the prices of the mother option to obtain the prices of thecompound option. In fact, we solve those PDEs in each of the subspaces on a parallel cluster,which makes the process very efficient.

We also implement a Monte Carlo Simulation scheme in conjunction with the method of lines tohave a benchmark method for the evaluation of the prices of American compound options. Com-paring the two approaches, we find that the modified sparse grid combination technique workswell in producing both efficient and accurate prices for the compound option under stochasticvolatility dynamics.

[1] Jean-Pierre Fouque and Chuan-Hsiang Han. Evaluation of compound options using pertur-bation approximation. Journal of Computational Finance, 9(1), Fall 2005.

[2] Robert Geske. The valuation of compound options. Journal of Financial Economics, 7,63–81, 1979.

[3] Chuan-Hsiang Han. Singular Perturbation on Non-Smooth Boundary Problems in Finance.Dissertation, North Carolina State University 2003.

[4] Steven L. Heston. A closed-form solution for options with stochastic volatility with appli-cations to bond and currency options. Review of Financial Studies, 6(2), 327–343, 1993.

[5] Alfredo Ibanez and Fernando Zapatero. Monte Carlo Valuation of American Optionsthrough Computation of the Optimal Exercise Frontier. Journal of Financial and Quan-titative Analysis, 39(2), 253–275, 2004

[6] Christoph Reisinger. Numerische Methoden fr hochdimensionale parabolische Gleichungenam Beispiel von Optionspreisaufgaben. Universitt Heidelberg, 2004.

[7] Christoph Reisinger and Gabriel Wittum. Efficient Hierarchical Approximation of High-Dimensional Option Pricing Problems. SIAM Journal on Scientific Computing, 29(1), 440–458, 2007.

Inverse Problems 77

Inverse Problems

Monday 9:30 – 9:50, Mathews-B

Minimization variational principles for acoustics, elastodynamics, and electromag-netism with applications to tomographyGraeme MiltonDepartment of Mathematics, University of [email protected]

Coauthors: Guy Bouchitte and Pierre Seppecher

The classical energy minimization principles of Dirichlet and Thompson are extended as mini-mization principles to acoustics, elastodynamics and electromagnetism in lossy inhomogeneousbodies at fixed frequency. This is done by building upon ideas of Cherkaev and Gibiansky, whoderived minimization variational principles for quasistatics. In the absence of free current theprimary electromagnetic minimization variational principles have a minimum which is the time-averaged electrical power dissipated in the body. The variational principles provide constraintson the boundary values of the fields when the moduli are known. Conversely, when the bound-ary values of the fields have been measured, then they provide information about the valuesof the moduli within the body. This should have application to acoustic and electromagnetictomography. We also derive saddle point variational principles which correspond to variationalprinciples of Gurtin, Willis, and Borcea.


Cloaking by anomalous localized resonanceNicolae-Alexandru P. NicoroviciSchool of Physics, University of [email protected]

Coauthors: Ross C. McPhedran, Graeme W. Milton, and Lindsay C. Botten

We discuss cloaking or hiding of objects from detection by probing with electromagnetic wavesusing the mechanism of anomalous localized resonance. This effect is also called reactive cloak-ing to distinguish it from the alternative method based on transformation optics or refraction.Cloaking by anomalous localized resonance occurs when the resonant field generated by a polar-izable line or point dipole acts back on the polarizable line or point dipole and effectively cancelsthe field acting on it from outside sources, so it has essentially no response to the external field.Numerically and analytically we show that a polarizable line or point dipole is effectively invis-ible to the external time harmonic field. This result extends to the case of an arbitrary numberof polarizable lines or line dipoles. We highlight the requirements for this type of cloaking,and compare them with those of refractive cloaking. We discuss the challenge common to bothmethods of achieving cloaking over extended spectral ranges and spatial regions, and possibleways of meeting the challenge.

78 Abstracts


On the evolution of curvelets under the wave equationHart SmithUniversity of Washington, [email protected]

I will discuss the problem of constructing approximations to the image of a curvelet type wavepacket as it evolves under the wave equation. The simple rigid approximation obtained bytranslating along the Hamiltonian flow is correct up to bounded errors which can be eliminatedthrough a convergent iteration scheme, but the approximation by itself leads to gaps forming inthe flowout of wavefronts. An approximation that involves the next order of expansion in theHamiltonian flow leads to better images, and compensates for expansion and curvature of thewavefront sets, but also leads to issues at caustic points.


Seismic imaging, illumination and partial reconstruction: a ‘curvelet’ transformperspectiveMaarten V. de HoopPurdue [email protected]

Coauthors: H. Smith, G. Uhlmann, R. D. van der Hilst, and H. Wendt

A key challenge in the imaging of (medium) coefficient discontinuities or reflectors from surfaceseismic reflection data is subsurface illumination, given available data coverage on the one handand complexity of the background model (of wavespeeds) on the other hand. The imagingis, here, described by the generalized Radon transform. To address the illumination challengewe develop a method for partial reconstruction of the mentioned coefficients. We make use ofthe curvelet transform, the associated matrix representation of the generalized Radon transform,which needs to be extended in the presence of caustics, and its structure, and phase-linearization.

We pair an image target with partial waveform reflection data, and develop a way to solve thematrix normal equations that connect their curvelet coefficients via diagonal approximation.Moreover, we develop an approximation, reminiscent of Gaussian beams, for the computationof the generalized Radon transform matrix elements only making use of multiplications andconvolutions, given the underlying ray geometry.

Throughout, we exploit the multi-scale features of the dyadic parabolic decomposition of phasespace underlying the curvelet transform and establish approximations that are accurate forsufficiently fine scales. The analysis we develop here can be extended to so-called wave-equationimaging; we will summarize partial reconstruction in the downward continuation approach.

Inverse Problems 79


Optimization algorithm for reconstructing interface changes of an inclusion frommodal measurementsHyeonbae KangInha [email protected]

Coauthors: Habib Ammari, Elena Beretta, Elisa Francini, and Mikyoung Lim

We propose an original and promising optimization approach for reconstructing interface changesof an inclusion (conductivity and elasticity) from measurements of eigenvalues and eigenfunctionsassociated with the transmission problem. Based on a rigorous asymptotic analysis, we derivean asymptotic formula for the perturbations in the modal measurements that are due to smallchanges in the interface of the inclusion. Using fine gradient estimates, we carefully estimate theerror term in this asymptotic formula. We then provide a key dual identity which naturally yieldsto the formulation of the proposed optimization problem. The viability of our reconstructionapproach is documented by a variety of numerical results. The resolution limit of our algorithmis also highlighted.


Reconstruction of a penetrable object in acousticsJenn-Nan WangDepartment of Mathematics, National Taiwan [email protected]

Coauthors: Sei Nagayasu and Gunther Uhlmann

We consider the reconstruction of penetrable obstacles in a plane region from acoustic measure-ments. Our method makes use of complex geometrical optics solutions with polynomial-typephase functions for the Helmholtz equation.

80 Abstracts

Tuesday 9:30 – 9:50, Mathews-B

Thermoacoustic tomography with variable sound speedPlamen StefanovPurdue [email protected]

Coauthors: Gunther Uhlmann

We study the thermoacoustic tomography problem with variable speed and measurements on atime interval [0, T ], where T is greater than the geodesic diameter of the domain. We show thatone can write an explicit solution in terms of a convergent Neumann series expansion.

Next, we study the case where the measurements are done on a part of the boundary. Weformulate sufficient and necessary condition that would guarantee that this inverse problem hasunique (and possibly unstable) solution, and another sufficient and necessary condition underwhich the solution is stable.


The Calderon problem in anisotropic mediaMikko SaloUniversity of [email protected]

Coauthors: D. Dos Santos Ferreira, C. Kenig, and G. Uhlmann

We consider the imaging of anisotropic materials by electrical measurements. This inverse prob-lem arises in Electrical Impedance Tomography (EIT), which has been proposed as a diag-nostic method in medical imaging and nondestructive testing. The mathematical model is theanisotropic Calderon problem, which consists in determining a matrix of coefficients in an ellipticequation from boundary measurements of solutions.

In geometric terms, the problem is to determine a Riemannian metric from Cauchy data ofharmonic functions on a manifold. Our approach is based on Carleman estimates. We charac-terize those Riemannian manifolds which admit a special limiting Carleman weight. By usingthese weights we construct complex geometrical optics solutions to elliptic equations, and proveuniqueness results in inverse problems for a class of Riemannian manifolds.


The wave equation on differential forms on manifolds with cornersAndras VasyStanford [email protected]

In this talk I will discuss the propagation of singularities for the wave equation on differentialforms with natural (i.e. relative or absolute) boundary conditions on Lorentzian manifolds withcorners, which in particular includes a formulation of Maxwell’s equations. These results areanalogous to those obtained by the author for the scalar wave equation and for the wave equation

Inverse Problems 81

on systems with Dirichlet or Neumann boundary conditions. The main novelty is thus thepresence of natural boundary conditions, which effectively make the problem non-scalar, even‘to leading order’, at corners of codimension at least 2.


Analytic extension and reconstruction of obstacles from few measurements for el-liptic second order operatorsGen NakamuraHokkaido [email protected]

Coauthors: Naofumi Honda and Mourad Sini

We deal with the inverse obstacle problem for general second order scalar operators with analyticcoefficients near the obstacle. We assume that the boundary of the obstacle is a closed non-analytic Lipschitz hypersurface. We show that, when we impose Dirichlet boundary condition,one measurement is enough to reconstruct the obstacle while in the Neumann boundary conditioncase, we need n− 1 measurements associated to n− 1 linearly independent inputs. Here n is thedimension of the space containing the obstacle. This is justified by investigating the analyticityproperties of the zero set of real analytic functions for the Dirichlet case and the zero set oftheir normal derivatives for the Neumann case. As for the zero set of real analytic solution, weproved that its set of critical points Z included in a closed topological manifold M is nowheredense and the complement taken in M of the union of Z and the boundary of M is analytic. Inaddition, we give a reconstruction procedure to recover the shapes. Similar results are true forthe associated inverse boundary value problems.


Reflectance optical tomography in layered tissuesArnold D. KimUniversity of California, [email protected]

Coauthors: Pedro Gonzalez-Rodriguez

We will discuss direct and inverse problems for light propagation in layered tissues. A two-layerhalfspace is a useful tissue model because it allows one to prescribe different optical properties insuperficial and deep regions of tissues. This difference between optical properties is necessary tomodel accurately light propagation through tissues systems comprised of a thin cellular epitheliallayer supported by an underlying stroma. We discuss an inverse obstacle scattering problem inlayered tissues with applications to detecting carcinomas in situ. This theory makes explicit useof the fact that there exists angular diversity in backscattered light measurements.

82 Abstracts


A new phase space method for recovering index of refraction from travel timesEric ChungChinese University of Hong [email protected]

Coauthors: Jianliang Qian, Gunther Uhlmann and Hong-Kai Zhao

A new phase space method for reconstructing the index of refraction of a medium from travel timemeasurements is developed. In particular this phase space formulation can deal with multiplearrival times. Numerical algorithms are designed and examples are shown to validate the newmethod.

Wednesday 9:30 – 9:50, Mathews-B

Stability and reconstruction for inverse problems in electromagnetic wave propaga-tionGang BaoMichigan State [email protected]

The talk is concerned with numerical solution and analysis of the classical inverse medium andinverse source problems for Maxwell’s or the Helmholtz equations. For multiple frequency data,the speaker will discuss a continuation approach based on the uncertainty principle as well as therelated issues on well-posedness and stability. The principle idea is to convert a highly ill-posedinverse problem into a sequence of well-posed problems. Progress of on-going related topics willalso be highlighted.


Stability in recovering nonlinear parameters for the bistable reaction-diffusion equa-tion using Carleman inequalitiesAxel OssesDIM-CMM Universidad de [email protected]

Coauthors: Muriel Boulakia and Celine Grandmont

We consider the bistable equation vt −∆v = f(v, x), f(v, x) = a(x)v(1− v)(v − α(x)) with ho-mogeneous Neumann boundary conditions in a bounded domain Ω ⊂ R3 with regular boundary.For this equation, we prove Lipschitz stability for the inverse problem of recovering parametersa and α from measurements of v in (0, T ) × ω, where ω is an arbitrary nonempty open subsetof Ω and measurements of v(t0) in the whole domain Ω at some positive time t0. The result isbased in some suitable global Carleman estimate for the nonlinear problem.

Inverse Problems 83


Models for modelling errorColin FoxUniversity of [email protected]

Inverse problems can be classified as problems where parameters are defined implicitly with thesolution suffering poorly both measurement errors and modelling errors. The difficulty of finitemeasurement error was solved in principle by Laplace and Poincare, and others in the interven-ing century, through the development of inverse probability. The more subtle issue of a prioriuncertainty has effectively been resolved in the following century, with the invariance argumentsof Jeffreys and Jaynes leading to ‘objective’ Bayesian methods, contrasting the subjective priordistributions constructed via elicitation and stochastic modelling. However, the more problem-atic issue of modelling error remains largely outstanding, despite it often being the major sourceof a posteriori uncertainty in practical inverse problems. How to quantitatively treat modellingerror is currently an active area of research with emerging ideas and some impressive successes.


Scattering resonances for several small convex bodies and the Lax-Phillips conjec-tureLuchezar StoyanovUniversity of Western [email protected]

This talk deals with a certain problem concerning obtaining geometric information about anobstacle in an odd-dimensional Euclidean space from the poles of the scattering matrix. Morespecifically, scattering by an obstacle is considered which is a finite disjoint union of strictlyconvex bodies with smooth boundaries contained in a given (large) ball and has some additionalproperties: its connected components have bounded eccentricity, the distances between differentconnected components are bounded from below, and a uniform ‘no eclipse condition’ is satisfied.It is shown that if an obstacle of this type has connected components of sufficiently smalldiameters, then there exists a horizontal strip near the real axis in the complex upper half-planecontaining infinitely many poles of the scattering matrix. That is, the so called Modified Lax-Phillips Conjecture holds (uniformly) for such type of obstacles. This generalizes a well-knownresult of M. Ikawa concerning balls with the same sufficiently small radius.


Sparse recovery in optical imagingHao GaoUniversity of California, [email protected]

Coauthors: Hongkai Zhao

Motivated by the efficiency and robustness of compressive sensing method for sparse signals, wedevelop a multi-level L1 minimization method to recover the sparse unknowns in optical imaging

84 Abstracts

based on radiative transfer equation or diffusion approximation, like bioluminescent sourcesin bioluminescence tomography, fluorescent yield and lifetime in fluorescence tomography, andabsorption and scattering coefficient in optical tomography.

Mathematics of Climate Change 85

Mathematics of Climate Change


Multi-scale processes and stochastic modeling of the climate systemChristian FranzkeBritish Antarctic Survey, Cambridge, [email protected]

The climate system has a wide range of temporal and spatial scales for important physicalprocesses. Examples include convective activity with an hourly time scale, organized synopticscale weather systems on a daily time scale, extra-tropical low-frequency variability on a timescale of 10 days to months, to decadal time scales of the coupled atmosphere-ocean system. Anunderstanding of the processes acting on different spatial and temporal scales is important sinceall these processes interact with each other due to the nonlinearities in the governing equations.Most of the current problems in understanding and predicting the climate systems stem fromthe multi-scale nature of the climate system in that all of the above processes interact with eachother and the neglect and/or misrepresentation of some of the processes lead to systematic biasesof the resolved processes and uncertainties in the climate response. A better understanding ofthe multi-scale nature of the climate system will be crucial in making more accurate and reliableweather and climate predictions.

In my presentation I will discuss systematic strategies to derive stochastic low-order models forclimate prediction. The stochastic mode reduction strategy accounts systematically for the effectof the unresolved degrees of freedom and predicts the functional form of the effective reducedequations. These procedures extend beyond simple Langevin equations with additive noise bypredicting nonlinear effective equations with both additive and multiplicative (state-dependent)noises. The stochastic mode reduction strategy predicts rigorously closed form stochastic modelsfor the slow variables in the limit of infinite separation of time-scales.


Conditional nonlinear optimal perturbation and its application to the studies ofENSO predictabilityWansuo DuanLASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, [email protected]

Coauthors: Mu Mu

Conditional nonlinear optimal perturbation (CNOP) is a nonlinear generalization of linear sin-gular vector (LSV) and features the largest nonlinear evolution at prediction time for the initialperturbations in a given constraint. It was proposed initially for predicting the limitation of pre-dictability of weather or climate. Then CNOP has been applied to the studies of the problemsrelated to predictability, stability, and sensitivity for weather and climate and even to those ofweather and climate dynamics, showing its superiority to LSV in revealing the nonlinear effect.In this talk, we focus on delivering the application of CNOP to the ENSO predictability. Withthe Zebiak-Cane model, we investigate the “spring predictability barrier” (SPB) for El Ninoevents by tracing the evolution of CNOP, where CNOP is superimposed on the El Nino events

86 Abstracts

and acts as the initial error with the biggest negative effect on the El Nino prediction. The resultsshow that the evolution of CNOP-type errors has obvious seasonal dependence and yields themost significant SPB. These CNOP-type errors can be classified into two types: one possessingan SSTA pattern with negative anomalies in the equatorial central-western Pacific and positiveanomalies in the equatorial eastern Pacific, and another with patterns almost opposite to thoseof the former type. Random errors in the initial conditions are also superimposed on El Ninoevents to investigate the SPB. We find that, whenever the predictions start, the random errorsneither exhibit an obvious season-dependent evolution nor yield a large prediction error, and thusmay not be responsible for the SPB phenomenon for El Nino events. These results suggest thatthe occurrence of the SPB could be closely related to particular initial error patterns. The twokinds of CNOP-type errors have opposite signs and, consequently, opposite growth behaviors,a result which may demonstrate two dynamical mechanisms of error growth related to SPB: inone case, the errors grow in a manner similar to El Nino; in the other, the errors develop witha tendency opposite to El Nino. The two types of CNOP errors may provide the informationregarding the “sensitive area” of ENSO predictions, due to their localized regions. If these typesof initial errors exist in the realistic ENSO predictions and if a target method can filter them,the ENSO forecast skill may be improved.


Pattern detection in multivariate climatic time series: detecting the influence ofsolar variability on the Earth’s atmosphereCharles D. CampCalifornia Polytechnic State University - San Luis [email protected]

Coauthors: Ka-Kit Tung and Jiansong Zhou

Many climatic data records are both short and noisy: short with respect to the time scales ofinterest and noisy in the sense that there are many processes which interact to create the datarecord. Therefore, it is often difficult to extract information about the underlying processes cre-ating the data. These issues are exacerbated when the processes of interest are not the dominantinfluences. If the data record consists of simultaneous measurements taken at ordered momentsin time (e.g., atmospheric temperature measured monthly at different spatial locations) thenmultivariate time series analysis techniques can be applied. Since these techniques simultane-ously analyze the full multivariate data set, they have access to more information and thereforeoffer a large improvement over techniques which analyze each time series independently or whichanalyze univariate time series constructed by spatial averaging. However, since the time seriesfor each variable are usually highly correlated, much of this additional information is redun-dant. There are two fundamental and related issues: Can we use the added information of amultivariate record to better isolate the underlying processes? Can we reduce the redundancyof information by reducing the dimensionality of the data set? In other words, can we findunderlying patterns which capture the fundamental behavior of the data? We will discuss somemultivariate analysis techniques in the context of detecting the influence of solar variability (ondecadal time scales) on the Earth’s atmosphere.



How mathematics can contribute to the issues of climate change?Kiminori ItohGraduate School of Engineering, Yokohama National [email protected]

I want to discuss mathematical analyses related to (1) the statistical estimation of climate sensi-tivity, a fundamental property of our climate system (e.g., how large the increase in temperaturewill be when the CO2 concentration is doubled?), and to (2) a possibility whether we can judgehow fast we can change our society, for instance, when we should largely reduce the amount ofCO2 emitted into the atmosphere (Is a social “adiabatic transition” analysis possible?).


Trends and interdecadal changes of weather predictabilityJianping LiState Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical FluidDynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of [email protected]

Coauthors: Ruiqiang Ding and Kyung-Ja Ha

To study the atmospheric predictability from the view of nonlinear error growth dynamics, a newapproach using the nonlinear local Lyapunov exponent (NLLE), is introduced by the authorsrecently. In this paper, the trends and interdecadal changes of weather predictability limit(WPL) during 1950s-1990s are investigated by employing the NLLE approach. The results showthat there exist significant trend changes for WPL over most of the globe. At three differentpressure levels in the troposphere (850, 500 and 200 hPa), spatial distribution patterns of lineartrend coefficients of WPL are similar. Significant decreasing trends in WPL could be found inthe most regions of the northern mid-latitudes and Africa, while significant increasing trendsin WPL lie in the most regions of the tropical Pacific and southern mid-high latitudes. In thelower stratosphere (50 hPa), the WPL in the whole tropics all shows significant increasing trends,while it displays significant decreasing trends in the most regions of the Antarctic and northernmid-high atitudes. By examining the temporal variations of WPL in detail, we find that theinterdecadal changes of WPL in most regions at different levels mainly happen in the 1970s, whichis consistent with the significant climate shift occurring in the late 1970s. Trends and interdecadalchanges of WPL are found to be well related to those of atmospheric persistence, which in turnare linked to the changes of atmospheric internal dynamics. Further analysis indicates thatthe changes of atmospheric static stability due to global warming might be one of main causesresponsible for the trends and interdecadal changes of atmospheric persistence and predictabilityin the southern and northern mid-high latitudes. The increased sea surface temperature (SST)variability exerts a stronger external forcing on the tropical Pacific atmosphere that tends toenhance the persistence of tropical Pacific atmosphere. This process appears to be responsiblefor the increase of atmospheric predictability and persistence in the tropical Pacific since thelate 1970s.

88 Abstracts


Identification and tracking of coherent features in oceanic and atmospheric flowsGary FroylandUniversity of New South [email protected]

Coauthors: Michael Dellnitz, Matthew England, Christian Horenkamp, Simon Lloyd, KathrinPadberg, Anthony Quas, Naratip Santitissadeekorn, Marcel Schwalb, and Anne Marie Treguier

Transport and mixing processes play an important role in many natural phenomena, includingocean circulation, atmospheric dynamics, and fluid dynamics. Ergodic theoretic approaches toidentifying transport barriers and slowly mixing structures in autonomous systems have been de-veloped around the Perron-Frobenius operator and its eigenfunctions. We describe an extensionof these techniques to general non-autonomous systems in which one can observe mobile, time-dependent, slowly dispersive structures, which we term coherent sets. We will outline the theoryand numerics behind these new approaches and contrast the results with geometric approachesbased upon time-dependent invariant manifolds and finite-time Lyapunov exponents (FTLEs).We will show that the latter approach can sometimes not identify the strongest transport barrier.Our new algorithms are based upon a Perron-Frobenius cocycle. We will discuss the structure ofthe Lyapunov spectrum of this cocycle, state a strengthened version the Multiplicative ErgodicTheorem for non-invertible matrices, and develop a numerical algorithm to approximate theOseledets subspaces that describe coherent sets. The underlying ideas and numerical results willbe illustrated with case studies from oceanic and atmospheric applications.


Likelihood-based inference for spatial extremesScott A. SissonSchool of Mathematics and Statistics, University of New South [email protected]

Coauthors: S. A. Padoan and M. Ribatet

Extreme value theory provides a powerful set of techniques to model the extremes of climateprocesses. Many applications of these methods involve the analysis of univariate extremes.The last decade has seen max-stable processes emerge as a common tool for the statisticalmodelling of spatial (multivariate) extremes. However, their application is complicated due tothe unavailability of the multivariate density function, and so likelihood-based methods remainfar from providing a complete and flexible framework for inference. In this talk I will presentan inferentially practical, likelihood-based method for fitting max-stable processes based on acomposite-likelihood approach. The procedure is sufficiently reliable and versatile to permitthe simultaneous modelling of marginal and dependence parameters in the spatial context at amoderate computational cost. I will illustrate the utility of this methodology via simulation,and through an analysis of U.S. precipitation extremes.



The emergence of stochasticity in climate modelsAdam MonahanSchool of Earth and Ocean Sciences, University of Victoria, [email protected]

Coauthors: Joel Culina

The Earth’s climate system displays variability over a broad range of space and time scales.It is common to refer to slower scales as “climate”, and faster scales as “weather” (althoughthe separation point is somewhat arbitrary). When concerned with the dynamics of climate,we do not need to explicitly resolve the weather – although we cannot ignore it, as dynamicalnonlinearities couple variability across time scales. Because weather processes are generallyturbulent, it is natural to represent these as stochastic processes in climate models.

This talk will consider systematic strategies for developing effective stochastic climate modelsfrom the dynamics of the coupled fast/slow weather-climate system. These strategies are exactin the limit of infinite timescale separation; this talk will consider the quality of these approxima-tions in the more realistic case where the separation is finite. Two examples will be considered:(1) coupled variability in the atmospheric and oceanic boundary layers, and (2) midlatitudeatmosphere low-frequency dynamics.


Data-driven quantification of uncertainty in water vapor dynamicsJinqiao DuanDepartment of Applied Mathematics, Illinois Institute of Technology, Chicago, [email protected]

Water vapor, as a greenhouse gas in the atmosphere, plays an important role in the climatesystem. Water vapor modeling and representation is one of the major uncertainties in climatechange predictions. Thus an understanding of the mechanisms for distributing water vaporthroughout the atmosphere is vital to estimating long-term changes in climate.

A nonlinear advection-diffusion-condensation equation for humidity is a usual model for under-standing water vapor dynamics. The speaker presents a stochastic approach to take the missingphysical mechanisms (e.g., convection) into account and thus obtain a stochastic model for watervapor evolution. Numerical experiments show that this new model has some merits.

This is an observational data-driven, stochastic analysis-based approach for quantifying modeluncertainty in water vapor dynamics.

90 Abstracts

Friday 11:00 – 11:45, Mathews-309

Thermal evolution of fluid transport in sea iceKenneth M. GoldenDepartment of Mathematics, University of [email protected]

Sea ice is both an indicator and agent of climate change. It also serves as a primary habitatfor microbial communities which sustain life in the polar oceans. Fluid flow through poroussea ice mediates a broad range of processes, such as the growth and decay of seasonal ice, theevolution of summer ice albedo, and biomass build-up. We will describe recent advances in usingpercolation, hierarchical, and network models to predict the fluid permeability of sea ice, as wellas rigorous, diffusion-based methods for bounding it. We’ll also discuss X-ray CT imaging of thebrine microstructure of sea ice and connectivity analysis of graphs derived from our tomographicimages. The results will help to improve predictions of how global warming will affect earth’sicepacks, and how polar ecosystems may respond. Related work on electrical properties whichwill help in monitoring ice thickness will be described as well. Video from a 2007 Antarcticexpedition where we measured fluid and electrical transport in sea ice will be shown.

Friday 12:00 – 12:45, Mathews-309

Using observed Fluctuation-Dissipation relationships to understand multi-scale cli-mate interactions in Tropical regionsPrashant D. SardeshmukhClimate Diagnostics Center, CIRES, University of [email protected]

Tropical weather and climate have a major impact on global weather and climate. Specifically,the quasi-periodic Madden-Julian Oscillation (MJO) with dominant power in the 30 to 70-dayperiod band, and the El Nino-Southern Oscillation (ENSO) with dominant power in the 2 to 7-yrperiod band, have been shown to exert important influences around the globe. And yet thesephenomena continue to be poorly represented in state-of-the-art numerical weather and climatemodels. It is widely thought that the difficulty arises partly from an inadequate treatment ofair-sea coupling in MJO dynamics, which not only causes errors in the MJO but also leads,through a distorted “MJO-ENSO connection”, to errors in ENSO.

In this study, we investigated the effect of air-sea coupling on tropical climate variability in acoupled linear inverse model (LIM) derived from observed fluctuation-dissipation relationshipsbetween the tropical atmospheric circulation and sea surface temperature (SST) variables. Wefirst demonstrated that the model successfully captures the time-lag covariance structure andpower spectra of these variables. We then investigated the importance of air-sea coupling onMJO and ENSO dynamics by shutting off the appropriate interaction terms in the model’s evo-lution operator. Our conclusion was surprisingly clear: air-sea coupling has a very small effect onthe MJO but a profound effect on ENSO. Consistent with this, the eigenvectors of the system’sdynamical evolution operator are also cleanly separated into two distinct, but nonorthogonal,subspaces: one governing the nearly uncoupled MJO dynamics, and the other governing thestrongly coupled ENSO dynamics. An important implication of this clean separation of uncou-pled and coupled tropical dynamics is that erroneous air-sea coupling in General CirculationModels (GCMs) may cause substantial errors in ENSO simulations and predictions, but prob-


ably not in MJO simulations and predictions. The “MJO-ENSO connection” often claimed tobe important in ENSO dynamics is also seen to be largely illusory, in that the same initialperturbation that sets off an ENSO event also tends to set off an MJO event, but without anydirect interaction between them.

92 Abstracts

Mathematical Finance


Comparison theorems for Backward Stochastic Differential Equations on MarkovChainsRobert ElliottUniversity of Adelaide and University of [email protected]

Coauthors: Sam Cohen

Most previous contributions on BSDEs, and the related theories of nonlinear expectation anddynamic risk measures, have been in the framework of continuous time diffusions or jump dif-fusions. Using solutions of BSDEs on spaces related to finite state, continuous time MarkovChains, we develop a theory of nonlinear expectations in the spirit of Peng. We prove basicproperties of these expectations, and show their applications to dynamic risk measures on suchspaces. In particular, we prove comparison theorems for scalar and vector valued solutions toBSDEs, and discuss arbitrage and risk measures in the scalar case.

Monday 12:00 – 12:45, Mathews-309

Down-side risk minimization as large deviation controlHideo NagaiOsaka [email protected]

We consider minimizing probability of falling below a target growth rate of the wealth processup to time horizon T in an incomplete market model and then study asymptotic behavior ofthe minimizing probability as T goes to infinity. We relate this asymptotics to an risk-sensitivestochastic control problem on infinite time horizon in the risk averse case. By regarding theasymptotic behavior as the dual to the latter problem we obtain an expression of the limit valueof the minimizing probability as the Legendre transformation of the value of the risk-sensitivestochastic control.


A benchmark approach to quantitative financeEckhard PlatenUniversity of Technology [email protected]

This lecture introduces into the benchmark approach, which provides a general framework forfinancial market modelling. It allows for a unified treatment of derivative pricing, portfoliooptimization and risk management. It extends beyond the classical asset pricing theories, withsignificant differences emerging for long dated derivative products and risk measures. The Lawof the Minimal Price will be presented for derivative pricing. A Diversification Theorem allows

Mathematical Finance 93

forming a proxy for the numeraire portfolio. The richer modelling framework of the benchmarkapproach leads to the derivation of tractable, realistic models under the real world probabilitymeasure. It will be explained how the approach differs from the classical risk neutral approach.Examples on long term and extreme maturity derivatives demonstrate the important fact that arange of contracts can be less expensively priced and hedged than suggested by classical theory.

[1] Platen, E.: A benchmark approach to finance. Math. Finance, No. 1, 131–151, (2006).

[2] Platen, E.; Heath, D.: A Benchmark Approach to Quantitative Finance, Springer Finance(2006).


Numerical calculations and simulations of G-normal distribution, G-Brownian mo-tion and applications to dynamic risk measuresShige PengInstitute of Mathematics, Shandong University, Jinan, [email protected]

Coauthors: Huaxiong Huang and Gang Wei

In this paper we present our numerically study results on G-normal distributions and G-Brownianmotions. We also show our random walk simulation of samples from a given G-normal distri-bution with and compare the simulation result with market data. The above result is appliedto dynamic risk measures of risk positions based on a underlying assets with drift and volatilityuncertainties. A comparison of numerical results between g-risk measures (small g) and G-riskmeasures (big G) will also be presented.


Independent random matchingYeneng SunNational University of [email protected]

Coauthors: Darrell Duffie

This talk will focus on a mathematical foundation for independent random matching of a largepopulation, as widely used in the economics and finance literature. We consider both static anddynamic systems with random mutation, partial matching arising from search, and type changesinduced by matching. Under independence assumptions at each randomization step, we showthat there is an almost-sure constant cross-sectional distribution of types in a large population,and moreover that the multi-period cross-sectional distribution of types is deterministic andevolves according to the transition matrices of the type process of a given agent. We also showthe existence of a joint agent-probability space, and randomized mutation, partial matching andmatch-induced type-changing functions that satisfy appropriate independence conditions, wherethe agent space is an extension of the classical Lebesgue unit interval.

94 Abstracts


A general equilibrium model of a multi-firm moral-hazard economy with financialmarkets: is relative performance evaluation necessary?Jaeyoung SungAjou University, [email protected]

Coauthors: Xuhu Wan

We present a general equilibrium model of a moral-hazard economy with an infinite numberof production opportunities and with financial markets, where stocks and bonds are traded.Contrary to the principal-agent literature, we argue that in the presence of financial markets,relative performance evaluation is irrelevant to optimal contracting. Consistent with a popularconjecture in the literature, we provide a proof that in optimal contracting in an economy withinfinitely many firms, the principal’s risk aversion is not important, because compensation riskis idiosyncratic.

In a finite economy, the risk-sharing role of each contract is still important, but the extent ofrisk sharing depends on the market price of risk, not on each principal’s risk aversion. Moreover,even in the economy with many firms, we confirm results from Sung and Wan’s [2009] single-firm results that, the first best riskfree interest rate is less than that of the first best, and thatsecond-best equity premium can be either higher or lower than that of the first best.

Friday 11:00 – 11:45, Mathews-102

American put options: a new mathematical frameworkShanjian TangDepartment of Finance and Control Sciences, School of Mathematical Sciences, Fudan [email protected]

In this talk, I shall describe a new mathematical framework for analyzing American put options.

Mathematical Physics 95

Mathematical Physics


Generalized Geometry, T-duality and 2D sigma modelsPeter BouwknegtAustralian National [email protected]

In this talk I will review some of the concepts of Generalized Geometry as introduced by Hitchin,and discuss some applications, in particular to mirror symmetry and T-duality in String Theory.I will also show how generalized (complex) geometries show up naturally in the study of two-dimensional sigma models.


The fate of the Landau levels under perturbations of constant signGueorgui RaykovFacultad de Matematicas, Pontificia Universidad Catolica de [email protected]

Coauthors: Frederic Klopp

We show that the Landau levels cease to be eigenvalues if we perturb the 2D Schroedingeroperator with constant magnetic field, by bounded electric potentials of fixed sign. We alsoshow that, if the perturbation is not of fixed sign, then any Landau level may be an eigenvalueof arbitrary, finite or infinite, multiplicity of the perturbed problem.

The partial support of the Chilean Science Foundation Fondecyt under Grant 1090467, and ofNucleo Cientıfico ICM P07-027-F “Mathematical Theory of Quantum and Classical MagneticSystems”, is gratefully acknowledged.


The BCS model with p + ip pairing symmetryJon LinksUniversity of [email protected]

Coauthors: Miguel Ibanez, German Sierra, and Shao-You Zhao

Cooper pairing with p-wave symmetry is believed to underlie the superfluidity of helium 3 andthe superconductivity of strontium ruthenate, as well as being relevant to current experimentswith cold fermi gases. In 2000 Read and Green conducted a mean-field analysis of the BCSHamiltonian with p + ip pairing and argued the existence of a topological quantum phase tran-sition. In the strong phase the ground-state wavefunction exhibits tightly bound Cooper pairs,while in the weak phase the wavefunction is asymptotically the Moore-Read Pfaffian fractionalquantum Hall state. The Moore-Read state, which has its origins in conformal field theory, iswidely studied as a trial state to describe non-abelian topological phases.

96 Abstracts

In this talk I will first review the mean-field studies of Read and Green. Then I will discuss analternative analysis of the p + ip model using the exact Bethe ansatz solution, with emphasis ondetermining the ground-state phase diagram.


Inter-relationships between spacing distributions in random matrix theoryPeter J. ForresterDepartment of Mathematics and Statistics, University of [email protected]

In random matrix theory there is a parameter β which controls the level repulsion betweenneighbouring eigenvalues. It has been known since the pioneering work of Dyson and Mehtain the early 60s that integrating over every second eigenvalue in a β = 1 ensemble gives aβ = 4 ensemble, while superimposing two β = 1 ensembles then integrating over every secondeigenvalue gives a β = 2 ensemble. The implications of these results will be discussed for theirconsequences to spacing distributions, and a generalization will be given, which in turn relies ona generalization of the Dixon-Anderson integral from the theory of the Selberg integral.


Eight vertex model and Painleve equations: properties of the eigenvectorsVladimir MangazeevDepatment of Theoretical Physics, RSPE, Australian National [email protected]

Coauthors: Vladimir Bazhanov

We consider the Baxter’s eight-vertex lattice model at the special point η = π/3 in the disorderedregime. It appears that the properties of the ground state at this point can be studied exactlyat any odd size of the lattice. We reveal a deep connection of the ground eigenvector and theeigenvalues of the Baxter’s Q-operator to polynomial solutions of Painleve VI equation.


Towards a deeper understanding of the integrable chiral Potts modelJacques H. H. PerkDepartment of Physics, Oklahoma State University; Department of Theoretical Physics and Cen-tre for Mathematics and its Applications, Australian National [email protected]

Coauthors: Helen Au-Yang

The integrable chiral Potts model is the first quantum-integrable model to have its spectralvariables (rapidities) lying on a high-genus curve. Much progress has been achieved on theeigenvalues of its transfer matrix and thermodynamic properties. Here we shall focus on theunderlying algebraic structure and the calculation of eigenvectors of the transfer matrix neededfor the evaluation of correlation functions.

Mathematical Physics 97


Periodicities of T-systems and Y-systemsAtsuo KunibaInstitute of Physics, University of Tokyo, [email protected]

Coauthors: Inoue, Iyama, Keller, Nakanishi, and Suzuki

The T and Y-systems originate in conformal field theory and Bethe ansatz studies of solvablelattice models during 80’s – 90’s. They are difference equations of Hirota or Toda type thatpossess a variety of aspects related to dilogarithm identity, Kirillov-Reshetikhin conjecture andq-character of quantum affine algebras and so forth. More recently, there has been a renewedinterest in their connection to the cluster algebras of Fomin-Zelevinsky, cluster category of Buan-Marsh-Reineke-Reiten-Todorov and the periodicity conjecture by Zamolodchikov and others. Ishall give an introductory overview on these topics.

Friday 11:00 – 11:45, Mathews-310

Critical percolation and qKZ equationsB. NienhuisInstituut voor Theoretische Fysica, Universiteit van [email protected]

Based on the work of Razumov and Stroganov it was found that certain correlation functionsfor critical bond percolation could be found for arbitrary system sizes and distances involved.These results were obtained by the study of the Perron-Frobenius eigenvector of the transfermatrix for the cylinder or strip. It turned out far more difficult to obtain such results for thesite percolation model on the triangular lattice.

In this paper we present an approach to both site and bond percolation, applicable to arbitraryrhombus tilings and to isoradial lattices respectively. It makes use of the relations known asq-Knizhnik-Zamolodchikov equations (qKZ). These relations are satisfied by the correlations inthe models. For lattices that are infinite in one directions and have a modest size in the otherdirection, these equations can be solved, yielding the correlation functions. For some specificcorrelation functions, these results can be extrapolated to arbitrary sizes.

Friday 12:00 – 12:45, Mathews-310

Lieb-Robinson bounds for quantum lattice dynamics and applicationsBruno NachtergaeleUniversity of California, [email protected]

Lieb-Robinson bounds demonstrate the existence of a finite speed of propagation of the effectof perturbations in spatially extended systems. Equivalently, they show that the diameter ofthe essential support of a local observable increases with time no faster than with a boundedspeed. We review recent proofs of Lieb-Robinson bounds for spin systems and lattice systemsof coupled oscillators and discuss several applications.

98 Abstracts

Partial Differential Equations

Wednesday 9:30 – 10:15, Mathews-C

Infinitely many bifurcations for nonlinear elliptic equationsE. N. DancerSchool of Mathematics and Statistics,University of [email protected]

We use analytic bifurcation theory and the theory of finite Morse index solutions to show thatin many cases where f grows rapidly at infinity the branch of positive solutions of Laplacianu = rf(u) in D, u = 0 on the boundary of D has infinitely many bifurcations.


Dynamic spike solutions to a singular parabolic equationChongchun ZengGeorgia Insitute of [email protected]

Coauthors: Peter Bates and Kening Lu

Consider a nonlinear parabolic equation ut = ε2∆u−u+f(u) with ε << 1 on a smooth boundeddomain U ⊂ Rn with the zero Neumann boundary condition. In the past years, there had beenextensive studies on steady spike solutions. Here a spike solution u is one which is almost equalto zero everywhere except on a ball of radius O(ε) where u = O(1). In this talk, we show thatthere exist dynamic spike solutions which maintain the spike profile for all t ∈ R with the spikemoving slowly on ∂U . Moreover, these dynamic spike states form an invariant manifold in someappropriate function space, which is diffeomorphic to ∂U . It is also proved that the leadingorder dynamics of the spike location follows the gradient flow of the mean curvature of ∂U .


A variational approach to perturbed nonlinear elliptic problemsJaeyoung ByeonDepartment of Mathematics, POSTECH, [email protected]

We are interested in the problems which can be regarded as a perturbation of a limiting problem.I would like to introduce a variational approach to find solutions of perturbed problems whichare close to structurally stable solutions of a limiting problem.

Partial Differential Equations 99


Stability of periodic orbits in celestial mechanicsShanzhong SunSchool of Mathematics, Capital Normal University, Beijing, [email protected]

Coauthors: Xijun Hu

Periodic solutions are primary objects in celestial mechanics. Their stabilities, say the stabilityof our solar system, are of fundamental importance. We try to understand the stability problemfrom the variational nature of the orbits. Our main tool is the Maslov index from Hamiltoniansystem theory. After surpassing the essential difficulties encountered in celestial mechanics, wecan get the relationship between the Morse index and the linear stability of the orbits, whichare applied to Lagrangian orbits and Figure-eight orbits.


Critical thresholds in hyperbolic relaxation systemsTong LiDepartment of Mathematics, University of Iowa, [email protected]

Coauthors: Hailiang Liu

Critical threshold phenomena in one dimensional 2 × 2 quasi-linear hyperbolic relaxation sys-tems are investigated. We prove global in time regularity and finite time singularity formationof solutions simultaneously by showing the critical threshold phenomena associated with the un-derlying relaxation systems. Our results apply to the well-known isentropic Euler system withdamping.

Thursday 9:30 – 10:15, Mathews-C

Classification and stability of Mach configurationsShuxing ChenSchool of Mathematical Sciences, Fudan [email protected]

Mach configuration is a wave structure occurring is irregular shock reflections in gas dynamics.It is composed of three shock fronts and a slip line (contact discontinuity) issuing from a point.The velocity of the flow behind the reflected shock and the Mach stem the flow can be subsonic-subsonic or supersonic-subsonic, separated by the slip line. In accordance, Mach configurationcan be distinguished as E-E type and E-H type. Based on the PDE analysis we proved thestability of Mach configurations.

100 Abstracts


Positive solutions of an elliptic equation with negative exponent: stability and crit-ical powerYihong DuUniversity of New [email protected]

Coauthors: Zongming Guo

We study positive solutions of the equation

∆u = |x|αu−p in Ω ⊂ RN (N ≥ 2),

where p > 0, α > −2, and Ω is a bounded or unbounded domain. We show that there is acritical power p = pc(α) such that this equation with Ω = RN has no stable positive solution forp > pc(α) but it admits a family of stable positive solutions when 0 < p ≤ pc(α). If p > pc(α

−)(α− = minα, 0), we further show that this equation with Ω = Br \0 has no positive solutionwith finite Morse index that has an isolated rupture at 0, and analogously it has no positivesolution with finite Morse index when Ω = RN \ BR. Among other results, we also classify thepositive solutions over Br \ 0 which are not bounded near 0.


Solutions of elliptic problems with nonlinearities of linear growthZhaoli LiuSchool of Mathematical Sciences, Capital Normal University, [email protected]

Coauthors: Jiabao Su and Zhi-Qiang Wang

Consider existence of solutions to the nonlinear elliptic equation

−∆u = f(x, u) in Ω, u = 0 on ∂Ω

and existence of solutions to the nonlinear elliptic system consisting of m equations

−∆u = ∇uV (x, u) in Ω, u = 0 on ∂Ω,

where Ω is a bounded domain in RN with smooth boundary ∂Ω, and f : Ω × R → R and∇uV : Ω× Rm → Rm, m > 2, are nonlinearities which have linear growth, i.e.,

f ∈ C1(Ω× R,R) and there exists c > 0 such that |f(x, u)| 6 c|u| for x ∈ Ω and u ∈ R;

V ∈ C2(Ω × Rm,R), V (x, 0) = 0, ∇uV (x, u) = 0, and there exists c > 0 such that−cIm 6 ∇2

uV (x, u) 6 cIm for x ∈ Ω and u ∈ Rm.

Here Im is the m×m identity matrix, and for two symmetric matrices A and B, A 6 B meansthat B − A is semi-positively definite. Existence of multiple solutions is studied.

Partial Differential Equations 101


Direct methods and variational principles for evolution equationsGiles AuchmutyUniversity of Houston, Houston, [email protected]

This talk will describe some variational principles for initial value problems for parabolic typeequations. The functionals to be minimized are constructed via methods from convex analysis.Direct variational methods can then be used to obtain existence, uniqueness and related resultsfor different classes of initial value problems for the equations.

Friday 9:30 – 10:15, Mathews-C

Bifurcation results for a nonlinear Schrodinger systemZhi-Qiang WangUtah State [email protected]

Coauthors: T. Bartsch and N. Dancer

We report some recent work on local and global bifurcation structure for a nonlinear system ofSchrodinger type equations, which give multiplicity results of positive bound state solutions ofthe system in the repulsive case.


The heat flow for H-systems on higher dimensional manifoldsMin-Chun HongDepartment of Mathematics, University of [email protected]

Coauthors: Deliang Hsu

In this talk, we investigate H-Systems on higher dimensional Riemannian manifolds and theirheat flow for a non-constant function H. We establish global existence and uniqueness of thesolution of the H-System flow under certain conditions.


From kinetic to macroscopic traffic flow models: modeling, analysis, simulationReinhard IllnerUniversity of Victoria, [email protected]

Coauthors: Michael Herty

This talk will explain how assumptions on microscopic (i.e., individual) traffic flow transferinto kinetic models of Vlasov or Fokker-Planck type, and how macroscopic PDE models arise

102 Abstracts

by moment expansions or a special solution ansatz. Models of such type (including the Aw-Rascle model of conservation laws) will be presented, and some analytical and simulation resultswill be shown. In particular, we explore the formation and propagation of braking waves inresponse to various types of triggers, such as speed limitations (temporal and spatial) or densityconcentrations.


An isoperimetric inequality for the elastically supported membraneDaniel DanersUniversity of [email protected]

Consider all membranes with boundary in the plane which have the same surface area andtension. Lord Rayleigh, in his book “The Theory of Sound”, conjectured 1877 that the circularmembrane has the lowest ground frequency. The conjecture was proved independently by Faberand Krahn 1923/24 if the membrane is fixed at the boundary. I will look at the correspondingconjecture for the elastically supported membrane, which remained unproved until recently.There was a partial proof by Bossel 1986 for the problem in two dimensions. I will outline theideas for a complete proof for the corresponding problem in arbitrary space dimensions and forthe p-Laplace operator. This is partly joint work with James Kennedy and Dorin Bucur


The inverse Calderon problem for Schodinger operator on Riemann surfacesLeo TzouStanford [email protected]

On a fixed smooth compact Riemann surface with boundary (M0, g), we show that the Cauchydata space (or Dirichlet-to-Neumann map) of the Schrodinger operator ∆g+V with V ∈ C2(M0)determines uniquely the potential V . This will be an generalization of various works on boundeddomains of R2. We will discuss the difficulties encountered because of the geometry and the toolswhich we used to overcome these difficulties. This is joint work with Colin Guillarmou of CNRSNice. The speaker is partially supported by NSF Grant No. DMS-0807502 during this work.

Scientific Computing 103

Scientific Computing

Wednesday 9:30 – 9:50, Mathews-D

Advances in advancing interfaces: efficient algorithms for inkjet plotters, semicon-ductors, medical scanners, and seismic imagingJames A. SethianDepartment of Mathematics, University of California, [email protected]

Propagating interfaces occur in a wide variety of settings, and include ocean waves, burningflames, and material boundaries. Less obvious boundaries are equally important, and includeiso-intensity contours in images, handwritten characters, and shapes against boundaries. Inaddition, some static problems can be recast as advancing fronts, including robotic navigationand finding shortest paths on contorted surfaces.

One way to frame moving interfaces is to recast them as solutions to fixed domain Eulerianpartial differential equations, and this has led to a collection of PDE-based techniques, includinglevel set methods, fast marching methods, and ordered upwind methods. These techniqueseasily accommodate merging boundaries and the delicate 3D physics of interface motion. Inmany settings, they been proven valuable.

The talk is an overview of this approach, with an eye towards fundamental mathematical ideasand their geometric and algorithmic interpretation. Applications will be framed around indus-trial engineering collaborations which have led to robust codes for semiconductor manufacturing,inkjet plotters for building plasma displays, image segmentation and tracking in cardiac scanners,robotic navigation, and seismic imaging in oil recovery.


Derivative spectroscopy and resolution enhancement of spectraBob AnderssenCSIRO Maths and Info [email protected]

Coauthors: Markus Hegland

Computer controlled instrumentation, such as various types of spectrometers, use the averagingof a large number of sweeps on a very fine grid to generate highly accurate approximations ofthe underlying signal being observed and/or monitored. Graphically, the plots of such datalook like the exact reproductions of smooth differentiable functions. As a consequence, suitablydesigned moving average numerical differentiators are able to accurately recover fourth andhigher derivatives of these approximations. This fact can be used to improve the applicabilityof derivative spectroscopy and to design robust resolution enhancement algorithms. Derivativespectroscopy has recently been utilized to classify barley mutants on the basis of their molecularstructure (Wiley et al. (2009)). A differentiation resolution enhancement algorithm has beenused to locate peak and sharpen (narrow) the peaks (Hegland and Anderssen (2005)). Thenature of the regularization being performed by such algorithm can be characterized using theconcept of dilational Hilbert scales.

104 Abstracts

[1] M. Hegland and R. S. Anderssen (2005) Resolution enhancement of spectra using differen-tiation, Inverse Problems 21 (2005), 915–934.

[2] P. R. Wiley, G. J. Tanner, P. M. Chandler and R. S. Anderssen (2009) The molecularclassification of barley (Hordeum vulgare L.) mutants using derivative NIR spectroscopy, J.Agric. and Food Chem. 57 (2009), 4042–4050.


Differentiation of matrix functionalsFrank de [email protected]

Coauthors: Bob Anderssen and Mark Lukas

Let the elements of a matrix A ∈ Rn×n depend on a vector of parameters x ∈ Rp. We considerthe evaluation of derivatives, with respect to x, of functionals w(A(x)) where w : Rn×n → R.

The original motivation for this study was to find an efficient algorithm for calculating thegeneralised cross validation (GCV) and robust generalised cross validation (RGCV) scores forsmoothing splines. For GCV, it is necessary to calculate the trace of the smoothing matrix, S(x)say, while for RGCV it is also necessary to calculate the trace of S2(x). Here, x > 0 is a scalarsmoothing parameter. For polynomial smoothing splines of degree 2m + 1, with n + m points ,

S(x) = I− xCA−1(x)CT

where A(x) = B + xCTC is a matrix pencil, B is a symmetric, positive definite band matrixwith bandwidth 2m−1 and C is an (n+m)×n, banded lower triangular matrix with bandwidthm + 1. It is easy to verify

tr(I−A(x)) = xd

dxlog(detA(x))

tr(I−A(x))2 = −x2 d2

dx2log(detA(x))

from which the required quantities can easily be derived. The advantage of formulating theproblem as one of differentiating a matrix functional, log(detA(x)) in this case, is that derivativescan generally be calculated with about the same complexity as the functional itself. Becausethe matrix A(x) is symmetric, positive definite and banded with bandwidth 2m + 1, the matrixfunctional can be calculated in O(m2n) operations using a Cholesky decomposition. Becausederivatives can be calculated in a similar number of operations, this approach yields two O(m2n)algorithms, one of which is new, for calculating the GCV score and two new O(m2n) algorithmsfor calculating the RGCV score for smoothing splines.

It turns out that the problem of calculating derivatives of matrix functionals occurs in a numberof applications, some of which will be described in this talk.



The stability of Pade and generalized Pade approximationsJ. C. ButcherUniversity of [email protected]

Generalized Pade approximations to the exponential function are represented by polynomials ofthe form

Φ(w, z) = P0(z)wr + P1(z)wr−1 + · · ·+ Pr(z),

where Pi is a polynomial of degree di and where Φ(exp(z), z) = O(zp+1), with p =∑r

i=0(di +1)− 2. If zero is not a branch-point of the Riemann surface defined by Φ(w, z) = 0, this meansthat, on one of the sheets, w(z) = exp(z) + O(zp+1). Approximations of this type arise inquestions concerning the stability of r-value methods for ordinary differential equations. TheEhle conjecture surmises that in the Runge-Kutta case (r = 1), a necessary condition for A-stability is 2d0 − p ≤ 2. This was proved using order stars by Hairer Nørsett and Wanner. Theso-called Butcher-Chipman conjecture makes a similar claim when r > 1. This has now beenproved using order-arrows.


The numerical solution of Volterra-type integro-differential equationsHermann BrunnerMemorial University of Newfoundland and Hong Kong Baptist [email protected]

Many of the Volterra integro-differential equations arising in mathematical modelling processesinvolving memory effects are highly nonlinear and/or contain delay arguments. In this talk we de-scribe recent approaches for the numerical solution of such functional differential equations. Theyinclude high-order collocation methods and hp-versions of the discontinuous Galerkin method.It will also be shown that many challenging computational issues remain to be addressed.

Thursday 9:30 – 9:50, Mathews-D

Integer Relation algorithms: an introductionJonathan BorweinUniversity of Newcastle and Dalhousie [email protected]

Integer Relation Methods were named as one of ‘top ten’ algorithms of the 20th century by“Computers in Science and in Engineering” (1999).

In my talk I will outline what Integer Relation Methods are and I will illustrate their remarkableutility on a variety of mathematical problems, some pure and some applied.

106 Abstracts


An efficient algorithm for high frequency exterior acoustic scattering in three di-mensionsStuart HawkinsMacquarie [email protected]

Coauthors: M. Ganesh

Standard discretization techniques are inefficient for three dimensional high frequency exteriorscattering simulations because they require the number of unknowns to grow like the squareof the frequency, leading to very large CPU time and memory requirements. We describe anefficient fully discrete Galerkin surface integral equation algorithm for simulating high frequencyacoustic scattering by three dimensional convex obstacles. Using a fixed number of unknowns,we demonstrate the visual accuracy and the efficiency of our algorithm for spherical and non-spherical convex scatterers with radii between 100 and 10000 wavelengths. Our algorithm re-quires only mild growth in CPU time as the frequency increases.


High dimensional challenges for scientific computingFrances Y. KuoSchool of Mathematics and Statistics, University of New South [email protected]

Many practical problems in statistics and mathematical finance involve integral with hundredsor even thousands of dimensions. These integrals often arise from multivariate expected values.In some cases the actual integrals are the goal (e.g., option pricing), while in others only thebest parameters for the model are required (e.g., maximum likelihood problems). In this talkI will take you through a non-technical tour of recent strategies for tackling these high dimen-sional integrals, and discuss the challenges that we face while attempting to lift the “curse ofdimensionality”.


To periodize or not to periodizeDirk NuyensSchool of Mathematics and Statistics, University of New South Wales, Australia andDepartment of Computer Science, K.U.Leuven, [email protected]

While quasi-Monte Carlo methods can give you better performance than the O(N−1/2) of MonteCarlo methods, typically one is happy with O(N−1). Using different techniques, amongst whichis periodization of the integrand, one is able to increase the order of convergence to O(N−a),a > 1. This talk addresses the question when it is useful to periodize the integrand.



Flow through a porous medium as a high-dimensional problemIan SloanUniversity of New South [email protected]

The problem of flow through a porous medium, with the permeability treated as a Gaussianrandom field, can be thought of as a high-dimensional problem: the dimensionality is for examplethe number of terms in a truncated Karhunen-Loeve expansion. In this paper, describing jointwork with F Kuo, I Graham and R Scheichl, we explore the use of quasi-Monte Carlo methodsto study the dispersion of the fluid as it seeps through the medium, and compare the resultswith Monte Carlo calculations. The preliminary results are encouraging.


Four-direction Fourier integration and B-forms of 3-D B-splinesJiachang SunInstitute of Software, Chinese Academy of Sciences, Beijing, Chinasun j [email protected]

It is essentially more difficult to construct splines in three variables case than in bivariate case.As an example, comparing to 2-D case, the construction of B-spline in space S1

3 with first-ordersmoothness is well-known more than twenty years, the 3-D analogy has been less studied [2].

In this talk, a B-form representation of B-splines of S14 with first-order smoothness over 4-

direction partitions is proposed. The minimum support consists of 73 tetrahedra and is dividedinto six kinds of tetrahedra according to their shapes. The detailed B-nets of correspondingpiecewise 3-D quartic are given.

With the help of so-called four-direction homogeneous coordinates in [1, 3], the related Fourierintegration representations of 3-D B-splines S2ν−1

4ν -S2ν4ν+1 (ν = 0, 1) are described over some

tetrahedra partition domains, such as isosceles tetrahedra, parallel dodecahedra and so on.

The result described in this talk can be extended into general high-dimensional cases.

[1] Sun J. Multivariate Fourier transform methods over simplex and super-simplex domains.Journal of Computational Mathematics, 2006, 24: 55–66.

[2] Sun J, Shi X. B-splines on 3-D tetrahedron partition mesh. Science in China (Series A),2001, 4: 491–496.

[3] Li H, Sun J, Xu Y. Discrete Fourier analysis, cubature and interpolation on a hexagon anda triangle. SIAM J. Numer. Anal. 46 (2008), 1653–1681.

108 Abstracts

Friday 9:30 – 9:50, Mathews-D

The role of Krylov subspace methods in modelling flow in porous mediaIan TurnerSchool of Mathematical Sciences, Faculty of Science and Technology, Queensland University [email protected]

A brief overview of the important role that Krylov subspace methods play in the computationalmodelling of flow in heterogeneous, porous media will be presented. The two key topics addressedwill be the solution of the nonlinear macroscopic transport equations and the approximation ofthe equations governing micro-scale transport.


Time discretization of a fractional diffusion equation via Laplace transformationWilliam McLeanSchool of Mathematics and Statistics, University of New South [email protected]

Coauthors: Vidar Thomee

Our scheme uses the Laplace inversion formula with a suitable choice of integration contour,combined with the Duhamel formula and quadrature. For t in a fixed time interval [0, T ], theerror is of order exp(−c

√N). We do not require any knowledge of the Laplace transform of the

inhomogeneous term.


Kernel based methods for vector data with correlated componentsRick BeatsonUniversity of Canterbury, Christchurch, New [email protected]

Coauthors: Wolfgang zu Castell and Stefan Shrodl

This talk discusses kernel based methods for vector data with correlated components. We giveconditions for a matrix kernel to be conditionally positive definite in an appropriate sense. Theconditions allow construction of matrix kernels from non-symmetric mixtures and scalings ofscalar kernels. In particular the kernel used to model the influence of component i on componentj can be different from that used to model the influence of component j on component i. Suchnon-symmetric models are appropriate in many circumstance, think for example of the influenceof acid rain on a forest and vice versa. The technique is particularly appropriate when there arerelatively few measurements of one quantity and relatively many of another ‘correlated’ quantity.The talk concludes with some numerical tests on model problems.



Solutions to pseudodifferential equations on a sphere using spherical splinesThanh TranSchool of Mathematics and Statistics, University of New South [email protected]

Coauthors: Duong T. Pham

Spherical splines are continuous piecewise homogeneous polynomials defined on a triangulationof a sphere. In this talk the use of these splines to find solutions of pseudodifferential equationson the sphere will be discussed. These equations arise from geodesy. Error analysis will bementioned, and numerical experiments corroborating the theoretical result will be presented.

110 Abstracts

Stringy Topology


Orbifold quantum differential equationsMartin GuestTokyo Metropolitan [email protected]

Coauthors: Hironori Sakai

It is well known that the quantum differential equations, which arise from mirror symmetry andwhich were developed by Alexander Givental, reflect faithfully the Gromov-Witten invariants ofa manifold. For orbifolds, the analogous phenomenon is less well understood. However it is tobe expected that the differential equations will provide confirmation of the known geometry anda source of conjectures for future work. We shall report on joint work with Hironori Sakai onthe orbifold quantum cohomology of hypersurfaces in weighted projective space.

Monday 10:00 – 10:20, Mathews-312

Ruan conjecture on singular flopsBohui ChenYangtze River Mathematical Center, Sichuan [email protected]

Coauthors: An-min Li, Qi Zhang, and Guosong Zhao

We study the singular flops related to the sigularities of the type given by

(x, y, z, t) ∈ C4|xy + z2r + t2 = 0/µr(a,−a, 1, 0),

where µr(a,−a, 1, 0) denotes the action of Zr with the specified weights. When two orbifoldsare related by such singular flops, we show that their orbifold quantum cohomology rings areisomorphic. This verifies a conjecture proposed by Ruan.

Monday 11:00 – 11:45, Mathews-312

Quantum ring of the singularity Xp + XY q

Huijun FanSchool of mathematcal sciences, Peking [email protected]

Coauthors: Yefeng Shen

I will show in this talk that the quantum ring of the quasi-homogeneous polynomial Xp +XY q(p ≥ 2, q > 1) with some admissible symmetry group G defined by Fan-Jarvis-Ruan-Wittentheory is isomorphic to the Milnor ring of its mirror dual polynomial XpY + Y q by constructingan concrete isomorphism. The construction is a little bit different in case (p− 1, q) = 1 and case(p − 1, q) = d > 1. Some other problems including the correspondence between the pairings ofboth Frobenius algebras will also be discussed.

Stringy Topology 111

Monday 12:00 – 12:20, Mathews-312

FJRW-ring and mirror symmetry of singularitiesMarc KrawitzUniversity of [email protected]

In physics, a Landau-Ginzburg theory is specified by a weighted homogeneous polynomial sat-isfying a mild non-degeneracy condition. The “chiral ring” associated to the theory is the orb-ifolded A-model constructed mathematically by Fan, Jarvis and Ruan (arXiv:0712.4021). Theunorbifolded B-model of the theory is given by the local algebra (Milnor ring) of the definingpolynomial. I will show how a natural transposition operation suggested by Berglund-Huebsch(doi:10.1016/0550-3213(93)90250-S) implements mirror symmetry for Landau-Ginzburg theo-ries having ‘invertible potentials’. This includes those specified by the simple and unimodalsingularities of Arnol’d’s classification.

I will describe a duality between symmetry groups for transposed potentials and an orbifoldingconstruction on the B-model, leading to a generalization of the main result, and suggesting arelationship with Arnol’d’s Strange Duality.

Monday 12:30 – 12:50, Mathews-312

Non-compact Frobenius algebras and OrbifoldsErnesto LupercioDeptartamento de Matematicas, [email protected]

Coauthors: Ana Gonzalez and Carlos Segovia

In this talk I will define the concept of non compact Frobenius algebra and explain how OrbifoldString Topology fits into this framework.

Thursday 9:30 – 9:50, Mathews-B

Commuting elements and simplicial spaces of homomorphismsAlejandro AdemUniversity of British [email protected]

Coauthors: F. Cohen and E. Torres-Giese

Using spaces of homomorphisms and the descending central series of the free groups, simplicialspaces are constructed for each integer q > 1 and every topological group G, with realizationsB(q, G) that filter the classifying space BG. In particular for q = 2 this yields a single spaceB(2, G) assembled from all the n-tuples of commuting elements in G. Homotopy properties ofthe B(q,G) are considered for finite groups, including their description as homotopy colimits.Cohomology calculations are provided for compact Lie groups. The spaces B(2, G) are describedin detail for transitively commutative groups. Stable homotopy decompositions of the B(q,G)are also provided, including a formula giving the cardinality of the set of commuting elementsin a finite group G in terms of the ranks of the homology groups for the associated filtration

112 Abstracts

quotients of B(2, G). Specific calculations for the first integral homology group of B(q,G) areshown to be delicate in case G is finite of odd order in the sense that resulting topologicalproperties (which are not yet fully understood) are equivalent to the Feit-Thompson theorem.


Stable decompositions and almost commuting elementsJose Manuel GomezUniversity of British [email protected]

Coauthors: Alejandro Adem and Fred Cohen

In this talk we show that the space of almost commuting elements in a Compact Lie group Gsplits after one suspension. Also we show how one can use almost commuting elements to studyin general the space of commuting elements for spaces of the form G/K, where K is a centralsubgroup.


Monoids of moduli spaces of manifoldsSoren GalatiusStanford University and Clay Math [email protected]

The d-dimensional cobordism category C has objects all closed (d− 1)-manifolds, and compactcobordisms as morphisms. The composition is gluing. There are also versions where all manifoldsare equipped with a tangential structure, specified by a fibration t : X → BO(d). In previouswork with Madsen, Tillmann and Weiss, we determined the homotopy type of the classifyingspace BC. One can ask if it is possible to replace the category C with a smaller category D,containing only certain manifolds, without changing the homotopy type of the classifying space.I will discuss recent joint work with O. Randal-Williams on this question. In dimension 2 ourmain theorem is that under a mild assumption on the tangential structure, there is a subcategoryD with this property, which is a homotopy commutative monoid, thought of as a category withone object.


Counting lattice points in the moduli space of curvesPaul NorburyUniversity of [email protected]

The moduli space of genus g curves with n labeled points has a cell decomposition which de-composes it into a collection of convex polytopes defined over the integers. It is natural to countintegral points in these polytopes and this leads to a polynomial in n variables. Its coefficientsinclude the Euler characteristic of the moduli space, and tautological intersection numbers on

Stringy Topology 113

the compactified moduli space. The polynomial is calculated via recursion relations as g and nvary and gives another proof of Witten’s conjecture for tautological intersection numbers on thecompactified moduli space. We will describe these results and their relationship to a broadercontext.


A string topology invariant of submanifolds and rational modelsVeronique GodinUniversity of [email protected]

Using string topology, I will define an A infinity algebra for any pairs (A,M) of a manifold Mand a submanifold A. I’ll mention some interesting computations.

I’ll also define a similar construction using rational models. I’ll talk about consequences to theoriginal invariant.

Friday 9:30 – 9:50, Mathews-B

Loop spaces and gamma generaRongmin LuUniversity of [email protected]

In recent years, the gamma function has appeared as a generating function for a multiplicativegenus (in the sense of Hirzebruch) in mirror symmetry. From some formal considerations onloop spaces, we show that two such genera can be constructed and relate our construction toHoffman’s study of multiple zeta values.


On completions of Verlinde ringsDan KneezelUniversity of [email protected]

Coauthors: Igor Kriz

Let G be a simple, simply-connected, compact Lie group, and let m be a non-negative inte-ger. The level m Verlinde ring of G, V (G,m)–a construction similar in spirit to an ordinaryrepresentation ring, related to certain representations of the loop group LG = Map(S1, G)–may be realized as a certain quotient of R(G), the representation ring of G. By a result ofFreed-Hopkins-Teleman and a twisted generalization of the Atiyah-Segal completion theorem,the (m + h(G))-twisted K-theory of LBG is isomorphic to the completion of V (G,m) at theaugmentation ideal of R(G) (as an R(G)-module), where h(G) is the dual Coxeter number of

G. Let V (G,m) denote this completion. After a brief review of relevant definitions, I will de-

114 Abstracts

scribe the additive structure of V (G,m). In particular, we will see that after further completingV (G,m) at a prime p, it splits as a finite sum of copies of the p-adic numbers.


T-duality, dimension reduction and loop group bundlesMathai VargheseUniversity of [email protected]

Coauthors: Peter Bouwknegt

I will begin by summarizing T-duality in type II string theory for spacetimes that are compacti-fied in one direction as principal circle bundles, with topologically nontrivial background H-flux.Then I will present a geometric approach to the dimension reduction account of T-duality forprincipal circle bundles endowed with a principal PU-bundle that represents the background H-flux. As a result, one is able to interpret T-duality as a duality of principal loop group bundles,exchanging the momentum and the winding number splittings.


Stabilization of Hurwitz spacesCraig WesterlandUniversity of [email protected]

Coauthors: Jordan Ellenberg and Akshay Venkatesh

We will describe the Hurwitz space of branched covers of the disc, and study its group completionunder “pants multiplication”. We will show that this stabilization is a double loop space, andgive some evidence that its rational stable homology is very small. If time permits, we will relatethis to some number-theoretic conjectures regarding the asymptotic growth of the number ofbranched covers of the line in finite characteristic.


Crepant Resolution Conjecture in all genera for type A surface singularitiesJian ZhouDepartment of Mathetmatical Sciences, Tsinghua [email protected]

We will talk about an all genera version of the Crepant Resolution Conjecture of Ruan andBryan-Graber for type A surface singularities.

Symplectic Geometry 115

Symplectic Geometry


On the homotopy cyclic A-infinity algebrasCheol-Hyun ChoSeoul National [email protected]

We introduce a homotopy notion of cyclic symmetric inner products of A-algebras and its poten-tial. We explain its relationship to the symplectic form on a non-commutative formal manifold.

Monday 11:00 – 11:45, Mathews-310

Multiple closed geodesics on spheresYiming LongChern Institute of Mathematics, Nankai University, Tianjin, [email protected]

A long standing conjecture in dynamical systems and differential geometry claims that thereexist always infinitely many geometrically distinct closed geodesics on every compact Riemannianmanifold. A similar conjecture for compact n-dimensional compact Finsler manifold claims thatthe number of distinct prime closed geodesics on such a manifold should be at least 2[n/2] or n.But when the dimension n is greater than 2, in general it is even not known whether there existalways at least two distinct closed geodesics on every such manifold so far in literatures. Herethe most difficult case and the current main research interests are on spheres. In this lecture, Ishall give a brief survey on the studies about existence and multiplicity of closed geodesics onspheres, including the new results proved recently by H. Duan and myself on the existences ofat least two distinct closed geodesics on every 3 or 4 dimensional Riemannian as well as Finslersphere, and sketch the ideas of the proofs.

Monday 12:00 – 12:45, Mathews-310

The exploded category, holomorphic curves and tropical geometryBrett ParkerUniversity of California, [email protected]

The exploded category is an extension of the category of smooth manifolds with a good holomor-phic curve theory. I will explain the relationship of the exploded category to tropical geometry,and how it is useful for the study of holomorphic curves in the symplectic setting.

116 Abstracts


The geometry of the moduli space of Brody curvesMasaki TsukamotoDepartment of Mathematics, Kyoto University, [email protected]

Brody curve is a kind of holomorphic map from the complex line to the complex projectivespace. Since the complex line is non-compact, the moduli space of Brody curves becomes infi-nite dimensional space. We study this infinite dimensional moduli space by using the ideas ofNevanlinna theory and Kodaira-Spencer theory. In particular, we give a result about Gromov’s“mean dimension” of the moduli space.


Rigidity of quasi-linear functions in symplectic geometryLeonid PolterovichTel Aviv [email protected]

Coauthors: Michael Entov

A real-valued function on a Lie algebra is called quasi-linear if it is linear on all abelian subal-gebras. We address the question of uniqueness of quasi-linear functions on some Lie algebrasarising in symplectic geometry. We discuss links to foundations of quantum mechanics (theGleason theorem) as well as to the group-theoretic notion of a quasi-morphism.


Floer thoery for Lagrangian submanifoldsKaoru OnoHokkaido [email protected]

I will present Floer thoery for Lagrangian submanifolds, which is a joint work with Kenji Fukaya,Yong-Geun Oh and Hiroshi Ohta. I would also like to include some of related topics.


Symplectic homology of stable Morse-Bott hypersurfacesLeonardo MacariniFederal University of Rio de [email protected]

Coauthors: Gabriel Paternain

We study the symplectic homology of compact subsets whose boundary is a stable Morse-Botthypersurface. Under some conditions on this hypersurface, we conclude the non-triviality of the

Symplectic Geometry 117

symplectic homology in certain degrees. Moreover, we address the question of the non-trivialityof the monotonicity maps.


Sutures and contact homologyKo HondaUniversity of Southern [email protected]

Coauthors: Vincent Colin, Paolo Ghiggini, and Michael Hutchings

We define a relative version of contact homology for contact manifolds with convex boundary,and prove basic properties of this relative contact homology. Similar considerations also hold forembedded contact homology.

118 Abstracts



Bhaskar Rao designs and the Hall-Paige conjectureDiana CombeUniversity of New South [email protected]

Coauthors: R. Julian R. Abel, Adrian M. Nelson, and William D. Palmer

A generalized Bhaskar Rao design over a group G is an array of group element entries and ‘zeros’satisfying particular row orthogonality conditions. There are well known necessary conditions onthe parameters for such a design to exist and it is conjectured that these conditions are sufficient.We outline evidence for this conjecture, including our latest work which has been energized bythe recent results concerning the Hall-Paige conjecture.

Monday 10:00 – 10:20, Mathews-307

Products of all elements in a loop, complete mappings, and the Hall-Paige conjectureKyle PulaUniversity of [email protected]

A loop is a set with a binary operation whose multiplication table is a normalized Latin square,i.e. a “non-associative group”. Motivated by the Hall-Paige conjecture and related results forfinite groups, we consider products of all elements in a finite loop and their relationship tocomplete mappings of the loop or, equivalently, transversals of its multiplication table.

Monday 11:00 – 11:20, Mathews-307

The combinatorics of involutions and twisted involutions in Weyl groupsRuth HaasSmith College, [email protected]

Coauthors: Aloysius G. Helminck

The set of involutions of a Weyl group can be generated starting from the identity giving a poset.This poset is similar to the weak order poset for the whole Weyl group, whose combinatorics isimportant in representation theory and has been studied extensively by many mathematicians.The combinatorics of the involution poset is also of fundamental significance in the study ofsymmetric spaces and their representations. This talk will focus on the combinatorics of thisposet.

Contributed Papers 1 119

Monday 11:30 – 11:50, Mathews-307

Computing in symmetric spacesAloysius HelminckNorth Carolina State [email protected]

In the last few decades much of the structure of Lie groups, Lie algebras, and their representationshas been implemented in several excellent computer algebra packages. The structure of reductivesymmetric spaces and more generally symmetric k-varieties in the case of arbitrary base fieldsrests on that of the underlying Lie group. Until a few years ago very few algorithms existedfor computations in these symmetric spaces, mostly due to the fact that their structure is morecomplicated then that of the underlying group. For example instead of just 1 root system thestudy of symmetric k-varieties involves 5 root systems.

In this talk we will give an introduction to symmetric k-varieties, discuss briefly the similaritiesbetween the structure of the real symmetric spaces and these symmetric k-varieties and explainfor which aspects of the structure there exists algorithms. One aspect of this structure willbe discussed in more detail, namely, the orbits of minimal parabolic k-subgroups acting on thesymmetric k-variety. These are of fundamental importance in the study of these symmetrick-varieties. For k = R a characterization of these orbits was given by Matsuki, for k = k bySpringer and for arbitrary fields by Helminck and Wang.

Monday 12:00 – 12:20, Mathews-307

Enhancing the nilpotent coneAnthony HendersonUniversity of [email protected]

Coauthors: Pramod N. Achar and Benjamin F. Jones

Many features of an algebraic group are controlled by the geometry of its nilpotent cone, whichin the case of GLn(C) is merely the variety N of n×n nilpotent matrices. The study of the orbitsof the group in its nilpotent cone leads to combinatorial data relating to the representations ofthe Weyl group, via the famous Springer correspondence. In the case of GLn(C), the basicmanifestation of this correspondence is the fact that conjugacy classes of nilpotent matrices andirreducible representations of the symmetric group are both parametrized by partitions of n.

Pramod Achar and I have shown that studying the orbits of GLn(C) in the enhanced nilpotentcone Cn×N leads to exotic combinatorial data of type B/C (previously defined by Shoji under thename of “limit symbols”). This is closely related to Syu Kato’s exotic Springer correspondencefor the symplectic group.

I will review this story and report on more recent joint work with Achar and Ben Jones, inwhich we consider the question of whether the orbit closures in the enhanced nilpotent cone arenormal varieties, as is known to be the case for the ordinary nilpotent cone N .

120 Abstracts

Monday 12:30 – 12:50, Mathews-307

String structures and characteristic classes for loop group bundlesRaymond VozzoUniversity of [email protected]

The string class of a loop group bundle P is the obstruction to lifting the structure group to thecentral extension of the loop group. The string class is related to the first Pontrjagyn class of acertain G-bundle associated to P . In this talk we will review the known results regarding thisclass and develop a notion of higher string classes for loop group bundles, which are associatedto characteristic classes of certain G-bundles.


Equisingular loci of simple singularities in positive characteristicHiroyuki ItoHiroshima University, [email protected]

Coauthors: Masayuki Hirokado and Natsuo Saito

In characteristic 0, since rational double points have “no moduli”, any one parameter deformationof a surface with a rational double point is locally a product of that surface with that singularityand the parameter space. But this is not the case in positive characteristic any more. Weshow that there exist simple singularities which have “moduli” in any positive characteristicand any positive dimension. We define equisingular loci of simple singularities, give a completeclassification of them and exhibit many pathological phenomena comes from this “moduli” ofsimple singularities as corollaries.


Factorization of linear ODEs using modular arithmeticIwan JensenDepartment of Mathematics and Statistics, University of [email protected]

We demonstrate how modular calculations can be used to factorize linear differential operators.The basic approach is to ‘follow’ the series pertinent to a specific local exponent at a givensingular point. Linear combinations of series with different local exponents can be studiedas well. Modular arithmetic of great help in this since, with the series and ODE being knownmodulo a prime, the coefficient in the linear combination can take only a finite number of integervalues, so that ‘guessing’ the correct combination can be done by exhaustive search.



Location of approximations in the context of Prasads Markoff-like chainRaman Kumar DasDepartment of Mathematics, St. Xavier’s College, Ranchi, Jharkhand, [email protected]

Coauthors: Manohar Lal

A Markoff-like Chain has been obtained by K. C. Prasad [Journal of Number Theory, Vol.20,No.2, pp 143 –148] for the set of irrational numbers whose simple continued fraction expansioncontain quotients greater than or equal to r eventually and r is greater than or equal to 2.Location of approximations of the first two theorems of this chain are well known as a consequenceof a result of Perron which is also alternatively proved by K. C. Prasad and M. Lari [Proceedingsof the American Math Soc., Vol.97, No.1, pp 19–20]. In this article we settle the question oflocation of approximations w.r.t. the third theorem of the Markoff-like chain.


Diophantine approximation of irrational numbers of a Perrons classK. C. PrasadDepartment of Mathematics, Ranchi University, [email protected]

Coauthors: Hrishikesh Mahto and B. B. Bhattacharya

In literature we come across a work of Perron where he conducts Markoff like examination of theset of irrational numbers whose simple continued fraction expansions contain quotients greaterthan or equal to 3 frequently. Here the chain stops at second theorem only because the secondcritical constant [65 + 9(3)1/2]/22 is necessitated by non-enumerably many irrational numbers.In this article we conduct a similar investigation over the set of irrational numbers whose simplecontinued fraction expansions contain quotients greater than or equal to 4 frequently. Hereagain we see that the chain stops at the second theorem . We have obtained the second criticalconstant which is a non-trivial finding.

122 Abstracts


Representational consistency: a paradox of simultaneous representation of numbersBurzin Bhavnagri

[email protected]

A paradox of simultaneous representation of numbers is presented. This is formulated as an al-gebraic notion of representational consistency. It yields some interesting results associated withprojections. Possible examples come from geometric analysis of symmetric spaces and Hopf al-gebras, like spin groups, Clifford algebras, complex projective spaces and Grassmannians. Thereare unsolved problems and applications to mathematical physics considering Oxygen metabolismand NMR/MRI.


Evolution of graphs in Carnot groups by horizontal Gauss curvatureErin MartinWestminster [email protected]

We will study the Gauss curvature flow of a graph in the sub-Riemannian setting of Carnotgroups. We extend to our context the level set method established by Chen, Giga and Goto andindependently by Evans and Spruck. By establishing a comparison principle, we will show theexistence and uniqueness of the flow.


Weighted Poincare inequalities on symmetric convex domainsSeng-Kee ChuaNational University of [email protected]

Coauthors: H. Y. Duan

Let α ≥ 0, β ∈ R, 1 ≤ p ≤ q < ∞ with

1− n

p+

n

q, 1− n + β

p+

n + α

q≥ 0.

Let Ω be a bounded convex domain in Rn that is symmetric with respect to its center. Defineρ(x) = inf|x− y| : y ∈ Ωc and ρα(E) =

∫E

ρ(x)αdx. Let f be a Lipschitz continuous functionon Ω and

fΩ,ρα =

∫

Ω

f(x)ρ(x)αdx/ρα(Ω).

We obtain the following weighted Poincare inequality:

‖f − fΩ,ρα‖Lqρα (Ω) ≤ Cη

βp−α

q |Ω|1/q−1/pdiam(Ω)1−βp+α

q ‖∇f‖Lp

ρβ (Ω)

where η is the eccentricity of Ω and C is a constant depending only on p, q, α β, and the dimensionn. Moreover, the exponent of η is sharp.



Statistical learning methods for uniform approximation bounds in multiresolutionspacesLouise A. RaphaelHoward University, Department of Mathematics, Washington, DC, [email protected]

Coauthors: Mark A. Kon

New constructive and non-constructive non-asymptotic uniform error bounds for approximatingfunctions in Sobolev spaces L2

s(Rd), s > 0, d ≥ 1, by finite compactly supported multiresolutionexpansions are proved using approximation theoretic bounds derived from statistical learningtheory.


Notes on classical and strict negative typeAnthony WestonCanisius College, New York, [email protected]

Coauthors: Ian Doust and Hanfeng Li

The metric space condition of p-negative type is classical in origin and may be traced back toArthur Cayley’s 1841 work on determinants and geometry. Determining a good positive lowerbound on the supremal p-negative type of a given finite metric space often turns out to be adifficult non-linear problem. The problem is important due to its connections with isometric,uniform and coarse embedding theories, as well as for having deep ties to fundamental issues intheoretical computer science such as the recently refuted Goemans-Linial conjecture.

A very closely related notion to classical p-negative type is strict p-negative type. A metricspace is said to have strict p-negative type whenever the corresponding non-trivial p-negativetype inequalities are all strict. In this talk a new and elementary procedure for determining alower bound on the supremal (strict) p-negative type of any given finite metric space will bedescribed. These lower bounds are rather good and sometimes even optimal. Moreover, thestrategy adopted leads to a notion of enhanced p-negative type and begins to codify a generaltheory of strict p-negative type for arbitrary metric spaces.

The theory developed in this way leads to non-trivial families of new examples such as: afinite isometric subspace (X, d) of a k-sphere Sk has maximal p-negative type = 1 if and onlyif X contains at least two pairs of antipodal points. Other examples – including an in-depthtreatment of finite metric trees (the actual stars of this talk) – will be interspersed throughoutthe presentation. These results reflect joint work of the speaker with Ian Doust (UNSW) andHanfeng Li (SUNY Buffalo).

124 Abstracts


On new notions of orthogonality via integral means in normed spacesEder KikiantyRGMIA, School of Engineering and Science, Victoria University, [email protected]

Coauthors: Sever S. Dragomir

In an inner product space, two vectors are orthogonal if their inner product vanishes. Notions oforthogonality in normed spaces have been defined via some equivalent propositions to the usualorthogonality; e.g. two vectors are orthogonal if and only if they satisfy Pythagorean law. Inthis talk, some new notions of orthogonality are introduced by utilizing the integral mean of thesquared norm (see, for example, Kikianty and Dragomir (2008); Kikianty, Dragomir, and Cerone(2008)) on a segment in a normed space. These notions of orthogonality are shown to be closelyrelated to the classical ones, namely Pythagorean orthogonality and Isosceles orthogonality (cf.James (1945)); and their generalization which was introduced by Carlsson (1962). The purposeof this talk is to discuss the main properties of these new orthogonalities and some useful conse-quences obtained by these properties. These consequences include characterizations of strictlyconvex spaces, as well as inner product spaces.

[1] S. O. Carlsson, Orthogonality in normed linear spaces, Ark. Mat. 4 (1962), 297–318.

[2] R. C. James, Orthogonality in normed linear spaces, Duke Math. J. 12 (1945), 291–302.

[3] E. Kikianty and S. S. Dragomir, Hermite-Hadamard’s inequality and the p − HH-normon the Cartesian product of two copies of a normed space, Math. Inequal. Appl., In Press.[http://www.mia-journal.com/files/mia/0-0/full/mia-1656-pre.pdf]

[4] E. Kikianty, S. S. Dragomir, and P. Cerone, Sharp inequalities of Ostrowski type for convexfunctions defined on linear spaces and applications, Comput. Math. Appl. 56 (2008), 2235–2246.

Friday 10:00 – 10:20, Mathews-308

Dixmier’s singular functional decomposition theorem on matrices over a C∗-algebra

Sing-Cheong OngCentral Michigan University, Mount Pleasant, [email protected]

Coauthors: Orapin Wootijiruttikal

A theorem of Dixmier states that for each bounded linear functional f on the algebra, B(H),of bounded linear operators on a separable Hilbert space, H, there exist, uniquely, a trace classoperator A

fand a bounded linear functional h on B(H) that vanishes on the compacts operators

such that f(B) = tr(AfB)+h(B) for every B ∈ B(H). Moreover if g denotes the trace functional

g(B) = tr(AfB), B ∈ B(H), then ‖f‖ = ‖g‖ + ‖h‖. This norm equality is a rare phenomenon

and is the most interesting part of the theorem. It says that the dual space of B(H) is the`1 direct sum of the dual space of the compact operators and the space consisting of the zerofunctional and the singular functionals h.


For a C∗-algebra A with state space s(A), endowed with the relative weak

∗topology on the

dual space A#, the space M of all matrices A =

[a

jk

]such that the map ϕ 7→ ϕ(A) =

[ϕ(a

jk)]

is continuous from s(A) to B(`2) is a Banach space with the norm ‖A‖ = sup

ϕ∈s(A)

‖ϕ(A)‖B(`

2)

. A

version of Dixmier’s theorem on M will be proved. Since the complex field C as a C∗-algebrahas only one state, the original Dixmier’s theorem follows as a corollary.

Friday 11:00 – 11:20, Mathews-308

Spectral shift functionsAnna SkripkaTexas A&M University, [email protected]

Coauthors: Ken Dykema

Lifshits-Krein’s spectral shift function (SSF) appeared first in the physical literature in 1952.Since then, a comprehensive mathematical theory for the SSF has been constructed and “pres-ence” of this object has been discovered in a number of abstract and concrete problems of thespectral perturbation theory. An assumption under which the original SSF is defined is that aperturbation be in the trace class. In 1984, L.S. Koplienko introduced a modified spectral shiftfunction which is applicable in the case of Hilbert-Schmidt perturbations. Koplienko’s SSF canbe recognized as the density of a measure representing the trace of the remainder of a Taylor-type approximation of the value of a function f at a perturbed self-adjoint operator H0 + V bythe zeroth and first order Frechet derivatives of H 7→ f(H) at an initial self-adjoint operator H0.We construct spectral shift functions for higher order Taylor remainders in both the traditionaland von Neumann algebra settings of the perturbation theory.

Friday 11:30 – 11:50, Mathews-308

Submanifold Lp estimates for eigenfunctions of a differential operatorMelissa TacyAustralian National [email protected]

Motivated by a desire to understand the high energy limit in Quantum Mechanics, we study Lp

norms of eigenfunction as λ → ∞. Concentration phenomena are of particular interest due tothe heuristic of a Quantum Mechanical probability density “converging” to a classical trajectory.We ask: Given a differential operator of the form

P = −∆ + V (x)

common in Quantum Mechanics what can we say about the Lp norms of the eigenfuntionsPu = λ2u? In this talk I will present estimates for the Lp norms of u restricted to a submanifoldY of a compact manifold M and discuss their relationship to the flow associated with the symbolof P .

126 Abstracts

Friday 12:00 – 12:20, Mathews-308

Stummel-Kato class and the generalized Morrey spaces with growth measuresIdha SihwaningrumGeneral Soedirman University and Bandung Institute of Technology, [email protected]

Coauthors: Wono Setya Budhi and Yudi Soeharyadi

We study a relation between Stummel-Kato class and the generalized Morrey spaces. Ourassumption involves the growth measures and the doubling condition of functions under consid-eration.



Monday 10:00 – 10:20, Mathews-308

Interacting self avoiding trails on a triangular latticeJason DoukasUniversity of [email protected]

Coauthors: Aleks Owczarek

Using a fast non-Markovian Monte Carlo simulation known as flatPERM (a flat histogramversion of the Pruned and Enriched Rosenbluth Method) we present numerical simulations ofthe critical phenomena of interacting self-avoiding trails on a triangular lattice.

Monday 11:00 – 11:20, Mathews-308

Worm algorithmsTim GaroniUniversity of [email protected]

Coauthors: Youjin Deng, Alan Sokal, and Wei Zhang

We will discuss Markov-chain Monte Carlo algorithms of “worm” type for studying a number ofquestions related to Ising models in statistical mechanics.

Monday 11:30 – 11:50, Mathews-308

Discrete Fourier transform for Ad lattice and its applications to Gaussian cubatureand interpolation in high dimensionHuiyuan LiInstitute of Software, Chinese Academy of Sciences, Beijing, [email protected]

Coauthors: Jiachang Sun and Yuan Xu

In this talk, a discrete Fourier transform (DFT) associated with lattice tiling is first devel-oped, which leads naturally to Gaussian quadrature formula for trigonometric polynomials andtrigonometric interpolation based on the equally spaced points. All three quantities, discreteFourier transform, quadrature and interpolation, are important tools in numerous applicationsand form an integrated part of the discrete Fourier analysis.

We then apply the result to the fundamental region of the homogeneous root lattice Ad in Rd,providing explicit formulas and detailed analysis. By restricting to functions that are invariantunder the group Ad, the results can be transformed to results on a simplex that makes up thefundamental domain, which define analogues of cosine and sine functions on the simplex andestablish a Fourier analysis on trigonometric functions on the simplex. In particular, a Lagrangeinterpolation on the simplex is shown to satisfy an explicit compact formula and the Lebesgueconstant of the interpolation is shown to be in the order of (log n)d.

128 Abstracts

We finally define generalized Chebyshev polynomials of the first and the second kind from thosegeneralized cosine and sine functions, respectively, and develop the discrete analysis of thesealgebraic polynomials. These come down to study common zeros of the generalized Chebyshevpolynomials and Gaussian cubature in general high dimension, a topic that does not seem tohave been studied systematically before.

Monday 12:00 – 12:20, Mathews-308

A Barzilai-Borwein algorithm for signal reconstructionRachael TappendenUniversity of [email protected]

Coauthors: Ian Coope, Peter Renaud, and Robert Broughton

Problems in signal processing and medical imaging often lead to calculating sparse solutionsto under-determined linear systems. These types of problems can often be reformulated asunconstrained convex optimisation problems where the objective function is a quadratic lossterm plus an l1-regularisation term. Here we present a Projected Barzilai-Borwein type algorithmwhich aims to determine a sparse solution to this convex optimisation problem. Numerical resultsare presented and compared with other currently used algorithms.

Monday 12:30 – 12:50, Mathews-308

Experiments with G-symplectic methodsYousaf HabibDepartment of Mathematics, University of Auckland, New [email protected]

The advantage of using symplectic methods for Hamiltonian and other problems preservingquadratic invariants is well understood and accepted. The use of G-symplectic methods is,however, not so well recognised. Such methods suffer from parasitic solution growth for manypractical problems. Some experiments with G-symplectic General Linear methods have beencarried out and the dependence of solution behaviour on the growth rate for the parasitic com-ponent is highlighted. If the growth rate is exactly zero, the methods seem to have some potentialas practical integrators for Hamiltonian and other problems.


On the interpretation of spin 1/2 Dirac particles in Clifford algebrasPeter RenaudUniversity of Canterbury, Christchurch, New [email protected]

A study of the Klein-Gordon, Maxwell and Proca equations shows not just a striking similaritybetween them but also provides strong motivation for looking at the Dirac equation from thesame standpoint. This point of view is very much a geometric one and so, the equations and


their consequences (such as conservation laws), find a natural setting in the Clifford algebra ofspace-time. The various spin representations of the Lorentz group are perhaps best described interms of this algebra and they illustrate very well not only why these equations are so similar,but where they might be expected to differ.


Models of quadratic algebras generated by second order superintegrable systemsSarah PostUniversity of [email protected]

Superintegrable systems are classical or quantum Hamiltonian systems with a maximal amount ofsymmetry. Often the symmetry is not evident in group structures (i.e., Lie algebras of first orderdifferential symmetry operators) but instead in the form of higher order differential operatorscommuting with the Hamiltonian. As in the case where there is group symmetry, we canuse representations of the algebra of the differential symmetry operators to obtain informationabout the system. In this talk, I present some models of (maximally) superintegrable systemsgenerated by second order differential operators, for quantum systems. In this case the algebrasof symmetry operators close under commutation to form quadratic algebras. I will describemodels of these algebras including both differential and difference operators. These modelscan be used to find energy values of the Hamiltonian as well as the eigenvalues of the operatorswhich correspond to separation of variables. Additionally, the models are of independent interestbecause the function space realizations often correspond to special functions and their identities.


Polyhedral manifolds with lower combinatorial curvature boundsWen-Haw ChenDepartment of Mathematics, Tunghai University, Taichung, [email protected]

In this work, we investigate compact polyhedral manifolds with lower combinatorial curvaturebounds. The notion of combinatorial Ricci curvature is introduced by R. Forman. This notionis purely combinatorial since it depends only on the relationships between the cell and its neigh-bors. Interestingly, some classical theorems in Riemannian geometry have their analogs in thiscombinatorial setting. We will give an obstruction to a compact combinatorial manifold withpositively combinatorial curvature and compare it with that in the Riemannian setting.

130 Abstracts


Pullbacks of complex analytic vector fields: Newton vector fieldsAlvaro Alvarez-ParrillaUniversidad Autonoma de Baja California, [email protected]

Coauthors: Jesus Mucino, Selene Solorza, and Carlos Yee

Some recent results concerning the study of complex analytic vector fields as pullbacks arepresented. In particular we show that complex analytic vector fields on Riemann surfaces arein fact Newton vector fields, and then proceed to show that this provides certain advantagesincluding an efficient visualization scheme.


Calabi-Yau 3-folds arising from fiber products of quasi-elliptic surfacesNatsuo SaitoHiroshima City [email protected]

Coauthors: Masayuki Hirokado and Hiroyuki Ito

We construct some examples of supersingular Calabi-Yau 3-folds in characteristic 2 and 3. Incharacteristic 0, C. Schoen constructed Calabi-Yau 3-folds as fiber products of two rationalelliptic surfaces over the projective line. We modify his method to consider fiber products of tworational quasi-elliptic surfaces, which exist only in characteristic 2 or 3. Such fiber products areno longer nonsingular, and their crepant resolutions give new examples. Each Calabi-Yau 3-foldwe obtain admits a fibration whose general fiber is a non-normal rational surface, and also afibration whose general fiber is a supersingular K3 surface. Furthermore, we find some of themdo not lift to characteristic 0.


Harmonic differential charactersRichard GreenUniversity of [email protected]

Coauthors: Varghese Mathai

Differential characters are a refinement of ordinary cohomology with real coefficients, simultane-ously incorporating both differential forms and torsion, that have proved useful for differentialgeometric problems.

In this talk I will discuss recent work with V. Mathai, where we introduce harmonic differentialcharacters on a compact Riemannian manifold. These form a finite dimensional subgroup ofthe usual differential characters. I will explain how they relate to the full differential charactergroup, and how they mimic many of its fundamental properties, including Pontrjagin-Poincareduality.



On a generic class of 3d Hamiltonian systemsRazvan Micu TudoranThe West University of Timisoara, [email protected]

Coauthors: Ana Ramona Tudoran

The aim of this talk is to introduce and study from the Poisson geometry and dynamics points ofview a generic class of three dimensional Hamiltonian dynamical systems, class that unifies theHamiltonian realizations of the most important three dimensional concrete mechanical systems.

The main problems considered are the stability analysis of the equilibrium states and the exis-tence of periodic solutions of the Hamiltonian systems from this generic class.

As a conclusion we get that the dynamical conditions that imply stability of equilibria or exis-tence of periodic orbits bifurcating from some families of equilibria, come together with an un-expected natural agreement between the canonical Euclidian geometry and the new introducedPoisson geometry of the ambient three dimensional model space of the Hamiltonian systems.


Modified Bellissard algebraSemail Ulgen YildirimNorthwestern [email protected]

Coauthors: Shmuel Weinberger

J. Bellissard defined the notion of a hull (Ω,Rd, T ) to model aperiodic solids. The hull (Ω,Rd, T )is a dynamical system with group Rd acting by homeomorphisms on a compact metrizable spaceΩ. In the case of a perfect crystal, with translation group G, the hull Ω = Rd/G is homeomorphicto Td. With any dynamical system, there is a canonical C∗-algebra, namely the crossed productC∗-algebra A = C(Ω)oRd We will modify this algebra by adding rotational action, and call itModified Bellissard Algebra. This algebra detecs more symmetry than Bellissard algebra. Wepresent some K-theory computations of this algebra.


Weak mixing and product recurrencePiotr OprochaDepartamento de Matematicas, Universidad de Murcia, [email protected]

A recurrent point is: product recurrent if its product with arbitrary recurrent point is recur-rent (in the product system); weakly product recurrent if its product with arbitrary uniformlyrecurrent point is recurrent.

In 2008, Haddad and Ott proved in [Recurrence in pairs. Ergodic Theory Dynam. Systems.28 (2008) 1135-1143] that there are weakly product recurrent points which are not uniformly

132 Abstracts

recurrent. That way they solved a problem whether product recurrence and weak productrecurrence are equivalent notions, raised by Auslander and Furstenberg in 1994.

In this talk we will describe a class of topologically weakly mixing maps (containing the class oftransitive maps considered by Haddad and Ott) with residual subset of weakly product recurrentpoints which are not product recurrent. We also comment on a construction of a weakly mixingminimal map without weakly product recurrent points.


Bifurcations from quotient coupled cell systemsMaria LeiteDepartment of Mathematics, University of [email protected]

Coauthors: M. A. D. Aguiar, A. P. S. Dias, and M. Golubitsky

A coupled cell system can be seen as a set of individual dynamical systems (the cells) withinteractions between them (the coupling). Therefore, every coupled cell system is a network,which are widely used to model dynamical behaviour of multicomponent systems. We discussthat every network, when restrict to a flow invariant subspace defined by equality of certaincell coordinates, is associated with a quotient network. Also, we describe a general method toconstruct coupled cell networks admitting a given (quotient) network. We further investigatehow local codimension-one synchrony-breaking bifurcation from a synchronous equilibrium inthe quotient network lift to local bifurcations in the full networks.


Numerical computations of atmospheric coherent sets in the Southern HemisphereNaratip SantitissadeekornSchool of Mathematics and Statistics, University of New South [email protected]

Coauthors: Gary Froyland and Simon Lloyd

It is well-known that the stratospheric polar vortex in the Southern Hemisphere often persistsfor a long period of time and is strongest during the Southern Hemisphere winter and earlyspring. The vortex boundary can be considered as a nearly zonal jet, which behaves as a barrierto meridional transport of passive tracers.

Our aim is to provide numerical evidence based on a transfer operator method to demonstratethat the coherent (or persistent) region, approximated by the push forwarded second largestsingular vector of the transfer operator, is nearly coincident with the core of the polar vortex.



Conditionally invariant measures and sets with low escape ratesOgnjen StancevicSchool of Mathematics and Statistics, University of New South [email protected]

Consider a dynamical system T : X → X, and let H ⊂ X be a “hole” such that almost everypoint eventually enters the hole. Such systems were first studied by Yorke and Pianigiani in1979. An important quantity associated with these open systems is the “escape rate”: howfast, asymptotically, do points enter the hole. In some cases, escape rates can be related toconditionally invariant measures as well as to eigenvalues of the Perron-Frobenius operator. Inthis talk I will give a brief review of escape rates and possible applications in detection of “almostinvariant” sets.


Non-existence of non-constant positive steady states of two Holling type-II predator-prey systems: strong interaction caseRui PengSchool of Science and Technology, Unversity of New [email protected]

Coauthors: Junping Shi

In this talk, we are concerned with two reaction-diffusion predator-prey models with Hollingtype-II functional response and prove the non-existence of non-constant positive steady statesolutions when the interaction between the predator and the prey is strong. The result impliesthat the global bifurcating branches of steady state solutions are bounded loops, and also stronglysuggests that temporal oscillatory patterns dominate the dynamics in the strong predator-preyinteraction. This provides another important step towards a complete understanding of thedynamics of the two models.


Traveling waves for a thin liquid film with surfactant on an inclined planeVahagn ManukianDepartment of Mathematics, University of [email protected]

Coauthors: Stephen Schecter

We show the existence of traveling wave solutions for a lubrication model of surfactant-drivenflow of a thin liquid film down an inclined plane in various parameter regimes via geometricsingular perturbation theory.

134 Abstracts


Fractal dimensions of attractors for fast rotating Lagrangian-averaged Navier-StokesAlpha-regularized equationsBong-Sik KimAmerican University of Ras Al [email protected]

Three-dimensional rotating Lagrangian-averaged Navier-Stokes Alpha-regularized system is con-sidered. It will be rigorously verified that the solution attractors of the given system have finitefractal dimensions and the number of degrees of freedom for turbulent fast rotating fluids are fi-nite. It will reveal that the asymptotic dynamics of the given system can be obtained from thoseof the reduced two-dimensional, three-component system rather than the full three-dimensionalsystem. The results will be compared to those of the exact rotating Navier-Stokes system.


Nonlinear convective stability of traveling fronts near Turing and Hopf instabilitiesAnna R. GhazaryanUniversity of [email protected]

Coauthors: Margaret Beck and Bjorn Sandstede

We analyze the instability of a front in a reaction-diffusion system when the instability is causedby the rest state behind the front undergoing a supercritical Turing or Hopf bifurcation. Onthe linear level there exists an exponentially weighted norm that stabilizes the front, i.e., theinstability of the front is convective. It is very restrictive to assume that the nonlinearity iswell behaved in that particular norm. For example, this is not true for polynomial nonlinear-ities. Therefore the nonlinear stability cannot be simply inferred from the linear stability inthe weighted norm. We show that the amplitude of any emerging pattern can be controlled interms of the bifurcation parameter, and then, using the interplay of norms with and withoutweight, we prove that, in the coordinate frame that moves together with the front, the patternis pushed away from the interface of the front. The result implies the convective character ofthe instability on the nonlinear level.



Monday 11:00 – 11:20, Mathews-104

A second-order positivity preserving central-upwind scheme for chemotaxis andhaptotaxis modelsAlina ChertockNorth Carolina State [email protected]

Coauthors: Alexander Kurganov

In this talk, I will present a new finite-volume method for a class of chemotaxis models andfor a closely related haptotaxis model. In its simplest form, the chemotaxis model is describedby a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupledwith a reaction-diffusion equation for the chemoattractant concentration. A common propertyof all existing chemotaxis systems is their ability to model a concentration phenomenon thatmathematically results in solutions rapidly growing in small neighborhoods of concentrationpoints/curves. The solutions may blow up or may exhibit a very singular, spiky behavior. Ineither case, capturing such singular solutions numerically is a challenging problem.

The first step in the derivation of the new method is made by adding an equation for the chemoat-tractant concentration gradient to the original system. We then show that the convective part ofthe resulting system is typically of a mixed hyperbolic-elliptic type and therefore straightforwardnumerical methods for the studied system may be unstable. We design a new method, whichis based on the application of the second-order central-upwind scheme, originally developed forhyperbolic systems of conservation laws, to the extended system of PDEs. We prove that theproposed central-upwind scheme is positivity preserving, which is a very important stabilityproperty of the method.

We apply the new method to a number of two-dimensional problems including the most com-monly used Keller-Segel chemotaxis model and its modern extensions as well as to a haptotaxissystem modeling tumor invasion into surrounding healthy tissue. Our numerical results demon-strate high accuracy, stability, and robustness of the proposed scheme.

Monday 11:30 – 11:50, Mathews-104

New models of chemotaxis: analysis and numericsAlexander KurganovTulane University, Mathematics [email protected]

Coauthors: Alina Chertock and Xuefeng Wang

Patlak-Keller-Segel (PKS) system is a classical PDE model of the chemotaxis. The systemadmits solutions that develop delta-type singularities within a finite time. Even though suchblowing up solutions model a concentration phenomenon, they are not realistic since biologicalcells do not converge to one point (while the cell density grows sharply, it must remain boundedat all times).

I will present a new chemotaxis model, which can be viewed as a regularized PKS system. The

136 Abstracts

proposed regularization is based on a basic physical principle: boundedness of the chemotacticconvective flux, which should depend on the gradient of the chemoattractant concentration in anonlinear way. Solutions of the new system may develop spiky structures that model the con-centration phenomenon. However, both cell density and chemotattractant concentration remainbounded as supported by both our analytical results and extensive numerical experiments.

Monday 12:00 – 12:20, Mathews-104

Optimizing hybrid power system with discrete filled function methodSiew Fang WoonCurtin University of Technology, Perth, [email protected]

Coauthors: Volker Rehbock and Ryan Loxton

Renewable energy resources are increasingly vital due to global environmental concerns. Inremote area, renewable energy is incorporated into systems along with generators and energystorage devices for electrification purposes. Such systems are known as hybrid power systems.This paper considers a PV-diesel-battery hybrid power system and introduces a heuristic ap-proach to optimize the operating schedule of the system. The model is first formulated as amixed-discrete optimization problem. Then, a new numerical algorithm, which uses a discretefilled function method in conjunction with computational optimal control techniques, is devel-oped for solving this problem. Promising results suggest the proposed algorithm is efficient indetermining a near globally optimal solution.


Exact models for k-connected minimum energy networksChristina BurtMASCOS, University of [email protected]

Coauthors: Yao-ban Chan

We consider the minimum energy problem for a mobile ad hoc network, where any node in thenetwork may communicate with any other node via intermediate nodes. To provide quality ofservice, the network must be connected, even if one or more of the nodes drop out. This leadsto the notion of k-connectedness. The minimum energy problem aims to optimise the totalenergy that all nodes spend for transmission. Previous work in the literature include mixed-integer programming formulations for a connected network. We extend these models for whenthe network is k-connected and investigate ways to improve the solvability of the models forlarge networks.



Modeling semiflexible polymer adsorptionGerasim IlievMASCOS, University of [email protected]

Coauthors: S. G. Whittington and E. Orlandini

We use several models of directed walks in two- and three-dimensions to study the phenomenonof polymer adsorption at an impenetrable surface. We investigate the nature and the order ofthe adsorption phase transition as we vary the persistence length within our polymer models.


Dynamical, evolutionary and molecular origins of redfield ratio N : P = 16Irakli LoladzeMathematics Department, University of Nebraska - Lincoln, Lincoln, [email protected]

Coauthors: Simon Levin

Among the biospheres largest patterns is atomic nitrogen:phosphorus ratio (N : P ) = 16 foundthroughout deep ocean; though N : P of individual phytoplankton species ranges from 6 to60, the average N : P of plankton is also 16. Discovered empirically by Redfield over 70years ago, this pattern is crucial to carbon sequestration, climate change and biogeochemicalcycling models. However, the rationale behind N : P = 16 is not known. Here, we show thatN : P = 16 is the result of biogeochemical homeostasis that originates on a molecular scale whileevolutionary forcing and feedback of upwelling amplify the pattern to the global scale. First,we show that when nutrients are replete, Redfield ratio stems from five fundamental molecularvalues, including N in amino acids, N and P in nucleotides. Next, we construct a dynamicalmodel that considers RNA:protein ratio as an evolutionary trait; it shows that when nutrientsare limiting, an evolutionary stable strategy is for N : P of plankton to deviate toward N : P ofthe inflow. Finally, we show that upwelling of nutrients in our model provides a feedback thatresults in the convergence of N : P of plankton to Redfield ratio over geological times.


Splitting rigid graphsWilson OngUniversity of Western [email protected]

Coauthors: Brad Yu and Brian D. O. Anderson

Consider a network of sensors able to move in 2-dimensional space. We may aim to impose dis-tance constraints between certain sensors to ensure every pair of sensors maintain their distancefrom one another under any continuous movement. This property is known as rigidity. Rigiditymay be required to ensure that no sensor will move out of range of any other sensor during move-ment. However, there arise situations which require us to decompose a rigid formation into twoor more rigid sub-formations, perhaps to avoid an obstacle, to pursue different missions, or to

138 Abstracts

allow merging of part of the original formation with another formation. The paper demonstratesthat it is not always possible to decompose a rigid formation into rigid sub-formations withoutadding new distance constraints. The paper also discusses how to decompose a formation intoconnected but not necessarily rigid sub-formations (to which edges could be added to ensurerigidity of the sub-formations). We show it is always possible to decompose a rigid formationinto two connected sub-formations of arbitrary orders without the addition of any new distanceconstraints, and we present an algorithm to do this. Although the sub-formations may not berigid, the connectedness property ensures that no agent or group of agents can deviate too faraway from the rest of the agents in the same connected component, and any agent can commu-nicate with any other agent (perhaps via intermediate agents) in the same sub-formation. Thiswill allow rigidity to be recovered within each connected sub-formation by applying existingalgorithms.


Infiltration in the nonlinear limitDimetre TriadisAMSI/MASCOS, University of [email protected]

Coauthors: Philip Broadbridge

Theoretical infiltration behaviour for a delta-function diffusivity soil has been a source of con-fusion and debate within hydrological literature. A family of cumulative infiltration functionshave recently been identified as a limiting case of a realistic analytical model of infiltration fromsupply at constant concentration. The exact analysis has provided new insights into historicalresults.


Diffraction from open and closed bodies of revolution: analytical regularisationPaul D. SmithMacquarie [email protected]

Coauthors: S. B. Panin, E. D. Vinogradova, Yu. A. Tuchkin and S. S. Vinogradov

Scattering and diffraction of acoustic or electromagnetic waves is of widespread interest, under-pinning many modern technologies in imaging and communications. A variety of analytical andnumerical methods have been developed to predict the scattering by obstacles. We examine amathematically rigorous and numerically efficient approach, based on analytical regularization,for solving the scalar wave diffraction problem with a Dirichlet boundary condition imposedon an arbitrarily shaped closed body of revolution. The problem may be posed as an integralequation over the surface. We determine the singular features of its kernel, and transform theinitial equation so that its kernel can be decomposed into a singular canonical part and a reg-ular remainder. After an analytical transformation, the problem is converted to an equivalentinfinite system of linear algebraic equations of the second kind. Such a system can be effectivelysolved with any prescribed accuracy by standard numerical methods. The smoothness of theremainder implies that the method is robust and efficient for calculating the matrix elements.


The approach extends to open bodies of revolution (closed bodies in which an axi-symmetricaperture has been opened); the conversion to second kind format is effected by the use of Abelintegral representations of a broad class of hypergeometric functions. Numerical investigationsof structures, such as the prolate spheroid and other non-canonical bodies of revolution, demon-strate that the condition numbers of the resulting matrix systems are well controlled, so thatreliable and accurate results can be obtained.


Modelling and estimating the forward price curve in the energy marketBoda KangSchool of Finance and Economics, University of Technology, [email protected]

Coauthors: Carl Chiarella and Les Clewlow

The stochastic or random nature of commodity prices plays a central role in the models forvaluing financial contingent claims on commodities. Forward contracts are widely traded onmany exchanges with prices easily observed – often the nearest maturity forward price is usedas a proxy for the spot price with longer dated contracts used to imply the convenience yield.In this paper, by enhancing a multi factor framework which is consistent not only with themarket observable forward price curve but also the volatilities and correlations of forward prices,we propose a two factor stochastic volatility model for the evolution of the gas forward curve.One volatility function primarily affects the short-end of the futures curve, and decays away astime to maturity increases; while another volatility function has a similar decaying term, butalso contains a seasonality adjustment term that persists for long futures maturities. We allowthe parameters (including the spot volatilities and the attenuation parameters) of the volatilityfunctions to take different values in different states of the world. The dynamics of the “states ofthe world”, for example an “on-peak” or “off-peak” time for gas, or a “good” or “bad” economicenvironment are represented by a Markov Chain. The evolution of the two volatility functionsdepend on the transition of the Markov Chain. Based on the structure of our volatility functionforms, we propose and implement the Markov Chain Monte Carlo (MCMC) method to estimatethe parameters of the above forward curve model. Applications to simulated data indicate thatthe proposed algorithm is able to accommodate more general features, e.g. regime switching,seasonality, certain functional form of forward volatility functions. Applications to the marketgas forward data shows that the MCMC approach provides stable estimates.


A general theory of Backward Stochastic Difference EquationsSamuel CohenUniversity of [email protected]

Coauthors: Robert Elliott

By analogy with the theory of Backward Stochastic Differential Equations, we define BackwardStochastic Difference Equations on spaces related to discrete time, finite state processes. Thispaper considers these processes as constructions in their own right, not as approximations to the

140 Abstracts

continuous case. We establish the existence and uniqueness of solutions under weaker assump-tions than are needed in the continuous time setting, and also establish a comparison theoremfor these solutions. The conditions of this theorem are shown to approximate those required inthe continuous time setting. We also explore the relationship between the driver and the set ofsolutions; in particular, we determine under what conditions the driver is uniquely determinedby the solution. Applications to the theory of nonlinear expectations are explored, including arepresentation result.


Survival probability in surplus processHasih PratiwiGadjah Mada [email protected]

Coauthors: Subanar, Danardono and J. A. M. van der Weide,

Ruin theory is concerned with the level of an insurer’s surplus for a portfolio or insurancepolicies. We simplify a real life insurance operation by assuming that the insurer starts withsome nonnegative amount of money, collects premiums, and pays claims as they occur. For themodel discussed in this paper, if the insurer’s surplus falls at zero or below, we say that ruinoccurs.

The aim of this work is to derive a survival probability in surplus process. We start by describinga classical risk process, a compound Poisson process, and a ruin probability. We then considerthe adjustment coefficient and prove Lundberg’s inequality to derive a survival probability.


College mathematical readiness of the senior high school students in the publicschools of District I in Davao CityMelanie Joyno OrigCollege of Arts and Sciences, University of Mindanao, Davao City, Philippinesmelanie [email protected]

Coauthors: none

The purpose of this study is to determine the level of mathematical proficiency of the seniorhigh schools students enrolled in the public schools of District I in Davao City. It also soughtto determine the level of readiness of the students for college mathematics. The students weregiven the mathematics achievement test where the contents include Number Sense, Geometry,Probability and Statistics, Algebra and Functions. The findings of the study were used to comeup with a bridging program sponsored by the University of Mindanao as part of its communityextension to help the incoming freshmen college students prepare for college mathematics.



Complex networks as a tool to study chaotic dynamical systemsMichael SmallHong Kong Polytechnic [email protected]

Coauthors: Xiaoke Xu and Jie Zhang

Since the first experimental observation of chaotic dynamics, the field of nonlinear time seriesanalysis has developed a wide range of tools and techniques to analyse chaotic time series in vari-ous domains. These methods chiefly rely on either statistical distributions and hypothesis testingor on estimation of dynamical invariants of the underlying deterministic attractor. We describea new method for analysing chaotic time series data: through complex network transformations,the time series data is represented as a complex network. We find that the topological propertiesof that complex network reflect the underlying dynamics of the deterministic system generatingthe observed data. In general we observe several different families of networks corresponding tofamilies of nonlinear dynamics. Within each family we see fine variation in the structure of thecomplex network which is intimately related to the distribution of unstable periodic orbits in theattractor of the deterministic system. In addition to providing new tools for analysing chaotictime series, we will show that the complex networks can also be used to generate additionalsurrogate time series data.


Establishment and translation of a rigid formation within a collision-avoidanceschemeAvinesh PrasadUniversity of the South Pacificprasad [email protected]

Coauthors: Bibhya Sharma and Jito Vanualailai

Establishment and translation of multi-agents fixed in rigid formation is a biologically inspiredproblem from nature that is gathering huge momentum and attracting attention of researchersall over. This paper presents a new formation control planner for a swarm of 2-link mobilemanipulators fixed in a prescribed formation in a priori known environment. To ensure arigid formation along a collision-free flight-path, data on moving ghost targets and heading ofthe individual manipulators are captured in the control planner. The final orientation of theformation is achieved by deploying the minimum distance technique (MDT). The control lawsare extracted from the Lyapunov-based control scheme that, in parallel, guarantees stability ofthe kinodynamic system governing the swarm. The effectiveness of the control scheme and itscontrollers are demonstrated by simulating interesting traffic-like situations.

142 Abstracts


Tunnel passing maneuvers of multi-agents in formationBibhya SharmaUniversity of the South Pacificsharma [email protected]

Coauthors: Jito Vanualaiali and Utesh Chand

The research essays the design of a motion planner that will simultaneously manage collisionand obstacle avoidances of teams of multi-agents fixed in prescribed formations and ensuredesirable tunnel passing maneuvers. This centralized planner, derived from the Lyapunov-basedcontrol scheme (APF method) works within a new leader-follower framework to generate eithersplit/rejoin maneuvers or expansion/contraction of the teams, as feasible solutions to the tunnelpassing problem. In either scenario, the prescribed formation will be re-established after thetunnel has been passed. Moreover, avoidance of the walls of the tunnel will be accomplished viaa new minimum distance technique. All-in-all, the research highlights a fairly broad conceptionthat reflects at least a certain degree of autonomy of swarms in nature. It is also a significantcontribution to the intelligent vehicle systems discipline.


Flocking in constrained environment: lane merging maneuversUtesh ChandUniversity of the South Pacificchand [email protected]

Coauthors: Bibhya Sharma and Jito Vanualailai

Flocking, arguably one of the most valuable concepts harnessed from nature, has in recent timesestablished a growing stature within the intelligent vehicle systems. In this paper, the authorsdesign a centralized motion planner for a convoy of nonholonomic car-like vehicles accomplishingdesired maneuvers.

Specifically, the new control laws extracted from the Lyapunov-based control scheme anchorcollision-free maneuvers for the lane merging problem. The control scheme, essentially a newartificial potential field method, works within a new leader-follower framework to accomplishthe required formation and reformation of the flock. The effectiveness of the proposed controllaws are demonstrated through interesting simulations mimicking real-world traffic situations.


Oscillations and multistability in (bio)chemical reaction networksMaya MinchevaNorthern Illinois [email protected]

Understanding the dynamics of interactions in complex biochemical networks is an importantproblem in modern biology. Mathematical models of biochemical reaction networks give rise tolarge nonlinear dynamical systems with many unknown kinetic parameters, making the models


challenging for computational analysis. However, important properties, such as the ability of abiochemical network to oscillate can be determined by the network’s structure. The structureof the bipartite graph associated with a biochemical reaction network can be used to predictmultistability and oscillations without knowing the kinetic parameters of the biochemical reac-tion. We will discuss the connection between the bipartite graph of a reaction network and thebipartite graph associated with the corresponding dynamical system model.

List of Delegates

146 List of Delegates

Alejandro [email protected]

Myles AllenDepartment of Physics, University of [email protected]

Alvaro Alvarez ParrillaUniversidad Autonoma de Baja [email protected]

Bob AnderssenCSIRO Maths and Info [email protected]

Federico ArdilaSan Francisco State [email protected]

Helen ArmstongUniversity of New South [email protected]

Giles AuchmutyUniversity of [email protected]

Matt BallardUniversity of [email protected]

Gang BaoMichigan State [email protected]

Murray BatchelorAustralian National [email protected]

Teresa BatesUniversity of New South [email protected]

Rick BeatsonUniversity of [email protected]

Steve BennounUniversity of British [email protected]

Burzin BhavnagriUnaffiliated member [email protected]

Alex BoikoUniversity of New South [email protected]

Jon BorweinUniversity of [email protected]

Chris BoseUniversity of [email protected]

Peter BouwknegtAustralian National [email protected]

Hugo Bowne-AndersonUniversity of New South [email protected]

Phil BroadbridgeLa Trobe [email protected]


Pete BrooksbankBucknell [email protected]

Bob BroughtonUniversity of [email protected]

Nils BruinSimon Fraser [email protected]

Hermann BrunnerMemorial University of [email protected]

Paul [email protected]

Keith BurnsNorthwestern [email protected]

Christina BurtMASCOS, University of [email protected]

John ButcherThe University of [email protected]

Jaeyoung [email protected]

Jim ByrnesPrometheus [email protected]

Charles CampCalifornia Polytechnic State [email protected]

John CannonMagma Group, University of [email protected]

Joshua CapelUniversity of New South [email protected]

Emma CarberryUniversity of [email protected]

Kenneth ChanUniversity of New South [email protected]

O-Yeat ChanDalhousie [email protected]

Yao-ban ChanUniversity of [email protected]

Utesh ChandUniversity of the South [email protected]

Chih-Chung ChangNational Taiwan [email protected]

Albert [email protected]

Bohui ChenSichuan [email protected]


Jingyi ChenUniversity of British [email protected]

Shuxing ChenFudan [email protected]

Wen-Haw ChenTunghai [email protected]

William ChenMacquarie [email protected]

Alina ChertockNorth Carolina State [email protected]

Hung-Jen Chiang-HsiehNational Chung Cheng [email protected]

Carl ChiarellaSchool of Finance and Economics,The University of Technology, [email protected]

Cheol-Hyun ChoSeoul National [email protected]

Sum ChowBrigham Young [email protected]

Seng-Kee ChuaNational University of [email protected]

Eric ChungChinese University of Hong [email protected]

Samuel CohenUniversity of [email protected]

Diana CombeUniversity of New South [email protected]

Marston ConderUniversity of [email protected]

Ian CoopeUniversity of [email protected]

Marıa Isabel Cortez MunozUniversidad de Santiago de [email protected]

Izzet [email protected]

Simon CrothersUniversity of New South [email protected]

David DamanikRice [email protected]

Norman DancerUniversity of [email protected]


Daniel DanersUniversity of [email protected]

Raman Kumar DasSt. Xavier’s College, [email protected]

Zajj DaughertyUniversity of [email protected]

Matt DavisUniversity of [email protected]

Frank de [email protected]

Maarten de HoopPurdue [email protected]

Jan DeGierThe University of [email protected]

Gary [email protected]

Michael DellnitzUniversity of [email protected]

Laura DeMarcoUniversity of Illinois at [email protected]

Mark DemersFairfield [email protected]

Josef DickUniversity of New South [email protected]

Alicia DickensteinUniversidad de Buenos [email protected]

Tony DooleyUniversity of New South [email protected]

Jason [email protected]

Ian DoustUniversity of New South [email protected]

Yihong DuUniv of New [email protected]

Jinqiao DuanIllinois Institute of [email protected]

Wansuo DuanLASG, Institute of Atmospheric Physics,Chinese Academy of [email protected]

David EasdownUniversity of [email protected]


Lawrence EinUniversity of Illinois at [email protected]

Itai EinavUniversity of [email protected]

David EisenbudUC [email protected], p51

Yasha EliashbergStanford [email protected]

Robert ElliottUniversity of [email protected]

Matthew EnglandUniversity of New South [email protected]

Huijun FanSchool of mathematics, Peking [email protected]

Claus FiekerMagma Group, University of [email protected]

Alexander FishThe Ohio State [email protected]

Peter ForresterUniversity of [email protected]

Colin FoxUniversity of [email protected]

Christian FranzkeBritish Antarctic [email protected]

Gary FroylandUniversity of New South [email protected]

Kenji FukayaKyoto [email protected]

Alex FunSydney [email protected]

Soren GalatiusStanford [email protected]

Hao GaoUC [email protected]

Tim GaroniThe University of [email protected]

Volker GebhardtUniversity of Western [email protected]

Anna GhazaryanUniversity of [email protected]


Alex GhitzaThe University of [email protected]

Nassif GhoussoubUniversity of British [email protected]

Veronique GodinUniversity of [email protected]

Ken GoldenUniversity of [email protected]

Jose Manuel Gomez GuerraUniversity of British [email protected]

Shiro GotoMeiji [email protected]

Richard GreenThe University of [email protected]

Martin GuestTokyo Metropolitan [email protected]

Tony GuttmannUniversity of [email protected]

Ruth HaasSmith [email protected]

Yousaf HabibUniversity of [email protected]

Rika HagiharaUniversity of New South [email protected]

Long HailongUniversity of [email protected]

Mike HarrisonMagma Group, University of [email protected]

Jane HawkinsUniversity of North Carolina at Chapel [email protected]

Stuart HawkinsMacquarie [email protected]

Chris HaysMichigan State [email protected]

Loek HelminckNorth Carolina State [email protected]

Anthony HendersonUniversity of [email protected]

Bruce HenryUniversity of New South [email protected]


Mike HochmanPrinceton [email protected]

Ko HondaUniversity of Southern [email protected]

Hoon HongNC State [email protected]

Min-Chun HongUniversity of [email protected], p101

Jun HoriuchiMeiji [email protected]

Yi HuangUniversity of [email protected]

Jun-Muk [email protected]

Gary [email protected]

Reinhard IllnerUniversity of Victoria, [email protected]

Masashi IshidaSophia [email protected]

Hiroyuki ItoHiroshima [email protected]

Kiminori ItohYokohama Notional [email protected]

Brian JefferiesUniversity of New South [email protected]

Iwan JensenDept. of Mathematics and Statistics,The University of [email protected]

Chris [email protected]

Boda KangSchool of Finance and Economics,The University of Technology, [email protected]

Hyeonbae KangInha [email protected]

Seok-Jin KangSeoul National [email protected]

Shu KawaguchiOsaka [email protected]

Masayuki KawakitaRIMS, Kyoto [email protected]


Yujiro KawamataUniversity of [email protected]

JongHae [email protected]

Masanari KidaUniversity of [email protected]

Eder KikiantyResearch Group in Mathematical Inequalitiesand Applications, School of Engineering andScience, Victoria [email protected]

Arnold KimUC [email protected]

Bong-Sik KimAmerican University of Ras Al [email protected]

Jan KiwiPUC [email protected]

Dan KneezelUniversity of [email protected]

Sandor KovacsUniversity of [email protected]

Marc KrawitzUniversity of [email protected]

Jonathan KressUniversity of New South [email protected]

Atsuo KunibaUniversity of [email protected]

Frances KuoUniversity of New South [email protected]

Kazuhiko KuranoMeiji [email protected]

Alexander KurganovTulane [email protected]

Yongnam LeeSogang [email protected]

Maria LeiteUniversity of [email protected]

Boris LernerUniversity of New South [email protected]

Huiyuan LiLab. of Parallel Computing,Institute of Software,Chinese Academy of [email protected]


Jianping LiLASG,Institute of Atmospheric Physics (IAP),Chinese Academy of Sciences (CAS)[email protected]

Tong LiThe University of [email protected]

Bing LinCentral Michigan [email protected]

Doug LindUniversity of [email protected]

Jon LinksThe University of [email protected]

Jiakun LiuMathematical Sciences Institute,Australian National [email protected]

Zhaoli LiuCapital Normal [email protected]

Simon LloydUniversity of New South [email protected]

Irakli LoladzeUniversity of Nebraska - [email protected]

Luigi LombardiUniversity of Illinois at [email protected]

Yiming LongChern Institute of [email protected]

Rongmin LuUniversity of [email protected]

Ernesto [email protected]

Gennady LyubeznikUniversity of [email protected]

Stefan MullerKorea Institute for Advanced [email protected]

Toshiki MabuchiOsaka [email protected]

Leonardo [email protected]

Diane MaclaganUniversity of [email protected]

Nikolai [email protected]

Vladimir MangazeevAustralian National [email protected]


Vahagn ManukianUniversity of [email protected]

Erin MartinWestminster [email protected]

Daniel MathewsStanford [email protected]

Tatsuo MatsubaraMeiji [email protected]

Anthony MaysMelbourne [email protected]

Scott McCallumMacquarie [email protected]

Bill McleanUniversity of New South [email protected]

Leo MeiUniversity of New [email protected]

Ryan MicklerUniversity of [email protected]

Eugen MihailescuInstitute of Mathematics of the [email protected]

Graeme MiltonUniversity of [email protected]

Maya MinchevaNorthern Illinois [email protected]

Adam MonahanUniversity of [email protected]

Dongho MoonSejong [email protected]

Jason MurckoUniversity of [email protected]

Rua MurrayUniversity of [email protected]

Kassem [email protected]

Hyo C. MyungKorea Institute for Advanced [email protected]

Bruno NachtergaeleUC [email protected]

Hideo NagaiOsaka [email protected]

Gen NakamuraHokkaido [email protected]


Yoshinori NamikawaKyoto [email protected]

Amnon NeemanAustralian National [email protected]

Mike [email protected]

Nicolae NicoroviciSchool of Physics, University of [email protected]

Bernard NienhuisInstitute for theoretical [email protected]

Paul NorburyUniversity of [email protected]

Masayuki NoroKobe [email protected]

Dirk NuyensUniversity of New South [email protected]

S. OgataTohoku [email protected]

Keiji OguisoDept. Math. Osaka [email protected]

Yong-Geun OhUniveristy of [email protected]

Sing-Cheong OngCentral Michigan [email protected]

Wilson OngThe University of Western [email protected]

Kaoru OnoHokkaido University,Department of [email protected]

Piotr OprochaDepartamento de Matematicas,Universidad de [email protected]

Alison [email protected]

Melanie OrigUniversity of Mindanao,Davao City, [email protected]

Axel OssesDIM-CMM U. de [email protected]

Makoto OzawaKomazawa [email protected]

Jinhyun ParkKAIST, Dept of Math. [email protected]


Kyewon Koh ParkAjou [email protected]

Brett ParkerUC [email protected]

Ronnie PavlovUniversity of British [email protected]

Rui PengSchool of Science and Technology,University of New [email protected]

Shige PengShandong [email protected], p93

Jacques PerkOklahoma State [email protected]

Sonja PetrovicUniversity of Illinois, [email protected]

Linda PetzoldUC Santa [email protected]

Thanh-Duong PhamUniversity of New South [email protected]

Tuan PhamUniversity of Illinois at [email protected]

Eckhard PlatenUniversity of Technology [email protected]

Dan PollackUniversity of [email protected]

Leonid PolterovichTel Aviv [email protected]

Anita PonsaingUniversity of [email protected]

Mihnea PopaUniversity of Illinois at [email protected]

Sarah PostUniversity of [email protected]

Cheryl PraegerUniversity of Western [email protected]

Avinesh PrasadUnversity of the South [email protected]

Krishna Chandra PrasadRanchi [email protected]

Hasih PratiwiGadjah Mada [email protected]


Kyle PulaUniversity of [email protected]

David RalstonThe Ohio State [email protected]

Arun RamUniversity of [email protected]

Louise RaphaelHoward [email protected]

Rishni [email protected]

Gueorgui [email protected]

Peter RenaudUni of Canterbury,Christchurch, New [email protected]

John RobertsUniversity of New South [email protected]

Jim RogersTulane [email protected]

Natsuo SaitoHiroshima City [email protected]

Mikko SaloUniversity of [email protected]

Naratip SantitissadekornUniversity of New South [email protected]

Prashant SardeshmukhCIRES Climate Diagnostics [email protected]

Tateaki SasakiUniversity of [email protected]

Takakazu SatoTokyo Institute of [email protected]

Neil SaundersUniversity of [email protected]

Justin SawonColorado State [email protected]

Eric SchostUniversity of Western [email protected]

Nick ScottUniversity of [email protected]

James SethianDepartment of Mathematics,University of California, [email protected]


Bibhya SharmaUniversity of the South [email protected]

Pablo ShmerkinUniversity of [email protected]

Idha SihwaningrumGeneral Soedirman University,Bandung Institute of [email protected]

Anurag SinghUniversity of [email protected]

Scott SissonUniversity of New South [email protected]

Anna SkripkaTexas A&M [email protected]

Callum SleighMelbourne [email protected]

Ian SloanUniversity of New South [email protected]

Michael SmallHong Kong Polytechnic [email protected]

Stanislav SmirnovUniversity of [email protected]

Greg SmithQueen’s [email protected], p57

Hart SmithUniversity of [email protected]

Paul SmithMacquarie [email protected]

Mark SorrellThe University of [email protected]

Ognjen StancevicUniversity of New South [email protected]

Allan SteelMagma Group, University of [email protected]

Plamen StefanovPurdue [email protected]

Greg StevensonAustralian National [email protected]

Lucho StoyanovUniversity of Western [email protected]

Fedor SukochevUniversity of New South [email protected]


Jiachang SunLab. of Parallel Computing, Institute ofSoftware Chinese Academy of [email protected]

Shanzhong SunCapital Normal [email protected]

Yeneng SunNational University of [email protected]

Jaeyoung SungAjou [email protected]

Tharatorn SupasitiUniversity of [email protected]

Melissa TacyAustralian National [email protected]

Ryo TakahashiShinshu [email protected]

Michael TaksarUniversity of [email protected]

Shanjian TangFudan [email protected]

Rachael TappendenUniversity of [email protected]

Don TaylorMagma [email protected]

Tomohide TerasomaUniversity of [email protected]

Natalie ThamwattanaUniversity of [email protected]

Gang TianPeking University and Princeton [email protected]

Chris TisdellUniversity of New South [email protected]

Tatiana ToroUniversity of [email protected]

Thanh TranUniversity of New South [email protected]

Dimetre [email protected]

Masaki TsukamotoKyoto [email protected]

Ramona TudoranThe West University of Timisoara, Faculty ofMathematics and Computer Science,[email protected]


Razvan TudoranThe West University of Timisoara, Faculty ofMathematics and Computer Science,[email protected]

Ian TurnerQueensland University of [email protected]

Leo [email protected]

Gunther UhlmannUniversity of [email protected]

Semail Ulgen YildirimNorthwestern [email protected]

Bill UngerUniversity of [email protected]

Mathai VargheseUniversity of [email protected]

Andras VasyStanford [email protected]

Mauricio VelascoUC [email protected]

Rahbar VirkUniversity of [email protected]

Raymond VozzoUniversity of [email protected]

Dave WalkerUniversity of [email protected]

James WanUniversity of [email protected]

Cecilia WangUniversity of British [email protected]

Jenn-Nan WangNational Taiwan [email protected]

Zhi-Qiang WangUtah State [email protected]

Kei-ichi WatanabeNihon [email protected]

Mark WatkinsMagma Group, University of [email protected]

Adrean WebbUniversity of Colorado [email protected]

Morris [email protected]


Craig WesterlandUniversity of [email protected]

Tony WestonCanisius [email protected]

Jerzy WeymanNortheastern [email protected]

Esther WidiasihSchool of Mathematics,University of [email protected]

Rob WomersleyUniversity of New South [email protected]

Siew Fang WoonCurtin University of [email protected]

Shuhei YamadaMeiji [email protected]

Sumio YamadaTohoku [email protected]

Kohji YanagawaKansai [email protected]

Martha YipUniversity of [email protected]

Ken-ichi YoshidaNagoya [email protected]

Chongchun ZengGeorgia Institute of [email protected]

De-Qi ZhangNational Univ of [email protected]

Xiao ZhangInstitute of Mathematics,Academy of Mathematics and SystemsScience,Chinese Academy of [email protected]

Bin ZhouMathematics Science Institute, AustralianNational [email protected]

Jian ZhouTsinghua [email protected]

Documents

CONGRESS SCHEDULE OVERVIEW