On Lars Hörmander

Lars Hörmander föddes den 24 Jan 1931, och påbörjade 1950 sinforskarutbildning i Lund där han handleddes av Marcel Riesz ochsedan även av Lars Gårding. Hörmander disputerade 1955 påen banbrytande avhandling om partiella differentialekvationer somblev en internationell sensation.

Hörmander tillträdde 1957 en professur i Stockholm vid 26 årsålder. År 1963 blev han professor vid Institute for Advanced Study iPrinceton. När Hörmander återkom till Lund 1968 blev matema-tiska institutionen ett världscentrum för forskningen inom området,då Hörmander och hans elever under 1970 och 80-talen utveckladehelt nya metoder.

Bland de många hedersbetygelser Hörmander mottagit är Fieldsmedaljen 1962 den främ-sta. Han fick även Wolfpriset 1988 och Steelepriset i matematisk skriftställning år 2006.Hörmander avled den 25 november 2012 vid en ålder av 81 år.

Lars Hörmander was born on January 24, 1931 and started his PhD studies in Lundin 1950, where his advisors were Marcel Riesz and Lars Gårding. He got his PhD in 1955with a groundbreaking thesis in Partial Differential Equations, which created an internationalsensation.

Hörmander then accepted a professorship at Stockholm in 1957 at the age of 26. In 1963he became a permanent member of the Institute of Advanced Study at Princeton. When hereturned to Lund in 1968, the department became a world centre for research in the subject,with Hörmander and his students developing entirely new methods in the 1970s and 1980s.

Hörmander received many scientific honours and prizes, among which the Fields Medalof 1962 is the foremost. He also received the Wolf Prize in 1988 and the Steele Prize forMathematical Exposition in 2006. Lars Hörmander passed away on November 25, 2012 atthe age of 81.

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Contents

Information 5Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Internet Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Social Programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Schedule 9Sunday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Monday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Tuesday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Wednesday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18ursday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Abstracts 25Plenary Talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26EMS Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Hörmander Lecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Homological Methods in Algebra . . . . . . . . . . . . . . . . . . . . . . . 31Dynamical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Pseudodifferential Operators . . . . . . . . . . . . . . . . . . . . . . . . . . 35Approximation and Related Problems . . . . . . . . . . . . . . . . . . . . . 37PDEs, Nonlinear Waves and Dispersive Equations . . . . . . . . . . . . . . . 40Operators, Functions and Systems . . . . . . . . . . . . . . . . . . . . . . . 45Harmonic Analysis and Operators . . . . . . . . . . . . . . . . . . . . . . . 48Classification of Operator Algebras: Complexity, Rigidity and Dynamics . . . 51Operator eory and Complex Analysis . . . . . . . . . . . . . . . . . . . . 53Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Math Education and e-learning . . . . . . . . . . . . . . . . . . . . . . . . 60Posters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Sponsors 67

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Internet Access

Eduroam users can connect using their eduroam credentials.You can also connect to the wifi network LU weblogon with the key lu2013-1 and thenlogin with one of these accounts using your web browser:

Username Passwordtemp688501 )vb2bHe2uotemp746144 7rfHrg)n4dtemp290296 mxga6iV)2g

Social Programme

ere will be various different tours of Lund for smaller groups on offer in the afternoonof Wednesday, June 12, after the Special Sessions.

Tour of Lund Cathedral

Lund Cathedral is by most counts the most important sacral building in Scandinavia, witha nearly 1000-year history. e guided tour will start Wednesday, June 12, 17:00 fromthe west portal and cost about SEK 50 per person (to be paid there).

Tour of Lund Botanical Garden

Lund Botanical Garden has its roots in the 17th century. It is situated in a pleasant parkbetween the Maths Department and the city centre. e tour (weather permitting) willstart Wednesday, June 12, 17:00 from the entrance of the Maths Department, there areno extra costs.

Museum of Sketches

is is a lovely and unusual museum close to the Maths Department, featuring sketches,models and outlines of artworks. e tour starts Wednesday, June 12, 17:00 at the en-trance of the museum, cost about SEK 70 per person, with guided tour (to be paid there).

Lund at Dusk

A tour about the history of Lund with a very entertaining and knowledgeable guide (nota mathematician!). e tour starts Wednesday, June 12, 21:00 from the west portal of theCathedral, cost about SEK 70 per person (to be paid there).

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Schedule

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Sunday

Registration & Wine Reception 17:50–19:00Kårhuset Restaurant

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Monday

Registration 08:15–08:50Annexe Foyer

Opening 08:50–09:00MA:7

Plenary Talk 09:00–09:50MA:7

Adrian Constantin, King’s College London & University of Vienna → p. 26Pressure beneath a travelling water wave

Plenary Talk 09:55–10:45MA:7

Viviane Baladi, University of Copenhagen → p. 26Breakdown of linear response for smooth families of dynamical systemswith bifurcations

Coffee 10:45–11:15Annexe Foyer

Plenary Talk 11:15–12:05MA:7

Håkan Hedenmalm, KTHHeisenberg’s uncertainty principle in the sense of Beurling

Lunch 12:05–13:30Kårhuset Restaurant

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Homological Methods in Algebra I 13:30–16:30MH:309A

Organiser(s): Petter Bergh, Marius Thaule (Trondheim)

13:30–14:20 Dag Oskar Madsen, University of Nordland → p. 31Hochschild homology and global dimension

14:35–15:25 Gunnar Fløystad, University of Bergen → p. 31Zipping Tate resolutions over an exterior algebra to get free resolutions over asymmetric algebra

15:40–16:30 Henning Krause, Bielefeld University → p. 31A local-global principle for triangulated categories

Dynamical Systems I 13:30–16:30MH:C

Organiser(s): Maria Saprykina (KTH), Anders Karlsson (Geneve)

13:30–14:20 Andreas Strömbergsson, Uppsala University → p. 33Effective Ratner equidistribution on ASL(2,R)

14:35–15:00 Giulio Tiozzo, Harvard University → p. 33Geodesic ray tracking for random walks on groups

15:00–15:25 Magnus Aspenberg, Lund University → p. 33Collet-Eckmann and Misiurewicz

15:40–16:30 Maarit Järvenpää, University of Oulu → p. 34Projection theorems and invariant measures

Pseudodifferential Operators Iin memory of Lars Hörmander

13:30–16:30MA:7

Organiser(s): Nicholas Lerner (Paris), Magnus Fontes (Lund)

13:30–14:20 Richard Melrose, MIT → p. 35Resonances, hyperbolic metrics and wave equations

14:35–15:25 Jean-Michel Bony, Ecole Polytechnique → p. 36e Principal Symbol of Fourier Integral Operators revisited

15:40–16:30 Nils Dencker, Lund University → p. 36e Solvability of Differential Equations

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Approximation and Related Problems I 13:30–16:30MH:333

Organiser(s): Anton Baranov (St. Petersburg), Konstatin Fedorovskiy(Moscow)13:30–14:20 Stephen Gardiner, University College Dublin → p. 37

Universal Taylor series and potential theory14:35–15:25 Konstantin Fedorovskiy, Bauman Moscow State Technical University

→ p. 38Cm-approximation by solutions of elliptic equations

15:40–16:05 Markus Nieß, TU Clausthal → p. 38On the behaviour of power series in the absence of Hadamard-Ostrowski gaps

16:05–16:30 Yurii Belov, Saint Petersburg State University → p. 38Approximation of L2 function on an interval by shifts and exponentials

Coffee 16:30–17:00Annexe Foyer

EMS Lecture 17:00–17:50MA:7

Tamar Ziegler, Technion – Israel Institute of Technology → p. 30Dynamics and prime solutions to linear equations

Poster Session & Reception 17:50–19:00Annexe Foyer

Hörmander Lecture 19:00–20:00MA:7

Vladimir Maz’ya, Linköping University and University of Liverpool → p. 30Hörmander’s impact on partial differential equations

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Tuesday

Plenary Talk 09:00–09:50MA:7

Carel Faber, KTH → p. 27Arithmetic aspects of the moduli space of curves

Plenary Talk 09:55–10:45MA:7

Jesper Grodal, University of Copenhagen → p. 27Groups via homotopy theory

Coffee 10:45–11:15Annexe Foyer

Plenary Talk 11:15–12:05MA:7

Agata Smoktunowicz, University of Edinburgh → p. 27Old and new questions in noncommutative ring theory

Lunch 12:05–13:30Kårhuset Restaurant

Homological Methods in Algebra II 13:30–16:30MH:309A

Organiser(s): Petter Bergh, Marius Thaule (Trondheim)

13:30–14:20 Marius aule, NTNU → p. 31e Grothendieck group of higher triangulated categories

14:35–15:25 Alexander Berglund, Stockholm University → p. 32Duality, descent and extensions I

15:40–16:30 Kathryn Hess, EPFL → p. 32Duality, descent and extensions II

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Dynamical Systems II 13:30–16:30MH:C

Organiser(s): Maria Saprykina (KTH), Anders Karlsson (Geneve)

13:30–14:20 Jörg Schmeling, Lund University → p. 34Multifractal analysis of some multiple ergodic average – e invariant spec-trum

14:35–15:25 Esa Järvenpää, University of Oulu → p. 35Hausdorff dimension of affine random covering sets in torus

15:40–16:30 Anders Öberg, Uppsala University → p. 35e ergodic theory of the Kusuoka measure

Pseudodifferential Operators IIin memory of Lars Hörmander

13:30–16:30MA:7

Organiser(s): Nicholas Lerner (Paris), Magnus Fontes (Lund)

13:30–14:20 Duong H. Phong, Columbia University → p. 37On Hörmander’s L2 estimates for the d-bar equation

14:35–15:25 Louis Boutet de Monvel, Universite Pierre et Marie Curie → p. 37Boundary problems for pseudodifferential operators; the ”transmission” prop-erty and Hörmander’s suggestions

15:40–16:30 Gerd Grubb, Copenhagen University → p. 37Boundary conditions

Approximation and Related Problems II 13:30–16:30MH:333

Organiser(s): Anton Baranov (St. Petersburg), Konstatin Fedorovskiy(Moscow)13:30–14:20 Anthony G. O’Farrell, NUI, Maynooth → p. 38

Some Approximation Problems14:35–15:00 Victor Buslaev, Steklov Mathematical Institute → p. 39

Convergence of two-point Pade approximants15:00–15:25 Alexander Komlov, Steklov Mathematical Institute → p. 39

On strong asymptotic for two-point Pade approximants15:40–16:05 André Boivin, University of Western Ontario → p. 39

On closed sets of approximation on Riemann surfaces16:05–16:30 Pavel Mozolyako, Saint-Petersburg State University → p. 40

Wavelet approximation of harmonic functions in growth spaces

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PDEs, Nonlinear Waves and Dispersive Equations I 13:30–16:30MH:B

Organiser(s): Mark Groves (Saarbruecken) and Mats Ehrnström (Trond-heim)13:30–13:55 Samuel Walsh, Courant Institute, NYU → p. 40

Nonlinear resonance for dispersive equations with a potential13:55–14:20 Sigmund Selberg, NTNU, Trondheim → p. 41

Finite-energy solutions of the Chern-Simons-Higgs system14:35–15:00 Erik Wahlén, Lund University → p. 41

A dimension-breaking phenomenon for steady water waves with weak surfacetension

15:00–15:25 Mark Groves, Universität des Saarlandes → p. 41Existence and Conditional Energetic Stability of Solitary Gravity-capillaryWater Waves with Constant Vorticity

15:40–16:00 Alfatih Ali, University of Bergen → p. 42Reconstruction of the pressure in long-wave models with constant vorticity

16:00–16:25 Wolf-Patrick Düll, Universität Stuttgart → p. 42Justification of the Nonlinear Schrödinger equation for the evolution of gravitydriven 2D surface water waves in a canal of finite depth

Operators, Functions and Systems I 13:30–16:30MH:362D

Organiser(s): Amol Sasane (Lund, LSE)

13:30–13:55 Andrew Wynn, Imperial College London → p. 45Weighted admissibility of linear systems on Bergman and Dirichlet spaces

13:55–14:20 Eskil Rydhe, Lund University → p. 45Weighted admissibility with respect to the right shift on L2(R+, dt)

14:35–15:00 Sandra Pott, Lund University → p. 46Weighted Admissibility and Embedding eorems in Bergman spaces

15:00–15:25 Annemarie Luger, Stockholm University → p. 46Generalized poles - About the lengths of Jordan chains

Coffee 16:30–17:00Annexe Foyer

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EMS Lecture 17:00–17:50MA:7

Tamar Ziegler, Technion – Israel Institute of Technology → p. 30Dynamics and prime solutions to linear equations

Conference Dinner 19:00–21:00Grand Hotel Lund

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Wednesday

Plenary Talk 09:00–09:50MA:7

Anton Alekseev, University of Geneva → p. 28The Horn problem and planar networks

Plenary Talk 09:55–10:45MA:7

Kristian Seip, NTNU → p. 28Polynomials on the polydisc

Coffee 10:45–11:15Annexe Foyer

Plenary Talk 11:15–12:05MA:7

Svante Janson, Uppsala University → p. 28Simply generated trees, conditioned Galton–Watson trees, random alloca-tions and condensation

Lunch 12:05–13:30Kårhuset Restaurant

PDEs, Nonlinear Waves and Dispersive Equations II 13:30–16:30MH:B

Organiser(s): Mark Groves (Saarbruecken) and Mats Ehrnström (Trond-heim)13:30–13:55 Espen R. Jakobsen, NTNU → p. 43

Well-posedness of fractional degenerate parabolic equations13:55–14:20 Katrin Grunert, NTNU → p. 43

Global solutions of the two-component Camassa–Holm system14:35–15:00 Vladimir Kozlov, Linköping University → p. 43

Steady water waves with vorticity: spatial Hamiltonian structure15:00–15:25 Mats Ehrnström, NTNU → p. 44

Triply-periodic steady water waves in two dimensions15:40–16:05 Maria Alessandra Ragusa, University of Catania → p. 44

New points of view of the classical P.D.E. theory in Morrey spaces

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Operators, Functions and Systems II 13:30–16:30MH:362D

Organiser(s): Amol Sasane (Lund, LSE)

13:30–13:55 Amol Sasane, Lund University → p. 46An analogue of Serre’s conjecture and Control eory

13:55–14:20 Hartmut Logemann, University of Bath → p. 47Infinite-dimensional Lur’e systems: the circle criterion, input-to-state stabilityand the converging-input-converging-state property

14:35–15:00 Lassi Paunonen, Tampere University of Technology → p. 47Reduced Order Internal Models in Robust Output Regulation

15:00–15:25 Mikael Kurula, Åbo Akademi → p. 48Proving existence of solutions of PDEs using feedback theory

Harmonic Analysis and Operators I 13:30–16:30MH:309A

Organiser(s): Tuomas Hytönen (Helsinki) and Andreas Rosen (Linköping)

13:30–14:20 Christoph iele, Universität Bonn → p. 48Lp theory for outer measures and its application in time-frequency analysis

14:35–15:00 Mikko Salo, University of Jyväskylä → p. 48Lp estimates in the Calderón problem

15:00–15:25 Andreas Rosén, Linköpings universitet och Göteborgs universitet→ p. 49

A local Tb theorem for vector-valued weighted paraproducts

Classification of Operator Algebras: Complexity,Rigidity and Dynamics I

13:30–16:30MH:333

Organiser(s): Sören Eilers (Copenhagen)

13:30–14:20 Hiroki Matui, University of Copenhagen → p. 51Recent progress in classification of simple C*-algebras

14:35–15:00 Eduard Ortega, NTNU → p. 51C*-algebras associated to Boolean dynamical systems

15:00–15:25 Deprez Steven, Københavns universitet → p. 51Endomorphism semigroups of II1 factors

19

Operator Theory and Complex Analysis I 13:30–16:30MH:C

Organiser(s): Olivia Constantin (Canterbury)

13:30–13:55 Miroslav Englis, Academy of Sciences, Prague → p. 53Dixmier trace for Toeplitz and Hankel operators on weighted Fock spaces

13:55–14:20 José Ángel Peláez, University of Málaga → p. 53Generalized Hilbert operators and a Muckenhoupt type condition

14:35–15:00 Jordi Pau, Universitat de Barcelona → p. 54Integration operators between Hardy spaces on the unit ball

15:00–15:25 Jan-Fredrik Olsen, Lund University → p. 54Boundary behavior in Hardy spaces on the infinite-dimensional polydisk

15:40–16:05 Anna-Maria Persson, Lund University → p. 55Deformations of Harmonic Maps with Finite Uniton Number

Probability I 13:30–16:30MH:332A

Organiser(s): Herman Thorisson (Iceland)

13:30–14:20 Marta Sanz-Solé, University of Barcelona → p. 57Probabilistic potential theory and applications to stochastic partial differentialequations

14:35–15:25 Sigurdur Orn Stefansson, Uppsala University → p. 58Scaling limits of planar maps with a uniqe large face

15:40–16:05 Ljiljana Petrovic, University of Belgrade → p. 58Generalizations of Granger’s Causality in Continuous Time

16:05–16:55 Hermann orisson, University of Iceland → p. 58Unbiased shifts of Brownian motion

Coffee 16:30–17:00Annexe Foyer

Free Evening / Social Programme 17:00–21:00

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Thursday

Plenary Talk 09:00–09:50MA:7

Xavier Tolsa, ICREA / Universitat Autònoma e Barcelona → p. 29Singular integrals, rectifiability, and the David-Semmes problem

Plenary Talk 09:55–10:45MA:7

Pekka Koskela, University of Jyvaskyla → p. 29Boundary blow up under Sobolev mappings

Coffee 10:45–11:15Annexe Foyer

Plenary Talk 11:15–12:05MA:7

Artur Avila, Institut de Mathématiques de JussieuTBA

Lunch 12:05–13:30Kårhuset Restaurant

Harmonic Analysis and Operators II 13:30–16:30MH:309A

Organiser(s): Tuomas Hytönen (Helsinki) and Andreas Rosen (Linköping)

13:30–14:20 Alan McIntosh, Australian National University, Canberra → p. 49Hardy Spaces HpL Associated with Elliptic Operators and their Connectionwith Lp Spaces

14:35–15:00 Maria Carmen Reguera, Universitat Autònoma de Barcelona → p. 50e two weight problem for the Bergman projection and Sarason Conjecture

15:00–15:25 Tuomas Hytönen, University of Helsinki → p. 50Sharp weighted bounds: towards rough operators

15:40–16:05 Kaj Nyström, Uppsala University → p. 50Boundary behavior for non-negative solutions to non-linear and degenerateparabolic pdes

16:05–16:30 Sorina Barza, Karlstad University → p. 50Weighted inequalities for the geometric maximal operator

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Classification of Operator Algebras: Complexity,Rigidity and Dynamics II

13:30–16:30MH:333

Organiser(s): Sören Eilers (Copenhagen)

13:30–14:20 Wojciech Szymanski, University of Southern Denmark → p. 52Endomorphisms of Graph C*-Algebras

14:35–15:00 Gunnar Restorff, University of the Faroe Islands → p. 52Classification of Cuntz-Krieger algebras and Graph algebras

15:00–15:25 Sara Arklint, University of Copenhagen → p. 52Corners of Cuntz-Krieger algebras

15:40–16:05 Johan Öinert, Lund University → p. 52Gradations on Leavitt path algebras

16:05–16:30 Maria Ramirez-Solano, University of Copenhagen → p. 53A non-standard hierarchical tiling

Operator Theory and Complex Analysis II 13:30–16:30MH:C

Organiser(s): Olivia Constantin (Canterbury)

13:30–13:55 Anton Baranov, Saint Petersburg State University → p. 55Spectral synthesis for systems of exponentials and reproducing kernels

13:55–14:20 Mikael Lindström, University of Oulu → p. 56e essential norm of a composition operator on BMOA

14:35–15:00 Eugenia Malinnikova, NTNU → p. 56Composition operators on model spaces

15:00–15:25 Antti Haimi, KTH → p. 56Bulk asymptotics for polyanalytic correlation kernels

15:40–16:05 Karl-Mikael Perfekt, Lund University → p. 57Spectral estimates for the double layer potential

16:05–16:30 Dragan Vukotić, Universidad Autónoma de Madrid → p. 57Compact and weakly compact operators between conformally invariant spacesof analytic functions

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Probability II 13:30–16:30MH:332A

Organiser(s): Herman Thorisson (Iceland)

13:30–14:20 Takis Konstantopoulos, Uppsala University → p. 59Infinitely iterated Brownian motion

14:35–15:25 Maria Deijfen, Stockholm University → p. 59e winner takes it all

15:40–16:30 Tatyana Turova, Lund University → p. 60Bootstrap percolation on a graph with random and local connections

Math Education and e-learning 13:30–16:30MA:7

Organiser(s): Jan-Fredrik Olsen, Anna Maria Persson and Kristina Juter(Lund)13:30–14:20 omas Lingeärd, Göteborgs universitet → p. 60

Dynamic Geometry14:35–15:25 Karsten Schmidt, e Technical University of Denmark → p. 61

How CAS and E-learning change the teaching and learning of introductoryengineering mathematics

15:40–16:30 Malin Christersson, Campus Helsingborg/Lund University → p. 62Programming as a means to learn mathematics in compulsory school

Coffee 16:30–17:00Annexe Foyer

EMS Lecture 17:00–17:50MA:7

Tamar Ziegler, Technion – Israel Institute of Technology → p. 30On the Mobius randomness principle

Closing 17:50–18:00MA:7

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24

Abstracts

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Plenary Talks

Pressure beneath a travelling water wave

Adrian Constantin Monday 09:00–09:50King’s College London & University of Vienna MA:7

Using complex and harmonic function theory we investigate the pressure within anirrotational fluid in a periodic, steady, two-dimensional gravity wave above a flat bed.We show that the pressure in the fluid strictly decreases horizontally away from the crestline. Furthermore, the pressure strictly increases with depth. e approach deals withthe governing equations (incompressible Euler equations with a free boundary) and doesnot rely on approximations. In particular, it applies to waves of large amplitude. We alsoaddress the issue of the recovery of the free surface profile from knowledge of the pressureat the bed. ese results present joint work with W. Strauss and D. Clamond.

Breakdown of linear response for smooth families of dynam-ical systems with bifurcations

Viviane Baladi Monday 09:55–10:45University of Copenhagen MA:7Coauthors: M. Benedicks and D. Schnellmann

Many interesting dynamical systems possess a unique SRB (”physical”) measure,which behaves well with respect to Lebesgue measure. Given a smooth one-parameter fam-ily of dynamical systems ft, is natural to ask whether the SRB measure depends smoothlyon the parameter t.

If the ft are smooth hyperbolic diffeomorphisms (which are structurally stable), theSRB measure depends differentiably on the parameter t, and its derivative is given bya ”linear response” formula (Ruelle, 1997). When bifurcations are present and struc-tural stability does not hold, linear response may break down. is was first observedfor piecewise expanding interval maps, where linear response holds for tangential fami-lies, but where a modulus of continuity t log t may be attained for transversal families(Baladi-Smania, 2008). e case of smooth unimodal maps is much more delicate. Ru-elle (Misiurewicz case, 2009) and Baladi-Smania (slow recurrence case, 2012) obtainedlinear response for fully tangential families (confined within a topological class).

After an introduction accessible to non-experts, we shall present our new results onthe transversal smooth unimodal case (including the quadratic family), where we obtainHolder upper and lower bounds (in the sense of Whitney, along suitable classes of param-eters).

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Arithmetic aspects of the moduli space of curves

Carel Faber Tuesday 09:00–09:50KTH MA:7

e moduli space Mg of nonsingular curves of genus g can be studied over any fieldand even over the integers. After discussing some of the most important properties of thisspace, I will highlight some of its arithmetic aspects and the close relation between Mgand modular forms. At first, this relation may not seem surprising, but I will attempt toshow that it is quite subtle and that we still are very far from a full understanding of it.

Groups via homotopy theory

Jesper Grodal Tuesday 09:55–10:45University of Copenhagen MA:7Coauthors: Kasper Andersen (Lund)

In algebraic topology, an old problem of Norman Steenrod asks which spaces havecohomology ring a finitely generated polynomial algebra? In group theory, celebratedresults include the classification of finite simple groups. And in between group theoryand topology, Hilbert’s 5th problem ask if a manifold that is also a topological group isnecessarily a Lie group? While these problems may not at first sight seem related, I will inmy talk survey some recent results showing that they are in fact intimately linked.

Old and new questions in noncommutative ring theory

Agata Smoktunowicz Tuesday 11:15–12:05University of Edinburgh MA:7

ere are many longstanding and tantalizing open questions in noncommutative al-gebra, which are easy to formulate and easily understood. One such problem is very wellknown, namely the Kurosh conjecture on domains. is asks whether a finitely generatedalgebraic algebra which is a domain is finite dimensional. A related open question (Laty-shev, 1970’s) asks whether there exists a finitely generated ring which is infinite and whichis also a division ring. Other basic open questions in noncommutative algebra include theKoethe conjecture on nil rings, the Jacobson conjecture on finitely presented algebras,and some more recent questions, such as whether there is a domain with a finite but non-integer Gelfand-Kirillov dimension, and whether finitely generated graded Noetherianalgebras need to have polynomial growth (Stafford). We will look at some methods whichare used in this area, for example the Golod-Shafarevich theorem, as well as some partialresults which are known to be related to these questions. We will also look at some relatednew and old results on algebraic algebras and free algebras, Golod-Shafarevich algebras,domains and Noetherian algebras, growth of algebras and the Gelfand-Kirillov dimension.

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Connections between noncommutative ring theory, group theory and noncommutative(projective) algebraic geometry and other areas of mathematics will also be mentioned.

The Horn problem and planar networks

Anton Alekseev Wednesday 09:00–09:50University of Geneva MA:7

e Horn problem is a classical problem of Linear Algebra which establishes a com-plete set of inequalities on eigenvalues of a sum of two Hermitian matrices with givenspectra. It was solved by Klyachko and Knutson-Tao in the end of 1990s.

Surprizingly, the same set of inequalities comes up in the problem of maximal multi-paths in a planar network equipped with Boltzmann weights on its edges. e link be-tween the two problems is via the tropical limit. In order to control this limit we are usingthe Liouville volume on the space of solutions of the Horn problem.

e talk is based on a joint work with M. Podkopaeva and A. Szenes.

Polynomials on the polydisc

Kristian Seip Wednesday 09:55–10:45NTNU MA:7

I will present some recent work dealing with estimates of Lp norms of holomorphicpolynomials on the distinguished boundary of the unit polydisc, and discuss how this sub-ject interacts with other topics. In particular, I will explain how a representation of certaingreatest common divisor sums as Poisson integrals on the polydisc leads us to the solutionof an old problem of G. Harman in the metric theory of diophantine approximation; thispart of the talk is based on joint work with Christoph Aistleitner and István Berkes.

Simply generated trees, conditioned Galton–Watson trees,random allocations and condensation

Svante Janson Wednesday 11:15–12:05Uppsala University MA:7

We give a unified treatment of the limit, as the size tends to infinity, of simply gen-erated random trees, including both the well-known result in the standard case of criticalGalton-Watson trees and similar but less well-known results in the other cases (i.e., whenno equivalent critical Galton-Watson tree exists). ere is a well-defined limit in the formof an infinite random tree in all cases; for critical Galton-Watson trees this tree is locallyfinite but for the other cases the random limit has exactly one node of infinite degree.

e random infinite limit tree can in all cases be constructed by a modified Galton-Watson process. In the standard case of a critical Galton-Watson tree, the limit tree has

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an infinite ”spine”, where the offspring distribution is size-biased. In the other cases, thespine has finite length and ends with a vertex with infinite degree. A node of infinite degreein the limit corresponds to the existence of one node with very high degree in the finiterandom trees; in physics terminology, this is a type of condensation. In simple cases, thereis one node with a degree that is roughly a constant times the number of nodes, while allother degrees are much smaller; however, more complicated behaviour is also possible.

e proofs use a well-known connection to a random allocation model that we callballs-in-boxes, and we prove corresponding results for this model.

Singular integrals, rectifiability, and the David-Semmes prob-lem

Xavier Tolsa Thursday 09:00–09:50ICREA / Universitat Autònoma e Barcelona MA:7

e notion of rectifiability plays an essential role in the L2 boundedness of someimportant operators arising in complex and harmonic analysis, such as the Cauchy andRiesz transforms. Indeed, by a well known result of David, it turns out that the Cauchytransform originates an operator bounded in L2 with respect to the arc length measure on(AD regular) rectifiable curves of the plane. In the converse direction, theL2 boundednessof the Cauchy transform with respect to arc length on a set E implies the rectifiability ofE.

In this talk I will report on analogous results concerning the n-dimensional Riesztransform in Rn+1 which are due to Nazarov, Tolsa and Volberg. ese results haveapplications to the characterization of the removable singularities for Lipschitz harmonicfunctions in Rn+1.

Boundary blow up under Sobolev mappings

Pekka Koskela Thursday 09:55–10:45University of Jyvaskyla MA:7

In 1995, Jones and Makarov established optimal criteria for a modulus of continuityof a conformal map of the unit disk to guarantee that the area of the boundary of the imagedomain be zero. Partially motivated by Peano curves, it is of interest to relax the confor-mality assumption. I will explain a suitable generalization and discuss the consequencesfor Peano curves.

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EMS Lectures

Dynamics and prime solutions to linear equations

Tamar Ziegler Monday & Tuesday 17:00–17:50Technion – Israel Institute of Technology MA:7

In the first two talks I will describe some of the ideas behind the recent developmentsin additive number theory and ergodic theory leading to the proof of Hardy-Littlewoodtype estimates for the number of prime solutions to systems of linear equations of finitecomplexity.

On the Mobius randomness principle

Tamar Ziegler Thursday 17:00–17:50Technion – Israel Institute of Technology MA:7

e Mobius function is one of the most important arithmetic functions. ere is avague yet well known principle regarding its randomness properties called the ”Mobiusrandomness law”, stating that the Mobius function should be orthogonal to any ”struc-tured” sequence. A few years ago P. Sarnak suggested a far reaching conjecture as a possi-ble formalization of this principle. Sarnak conjectured that ”structured sequences” shouldcorrespond to sequences arising from deterministic dynamical systems. We will discussthis conjecture as well as some recent progress establishing several special cases.

Hörmander Lecture

Hörmander’s impact on partial differential equations

Vladimir Maz’ya Monday 19:00–20:00Linköping University and University of Liverpool MA:7

Lars Hörmander, one of the most influential mathematicians of our time, passed awayNovember 25, 2012. His work ranged widely across the theories of partial differential,pseudo–differential and Fourier operators. In the present talk, I will speak about someaspects of Hörmander’s huge heritage and contributions of his followers.

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Homological Methods in AlgebraOrganiser(s): Petter Bergh, Marius Thaule (Trondheim)

Hochschild homology and global dimension

Dag Oskar Madsen Monday 13:30–14:20University of Nordland MH:309A

In this talk I will discuss the current status of Han’s conjecture. is conjecture saysthat a finite dimensional associative algebra whose higher Hochschild homology groupseventually vanish must be of finite global dimension.

Zipping Tate resolutions over an exterior algebra to get freeresolutions over a symmetric algebra

Gunnar Fløystad Monday 14:35–15:25University of Bergen MH:309A

e bounded derived category of coherent sheaves on the projective space P(W ) isequivalent to the category of Tate resolutions over the exterior algebra ⊕i ∧i W ∗. Givensuch a resolution, it may be amalgamated, ”zipped”, with the exterior powers ∧iV of anew vector space V , to get a bounded complex of free modules over the polynomial ringSym(V ⊗W ∗). We describe this construction and its properties, and apply this to giveexplicit constructions of several notable classical and recent resolutions over polynomialrings, like the Eagon-Northcott complex, Buchsbaum-Eisenbud complexes, pure free res-olutions, and the recent tensor complexes.

A local-global principle for triangulated categories

Henning Krause Monday 15:40–16:30Bielefeld University MH:309A

One of the cornerstones of commutative algebra is the local-global principle. In mytalk I discuss a version of this principle for triangulated categories. Some applications fromrepresentation theory will serve as an illustration. is is based on joint work with DaveBenson and Srikanth Iyengar.

The Grothendieck group of higher triangulated categories

Marius Thaule Tuesday 13:30–14:20NTNU MH:309ACoauthors: Petter Andreas Bergh

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e Grothendieck group of a triangulated category is the free abelian group on the (setof ) isomorphism classes of objects, modulo the Euler relations corresponding to the distin-guished triangles. omason proved that the set of subgroups of the Grothendieck groupclassifies the dense triangulated subcategories. Namely, there is a bijective correspondencebetween the set of subgroups and the set of dense triangulated subcategories.

In my talk I will discuss an extension of this result to the case of n-angulated categoriesfor n odd. is is joint work with Petter Bergh.

Duality, descent and extensions I

Alexander Berglund Tuesday 14:35–15:25Stockholm University MH:309ACoauthors: Kathryn Hess

I will talk about joint work with Kathryn Hess on connections between homotopicalnotions of Koszul duality, Grothendieck descent and Hopf-Galois extensions. My talk willfocus on describing a general categorical framework that allows for a comparison of thethree notions. Roughly speaking, it turns out that each of the notions can be formulatedas asserting that a certain morphism of corings induces a Quillen equivalence betweenthe associated categories of comodules. is realization led us to develop what could bethought of as a homotopical version of Morita theory for model categories of comodules.Kathryn’s talk will then formulate the main theorems that connect the three differentnotions, as well as discuss further examples and applications.

Duality, descent and extensions II

Kathryn Hess Tuesday 15:40–16:30EPFL MH:309ACoauthors: Alexander Berglund, Varvara Karpova

I will present joint work with Alexander Berglund on the close relations among ho-motopical notions of Koszul duality, Grothendieck descent and Hopf-Galois extensions,based on the categorical framework that Alexander will describe in his talk. I will alsosketch recent progress on properties of Hopf-Galois extensions of commutative differen-tial graded algebras, due to my graduate student, Varvara Karpova.

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Dynamical SystemsOrganiser(s): Maria Saprykina (KTH), Anders Karlsson (Geneve)

Effective Ratner equidistribution on ASL(2,R)

Andreas Strömbergsson Monday 13:30–14:20Uppsala University MH:C

I will present a result giving effective equidistribution of 1-dimensional unipotentorbits in ASL(2,Z)\ASL(2,R), where ASL(2,R) is the affine special linear group of order2, i.e. the semidirect product of SL(2,R) and R2. e proof involves spectral analysis anduse of Weil’s bound on Kloosterman sums. I will also discuss applications to effectiveresults for variants of the Oppenheim conjecture on the density of Q(Zn) on the real line,where Q is an irrational indefinite quadratic form.

Geodesic ray tracking for random walks on groups

Giulio Tiozzo Monday 14:35–15:00Harvard University MH:C

Given a finitely generated group G acting on a geodesic space X and a probabilitymeasure on G, one can construct a random walk by choosing at each step a random groupelement and letting it act on X.

e natural question arises whether the sample paths can be approximated by somegeodesic in X. We will prove that, in a quite general setting, the sample path and thelimiting geodesic lie within sublinear distance.

Our argument applies to the case of the mapping class group acting on Teichmuellerspace, answering a question of Kaimanovich. Another application includes the statisticsof excursions of random Teichmueller geodesics in the thin part of moduli space.

Collet-Eckmann and Misiurewicz

Magnus Aspenberg Monday 15:00–15:25Lund University MH:C

Uniformly expanding dynamical systems in the complex setting (also called hyper-bolic maps) is believed to be generic (open and dense) in the parameter space. is wasconjectured already by P. Fatou in the beginning of the 20th century and still unsolved.Uniformly expanding here means on the Julia set, and hence in particular there cannot beany critical points on it. To relax this strong condition other non-uniformly expandingconditions were introduced, for instance the so called Collet-Eckmann condition. ismeans that there are critical points on the Julia set but the derivative of iterates of the

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critical value(s) grow exponentially. Collet-Eckmann maps have positive measure in theparameter space for rational functions, and moreover one has to admit that the criticalorbit(s) approach the critical point(s). Critically non-recurrent maps, such as Misiurewiczmaps, are a special type of Collet-Eckmann maps but they have measure zero. I will sum-marize the measure theoretic picture for these maps and also set them in connection tohyperbolic maps.

Projection theorems and invariant measures

Maarit Järvenpää Monday 15:40–16:30University of Oulu MH:CCoauthors: R. Hovila, E. Järvenpää and F. Ledrappier

I discuss well-known projection theorems in geometric measure theory and their con-sequences to the study of invariant measures.

Multifractal analysis of some multiple ergodic average – Theinvariant spectrum

Jörg Schmeling Tuesday 13:30–14:20Lund University MH:CCoauthors: Ai-Hua FAN, and Meng WU

Let (X,T ) be a topological dynamical system where T is a continuous map on a com-pact metric space X . Fürstenberg had initiated the study of the multiple ergodic average:

1

n

n∑k=1

f1(Tkx)f2(T

2kx) · · · fs(T skx) (1)

where f1, · · · , fs are s continuous functions on X with s ≥ 2 when he proved theexistence of arithmetic sequences of arbitrary length amongst sets of integers with positivedensity. Later on, the research of such a kind of average has attributed a lot of attentions.

We study the multiple ergodic averages

1

n

n∑k=1

φ(xk, xkq, · · · , xkqℓ−1)

on the symbolic space Σm = {0, 1, · · · ,m − 1}N where m ≥ 2, ℓ ≥ 2, q ≥ 2 areintegers. We will consider the invariant part of the multifractal level sets, i.e. we willstudy the maximal dimension of an invariant or multiple mixing measure supported onthese level sets. Here many new interesting phenomena occur. In general there will beno invariant measure with the same dimension as the level sets. Moreover the invariant

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and the mixing spectra differ. On the other hand we will point on some connections toprobability theory (von Mise statistics), ergodic optimization of multiple integrals and alsoindicate some new phase transition phenomena.

Hausdorff dimension of affine random covering sets in torus

Esa Järvenpää Tuesday 14:35–15:25University of Oulu MH:CCoauthors: Maarit Järvenpää, Henna Koivusalo, Bing Liand Ville Suomala

We calculate in d-dimensional torus the almost sure Hausdorff dimension of the ran-dom covering set generated by linear images of a set with non-empty interior. e dimen-sion formula is derived from the singular values of the linear maps.

The ergodic theory of the Kusuoka measure

Anders Öberg Tuesday 15:40–16:30Uppsala University MH:C

In this talk I will describe the Kusuoka measure, which is defined via the energy formon a fractal set, and which in turn gives rise to an energy Laplacian. I will characterize theKusuoka measure as a g-measure and describe its properties from an ergodic theory pointof view.

Pseudodifferential Operatorsin memory of Lars Hörmander

Organiser(s): Nicholas Lerner (Paris), Magnus Fontes (Lund)

Resonances, hyperbolic metrics and wave equations

Richard Melrose Monday 13:30–14:20MIT MA:7

In this talk I will use joint work with Antônio Sá Barreto and András Vasy, and sub-sequent developments, to illustrate the influence of ideas of Lars Hörmander concerningspectral asymptotics and wave equations.

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The Principal Symbol of Fourier Integral Operators revisited

Jean-Michel Bony Monday 14:35–15:25Ecole Polytechnique MA:7

A general theory of Fourier Integral Operators, associated to non necessarily homo-geneous canonical transformations, will be described. Emphasis will be placed on a resultof differential geometry which allows to define the principal symbol of such operators.at symbol is a section of a line bundle defined concretely in terms of the symplectic andmetaplectic groups.

In the particular case where the canonical transformation is homogeneous, we willshow how this symbol can be identified with the principal symbol defined by Hörmander,giving thus an alternative definition of the Maslov bundle.

The Solvability of Differential Equations

Nils Dencker Monday 15:40–16:30Lund University MA:7

Hörmander proved in his thesis 1955 the solvability of linear partial differential equa-tions with simple characteristics for which the Poisson bracket of the real and imaginaryparts of the highest order term vanishes identically. It was at that time expected that alllinear partial differential equations were solvable.

erefore it was a great surprise when Hans Lewy in 1957 presented a non-vanishingcomplex vector field that is not solvable. Actually, the vector field is the tangential Cauchy-Riemann operator on the boundary of a strictly pseudoconvex domain. Hörmanderproved in 1960 that almost all linear partial differential equations are not solvable, be-cause the vanishing of the bracket at the characteristics is both a necessary and non-genericcondition. is bracket condition also has consequences for the spectral instability of non-selfadjoint semiclassical operators and the solvability of the Cauchy problem for non-linearanalytic vector fields.

Hörmander was one of the leaders of the development of the research field, whichculminated in 2006 with the resolution of the Nirenberg-Treves conjecture: that condi-tion (PSI) is necessary and sufficient for the local solvability of differential equations withsimple characteristics. is condition refines the bracket condition, it only involves thesign changes of the imaginary part of the highest order terms along the bicharacteristicsof the real part.

In this talk, we shall present the background, the main results, and some generaliza-tions to equations with double characteristics and to systems of differential equations.

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On Hörmander’s L2 estimates for the d-bar equation

Duong H. Phong Tuesday 13:30–14:20Columbia University MA:7

One of the most powerful tools in complex analysis and complex geometry are theL2 estimates of Hörmander for solutions of the d-bar equation. On this occasion inHörmander’s honor, we take the opportunity to review this classical work of his, anddiscuss some more recent developments such as Ohsawa-Takegoshi extensions, Blocki’ssolution of the Suita conjecture, and joint work of the speaker with J. Song and J. Sturmon the degeneration of Kähler-Ricci solitons.

Boundary problems for pseudodifferential operators; the”transmission” property and Hörmander’s suggestions

Louis Boutet de Monvel Tuesday 14:35–15:25Universite Pierre et Marie Curie MA:7

In this talk I wish to review the transmission property for pseudodifferential operators,how it was used for boundary value problems, and a point of view of Hörmander.

Boundary conditions

Gerd Grubb Tuesday 15:40–16:30Copenhagen University MA:7

e talk will recollect some of Lars Hörmander’s writings connected with boundaryconditions, as well as some scientific exchanges between our neighboring universities.

Approximation and Related ProblemsOrganiser(s): Anton Baranov (St. Petersburg), Konstatin Fedorovskiy(Moscow)

Universal Taylor series and potential theory

Stephen Gardiner Monday 13:30–14:20University College Dublin MH:333

Broadly speaking, the notion of universality refers to a situation where a single object,together with a countable process, yields approximations to every object in some universalcollection of interest. is talk will discuss this phenomenon in relation to Taylor seriesfor holomorphic functions, and how potential theory has shed new light on the subject.

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Cm-approximation by solutions of elliptic equations

Konstantin Fedorovskiy Monday 14:35–15:25Bauman Moscow State Technical University MH:333

It is planned to discuss recently obtained results in the qualitative theory of approxima-tion of functions by solution of elliptic partial differential equations (including, in partic-ular, holomorphic, harmonic and polyanalytic functions and corresponding polynomials)in the norms of Whitney-type spaces Cm on compact subsets of Euclidean spaces.

On the behaviour of power series in the absence ofHadamard-Ostrowski gaps

Markus Nieß Monday 15:40–16:05TU Clausthal MH:333Coauthors: Thomas Kalmes, Jürgen Müller

We show that the partial sums of a power series f with radius of convergence onetend to infinity in capacity on (arbitrarily large) compact subsets of the complement ofthe closed unit disk, if f does not have so-called Hadamard-Ostrowski gaps. Regardinga recent result of Gardiner, this covers a large class of functions holomorphic in the unitdisk.

Approximation of L2 function on an interval by shifts and ex-ponentials

Yurii Belov Monday 16:05–16:30Saint Petersburg State University MH:333Coauthors: Anton Baranov, Alexander Borichev

Let f be a function inL2[0, 1]with support in [0, a], 0 < a < 1. Consider the familyof shifts f(x− t), 0 < t < 1−a. In contrast to the classical Wiener theorem, this familyis never complete in L2[0, 1], and the orthogonal complement contains the exponentialscorresponding to the zeros of the Fourier transform of f . e question posed by M.Carlsson and C. Sundberg is whether the system consisting of such exponentials and ofthe initial family of shifts is complete inL2[0, 1]. We show that the answer to this questionis positive.

Some Approximation Problems

Anthony G. O’Farrell Tuesday 13:30–14:20NUI, Maynooth MH:333

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e talk will describe some open problems in approximation, and the state of knowl-edge about them.

Convergence of two-point Pade approximants

Victor Buslaev Tuesday 14:35–15:00Steklov Mathematical Institute MH:333

Assume that algebraic functions f0 and f∞ are holomorphic at the points z = 0 andz = ∞ respectively and have nonempty finite sets of branch points. Let πn be a two-point Pade approximant of f0 and f∞, i.e. πn is a rational function Pn/Qn such thatdegPn ≤ n, degQn ≤ n, Qn ̸≡ 0 and

(Qnf0 − Pn)(z) = O(zn), z → 0,

(Qnf∞ − Pn)(z) = O(z−1), z → ∞.Using potential theory methods we will show that the sequense of Pade approximants

{πn}∞n=1 converges in capacity to the function f0 in some domain D0 ∋ 0 and to thefunction f∞ in some domain D∞ ∋ ∞. e geometrical properties of the complementC \ (D0 ∪D∞) will be described.

On strong asymptotic for two-point Pade approximants

Alexander Komlov Tuesday 15:00–15:25Steklov Mathematical Institute MH:333Coauthors: Sergey Suetin

For two-point Pade approximants of analytic functions the weak asymptotics is known(it was proved by Victor Buslaev in 2012). We plan to discuss the derivation of the strongasymptotics formula for two-point Pade approximants of the multivalued analytic func-tions of the type

f(z) =

p∏j=1

(z − zj)αj , where p ≥ 2, αj ∈ C\Z,p∑

j=1

αj = 0.

For this goal we obtain a differential equation of the second order satisfied by numeratorsof these two-point Pade approximants and the corresponding remainder functions. Afterthat we apply the classical Liuville–Steklov method to this equation.

On closed sets of approximation on Riemann surfaces

André Boivin Tuesday 15:40–16:05University of Western Ontario MH:333Coauthors: with Nadya Askaripour

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A closed subsetE of a (non-compact) Riemann surfaceR is called a set of holomorphic(respectively meromorphic) approximation if every function holomorphic on E can beapproximated uniformly on E by functions holomorphic (resp. meromorphic) on R. Awell-known theorem of C. Runge dating from 1885 gives a complete characterization ofthese sets when E is compact and R = C. e case E closed and R = C was solvedby A. Roth in 1938. Runge’s theorem (with E compact) was generalized to Riemannsurfaces in 1949 by H. Behnke and K.Stein. But, maybe somewhat surprisingly, for thegeneral case this problem is still open. We will give a survey of what is known includingthe construction of a two-sheeted Riemann surface with intriguing properties and someresults obtained more recently with Nadya Askaripour.

Wavelet approximation of harmonic functions in growthspaces

Pavel Mozolyako Tuesday 16:05–16:30Saint-Petersburg State University MH:333Coauthors: K. Eikrem, E. Malinnikova

For a nonincreasing function v : R+ 7→ R+ consider the space h∞v of harmonicfunctions in Rn+1+ which satisfy the following growth restriction

|u(x, t)| ≤ Kv(t), x ∈ Rn, t ∈ R+. (2)

We give description of the functions in this space in terms of their multiresolution ap-proximation. When the weight grows faster than t−a for some a, our result is in terms ofthe wavelet coefficients, for slow growing weights we consider partial sums of the waveletseries.We then use this description to study the boundary oscillation of the functions in h∞v .

PDEs, Nonlinear Waves and Dispersive EquationsOrganiser(s): Mark Groves (Saarbruecken) and Mats Ehrnström (Trond-heim)

Nonlinear resonance for dispersive equationswith a potential

Samuel Walsh Tuesday 13:30–13:55Courant Institute, NYU MH:BCoauthors: Pierre Germain and Zaher Hani

In this talk we shall present a general framework for proving global in time existenceand asymptotic properties of solutions for nonlinear dispersive equations with a potential.ese problems arise naturally in many contexts, e.g., quantum mechanics, nonlinear

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optics, general relativity, and in the study of soliton stability. e main building block isa theory of space-time resonance generalized to the spectral setting of the correspondingSchrödinger operator. As an example of the technique, we provide the proof of smalldata global in time well posedness and scattering for a quadratic nonlinear Schrödingerequation in three-dimensions.

Finite-energy solutions of the Chern-Simons-Higgs system

Sigmund Selberg Tuesday 13:55–14:20NTNU, Trondheim MH:BCoauthors: Achenef Tesfahun, NTNU

e Chern-Simons-Higgs system describes electromagnetic phenomena in planar do-mains, such as the Quantum Hall Effect. We will present recent results concerning thewell-posedness of the Cauchy problem for this system of nonlinear dispersive PDEs. Akey feature is the gauge invariance. By a judicious choice of gauge, favorable nonlinearcancellation properties are revealed, and moreover one is able to control the solution interms of the conserved energy, assuming that the initial energy is finite.

A dimension-breaking phenomenon for steady water waveswith weak surface tension

Erik Wahlén Tuesday 14:35–15:00Lund University MH:BCoauthors: Mark Groves, Shu-Ming Sun

I will discuss the bifurcation of three-dimensional periodically modulated solitarywaves from two-dimensional line solitary waves in the presence of weak surface tension.e new waves decay in the direction of propagation and are periodic in the transversedirection. e proof is based on spatial-dynamics and an infinite-dimensional version ofthe Lyapunov centre theorem. e method also reveals that the line solitary waves arelinearly unstable to transverse perturbations.

Existence and Conditional Energetic Stability of SolitaryGravity-capillary Water Waves with Constant Vorticity

Mark Groves Tuesday 15:00–15:25Universität des Saarlandes MH:BCoauthors: Erik Wahlén (Lund)

We present an existence and stability theory for gravity-capillary solitary waves withconstant vorticity on the surface of a body of water of finite depth. Exploiting a classicalvariational principle, we prove the existence of a minimiser of the wave energy E subject

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to the constraint I = 2µ, where I is the wave momentum and 0 < µ≪ 1. Since E andI are both conserved quantities a standard argument asserts the stability of the set Dµ ofminimisers: solutions starting near Dµ remain close to Dµ in a suitably defined energyspace over their interval of existence.

In the applied mathematics literature solitary water waves of the present kind are mod-elled as solutions of the long-wave equations of KdV or NLS type. We show that the wavesdetected by our variational method converge (after an appropriate rescaling) to solutionsof the appropriate model equation as µ ↓ 0.

Reconstruction of the pressure in long-wavemodelswith con-stant vorticity

Alfatih Ali Tuesday 15:40–16:00University of Bergen MH:BCoauthors: Henrik Kalisch (University of Bergen)

e effect of constant background vorticity on the pressure beneath steady long gravitywaves at the surface of a fluid is investigated. Using an asymptotic expansion for thestreamfunction, we derive a model equation and a formula for the pressure in a flow withconstant vorticity. e model equation was previously found by Benjamin (1962), andis given in terms of the vorticity ω0, and three parameters Q, R and S representing thevolume flux, total head and momentum flux, respectively.

e focus of this work is on the reconstruction of the pressure from solutions of themodel equation and the behavior of the surface wave profiles and the pressure distributionas the strength of the vorticity changes. In particular, it is shown that for strong enoughvorticity, the maximum pressure is no longer located under the wave crest, and the fluidpressure near the surface can be below atmospheric pressure.

Justification of the Nonlinear Schrödinger equation for theevolution of gravity driven 2D surface water waves in a canalof finite depth

Wolf-Patrick Düll Tuesday 16:00–16:25Universität Stuttgart MH:BCoauthors: Guido Schneider, C. Eugene Wayne

In 1968 V.E. Zakharov derived the Nonlinear Schrödinger equation for the 2D waterwave problem in the absence of surface tension, i.e., for the evolution of gravity drivensurface water waves, in order to describe slow temporal and spatial modulations of a spa-tially and temporarily oscillating wave packet. In this talk we give a rigorous proof thatthe wave packets in the two-dimensional water wave problem in a canal of finite depthcan be accurately approximated by solutions of the Nonlinear Schrödinger equation.

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Well-posedness of fractional degenerate parabolic equations

Espen R. Jakobsen Wednesday 13:30–13:55NTNU MH:BCoauthors: Nathael Alibaud, Simone Cifani

We consider convection diffusion equation with nonlinear convection and fractionalnonlinear diffusion terms. We give motivation for these equations, which are of mixedtype and can be seen e.g. as viscous conservation laws. en we motivate and intro-duce the relevant notion of solutions, entropy solutions, and show well-posedness of suchsolutions.

Global solutions of the two-component Camassa–Holm sys-tem

Katrin Grunert Wednesday 13:55–14:20NTNU MH:BCoauthors: Helge Holden, Xavier Raynaud

e two-component Camassa-Holm (2CH) system

ut − utxx + κux + 3uux − 2uxuxx − uuxxx + ηρρx = 0,ρt + (uρ)x = 0,

with arbitrary κ ∈ R and η ∈ (0,∞), serves as a model for shallow water. Furthermore,it is a generalization of the famous Camassa–Holm (CH) equation which has been studiedintensively. us naturally the question arises which results derived for the CH equationare also valid for the 2CH system. In this talk we will show how to describe global so-lutions. is question is of special interest since the 2CH system, like the CH equation,enjoys wave breaking and in general there are two possibilities how to continue solutionsthereafter. Namely, either the energy is preserved which yields conservative solutions orif energy vanishes from the system, we obtain dissipative solutions. Additionally, we willadmit initial data and hence solutions with nonvanishing asymptotics.

Steadywater waves with vorticity: spatial Hamiltonian struc-ture

Vladimir Kozlov Wednesday 14:35–15:00Linköping University MH:BCoauthors: Nikolay Kuznetsov

We consider the two-dimensional nonlinear problem of steady waves in a horizontalopen channel. e motion of water occupying the channel is supposed to be rotational

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with a prescribed vorticity distribution which is a Lipschitz function. We impose no re-striction on the type of waves and our considerations cover flows with counter-currents.Our aim is to derive Hamiltonian systems equivalent to the original problem of steadywaves.

Triply-periodic steady water waves in two dimensions

Mats Ehrnström Wednesday 15:00–15:25NTNU MH:BCoauthors: Erik Wahlén

We construct three-dimensional families of small-amplitude gravity-driven rotationalsteady water waves on finite depth. e solutions contain counter-currents and multiplecrests in each minimal period. e proof relies on a bifurcation argument which takesadvantage of a linear vorticity distribution, the strength of the background stream, andthe wave-length parameter.

New points of view of the classical P.D.E. theory in Morreyspaces

Maria Alessandra Ragusa Wednesday 15:40–16:05University of Catania MH:B

Aim of the author is to obtain some qualitative properties, in Morrey spaces, of thesolutions of partial differential equations of second order. ese are considered of elliptic,parabolic and ultraparabolic type, in divergence and nondivergence form. Basic idea is tostudy the behaviour of some singular integral operators in these classes. en, writing therepresentation formula of the higher order derivatives of the solutions of the equations interms of these operators it is possible to gain some regularity results. Let us point out thatthe coefficients of the higher order terms could be discontinuous. As a consequence of theabove results local Holder continuity of the solutions is also proved. First step is to studya nondivergence form equation of elliptic type. en, the parabolic one and later theultraparabolic equations, We point out that the natu- ral geometry for the ultraparabolicoperators is not euclidean but is given by a suitable groups structure. Moreover, reguarityproperties are also showed for some kind of systems. Keywords: Second order partialdifferential equations, Morrey spaces, discontinuous coeffcients.

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Operators, Functions and SystemsOrganiser(s): Amol Sasane (Lund, LSE)

Weighted admissibility of linear systems on Bergman andDirichlet spaces

Andrew Wynn Tuesday 13:30–13:55Imperial College London MH:362DCoauthors: Birgit Jacob, Sandra Pott, Eskil Rydhe

Admissibility of an observation operator is a key ingredient of a well posed linearsystem. In this talk we consider discrete time infinite dimensional linear systems of theform

xn+1 = Txn, yn = Cxn, n ∈ N,where the observation operator C ∈ X∗ is said to be α-admissible for T ∈ L(X) if

∞∑n=0

(1 + n)α |CTnx0|2 dt ≤M2∥x0∥2X , x0 ∈ X.

It is easy to show that α-admissibility implies the resolvent growth bound

∥C(I − ω̄T )−1∥X∗ ≤M

(1− |ω|2) 1−α2, ω ∈ D,

but deciding whether the converse is true is a difficult question. Originally the questionwas posed in the case α = 0 (and for continuous time systems) and became known as theWeiss conjecture. e original conjecture is true for some important classes of operator(e.g. normal, contractive) but is false in general.

In the weighted case, the situation is more complicated. IfT is normal then admissibil-ity is closely related to Carleson measures on either weighted Bergman (positive weights) orDirichlet (negative weights) spaces. In this case, the conjecture is true for positive weightsbut false for negative ones, reflecting the differing characterisations of Carleson measuresfor these function spaces. We show that a sufficient condition for weighted admissibilitycan be used to produce a simple sufficient condition for Carleson measures on Dirichletspaces. Finally, we discuss the truth of the Weiss conjecture for the unilateral shift S onthe Hardy space H2(D) and on weighted Bergman spaces.

Weighted admissibility with respect to the right shift onL2(R+, dt)Eskil Rydhe Tuesday 13:55–14:20Lund University MH:362DCoauthors: Birgit Jacob, Andrew Wynn.

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In this talk I consider scalar valued observation operators that areα-admissible (α ≥ 0)with respect to the right shift semigroup on L2(R+, dt). e main theorem is that suchoperators can be characterized using a resolvent type condition. For α = 0 this is aspecial case of the Weiss conjecture for contractive semigroups, which was proved by Jacob,Partington and Weiss around 2000. e proof uses a wavelet technique and exploits aconnection to a generalized form of Hankel operators.

Weighted Admissibility and Embedding Theorems inBergman spaces

Sandra Pott Tuesday 14:35–15:00Lund University MH:362DCoauthors: Birgit Jacob (Universität Wuppertal, Ger-many), Jonathan R. Partington (University of Leeds, UK)

We consider weighted admissibility for diagonal semigroups in a fairly general settingby proving new embedding theorems for weighted Bergman spaces with radial weights.

Generalized poles - About the lengths of Jordan chains

Annemarie Luger Tuesday 15:00–15:25Stockholm University MH:362D

Let A be a symmetric matrix, then for each eigenvalue of A the algebraic and geo-metric multiplicity coincides. is is reflected in the fact that the resolvent (and boardedresolvents) have poles of order not larger than 1.

In the talk we are discussing the more interesting situation of an operator A in an infi-nite dimensional space, where eigenvalues can be embeddeed in the continous spectrum,which leads to non-isolated singularities. Instead of self-adjointness we require anotherkind of symmetry: Let B be a self-adjoint boundedly invertible self-adjoint operator, forwhich the spectrum on the negative halfline consists of finitely many eigenvalues only.For A, the operator of interest, it is now assumed that BA is selfadjoint.

In this case A can have Jordan chains (with finite length). And the question appearshow can the length of such a Jordan chain can be obtained from analytic properties ofboarded resolvents. We will give an overview of the history of the problem (which isabout 30 years old) and present the recently obtained solution.

An analogue of Serre’s conjecture and Control Theory

Amol Sasane Wednesday 13:30–13:55Lund University MH:362D

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e Quillen-Suslin eorem, formerly known as Serre’s Conjecture, is a result in com-mutative algebra about the relationship between free modules and projective modules overpolynomial rings. It states that every finitely generated projective module over a poly-nomial ring is free. Certain rings of holomorphic functions arise naturally as classes oftransfer functions of stable control systems. Algebraic properties of these rings of transferfunctions then play an important role in solving control theoretic problems. In particular,in this talk we will show an analogue of the Quillen-Suslin eorem for a particular ringof holomorphic functions and explain the role this plays in the Stabilization Problem inControl eory.

Infinite-dimensional Lur’e systems: the circle criterion, input-to-state stability and the converging-input-converging-stateproperty

Hartmut Logemann Wednesday 13:55–14:20University of Bath MH:362D

e generic system under consideration is of Lur’e type: a feedback interconnection ofa well-posed infinite-dimensional linear system and a static nonlinearity. It is shown thatthe conditions of the well-known circle criterion guarantee input-to-state stability of theLur’e system. is result is then used to prove that the Lur’e system has the converging-input-converging-state property, provided an ’incremental’ version of the circle criterionconditions holds.

Reduced Order Internal Models in Robust Output Regulation

Lassi Paunonen Wednesday 14:35–15:00Tampere University of Technology MH:362DCoauthors: Seppo Pohjolainen

In this presentation we consider robust output regulation for distributed parametersystems. In particular we are interested in the internal model principle, which can be usedin characterizing controllers that achieve robust output tracking and disturbance rejectionfor a linear system. We show that if we do not require robustness with respect to arbitraryperturbations to the operators of the plant, then there may exist robust controllers that donot contain a full-sized internal model of the exosystem’s dynamics. e existence of suchcontrollers depends on the class of admissible perturbations. We also introduce a straight-forward way of testing the robustness of a controller with respect to given perturbations.e theoretic results are illustrated with examples.

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Proving existence of solutions of PDEs using feedback theory

Mikael Kurula Wednesday 15:00–15:25Åbo Akademi MH:362DCoauthors: Hans Zwart

In careful analysis of linear PDEs one often needs to prove that a certain PDE isgoverned by a contraction semigroup. In this talk a recent method for achieving this ispresented, using the example of a heat equation on an n-D bounded Lipschitz domain.Techniques used are Cayley transformation and feedback theory for continuous-time lin-ear systems. Assuming sufficient time, examples of damped wave equations are also pre-sented.

Harmonic Analysis and OperatorsOrganiser(s): Tuomas Hytönen (Helsinki) and Andreas Rosen (Linköping)

Lp theory for outer measures and its application in time-frequency analysis

Christoph Thiele Wednesday 13:30–14:20Universität Bonn MH:309ACoauthors: Yen Do

Outer measures are subadditive set functions. Classically an outer measure is usedas stepping stone towards a measure, via restriction of the set function to Caratheodorymeasurable sets. We are interested in outer measures which do not give rise to manyCaratheodory measurable sets. A classical example of such an outer measure is Newtoncapacity. With some care one can develop a theory of Lp spaces on outer measure spaces.Our main new application of this is a reformulation of time frequency analysis as Lp theoryfor some particular outer measures, in particular we reformulate a proof of boundednessof the bilinear Hilbert transform.

Lp estimates in the Calderón problem

Mikko Salo Wednesday 14:35–15:00University of Jyväskylä MH:309A

In this talk we discuss certain estimates that arise in the study of the inverse problem ofCalderón, where one tries to determine coefficient functions in an elliptic equation fromboundary measurements of solutions. ese estimates are of general interest as well.

We will focus on Lp resolvent estimates and Lp Carleman estimates with limitingweights in variable coefficient (non-Euclidean) situations. Such estimates were known

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before for the standard Laplacian in Euclidean space and on the torus. e proofs are basedon a Hadamard parametrix construction together with oscillatory integral bounds due toHörmander, Carleson-Sjölin and Stein. As an application, we discuss a uniqueness resultfor determining a nonsmooth potential from boundary measurements for the stationarySchrödinger equation.

e talk is based on joint works with David Dos Santos Ferreira (Université de Lor-raine) and Carlos Kenig (University of Chicago).

A local Tb theorem for vector-valued weighted paraproducts

Andreas Rosén Wednesday 15:00–15:25Linköpings universitet och Göteborgs univer-sitet

MH:309A

I will present a substantial improvement of the local Tb argument which has beenused in the proof of the Kato square root estimate, that applies to paraproducts withvector-valued weighted expectation, under suitableA2 assumptions on weights. is newresult was found recently in connection with joint work with P. Auscher, D. Rule and Y.Sire on boundary value problems for degenerate elliptic divergence form equations. eproof combines the stopping time and compactness argument from the Kato estimate,with another parallel stopping time and compactness argument in corona style for theweights.

Hardy Spaces HpL Associated with Elliptic Operators and theirConnection with Lp Spaces

Alan McIntosh Thursday 13:30–14:20Australian National University, Canberra MH:309A

ere is by now a body of knowledge about Hardy spacesHpL associated with secondorder elliptic operators L. In these spaces, certain bounded functions of L, or Riesz trans-forms associated with L, may automatically be bounded operators. It is then of interestto know how these spaces relate to Lebesgue spaces Lp. I shall survey some of the resultswhich are known - or not known - on this subject, with reference to corresponding resultsconcerning Hardy spaces associated with first order systems. I shall then present resultsfrom a recent paper of mine with Auscher and Morris, and from ongoing work with Freyand Portal.

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The two weight problem for the Bergman projection andSarason Conjecture

Maria Carmen Reguera Thursday 14:35–15:00Universitat Autònoma de Barcelona MH:309ACoauthors: A. Aleman and S. Pott

We will present some partial results on the two weight problem for the Bergman pro-jection on the disc. is problem is connected to a conjecture of Sarason on the composi-tion of Toeplitz operators in the Bergman space. In the setting of Sarason’s Conjecture wewill provide a complete characterization. is is joint work with A. Aleman and S. Pott.

Sharp weighted bounds: towards rough operators

Tuomas Hytönen Thursday 15:00–15:25University of Helsinki MH:309A

e A2 conjecture (a sharp quantitative bound for the weighted norm of singular in-tegral operators) was first confirmed for special classical transforms with infinitely smoothkernels, then finally under general Calderon-Zygmund standard conditions. e currentlyknown minimal assumptions require slightly more than the classical Dini-continuity onthe kernel. I will also discuss an interesting open problem concerning rough (boundedbut non-continuous) kernels for which weighted bounds are known qualitatively, but theprecise quantitative estimate remains unknown.

Boundary behavior for non-negative solutions to non-linearand degenerate parabolic pdes

Kaj Nyström Thursday 15:40–16:05Uppsala University MH:309A

In this talk I will describe recent joint works concerning the boundary behavior ofnon-negative solutions to equations generalizing second order parabolic pdes in divergenceform. Equations of interest include non-linear equations with linear growth, degenerateequations with ellipticity measured byAp-weights as well as non-linear parabolic equationof p-parabolic type.

Weighted inequalities for the geometric maximal operator

Sorina Barza Thursday 16:05–16:30Karlstad University MH:309A

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We will characterize the two-weight strong- and weak-type Lebesgue norm inequalitiesfor the multidimensional geometric fractional operator. Although we also have to assumean extra condition on the weight on the right-hand side it is much more transparentthan that imposed in a previous work, Cruz-Uribe, D., e minimal operator and thegeometrical maximal operator in Rn, Studia Math. 144(1)(2001).

Classification of Operator Algebras: Complexity,Rigidity and Dynamics

Organiser(s): Sören Eilers (Copenhagen)

Recent progress in classification of simple C*-algebras

Hiroki Matui Wednesday 13:30–14:20University of Copenhagen MH:333

We discuss classification of unital simple separable nuclear stably finite C*-algebras byK-theory. When the algebra has a unique tracial state, we prove that it has decompositionrank at most three if and only if it is quasidiagonal and has strict comparison. Moreover,such an algebra tensored with a UHF-algebra is shown to have tracial rank zero. We alsodiscuss several applications. is is joint work with Y. Sato.

C*-algebras associated to Boolean dynamical systems

Eduard Ortega Wednesday 14:35–15:00NTNU MH:333Coauthors: T.M. Carlsen

I am going to explain what a Boolean dynamical system is, and how to define a uni-versal C*-algebra associated to it. We will give basic background and examples.

Endomorphism semigroups of II1 factors

Deprez Steven Wednesday 15:00–15:25Københavns universitet MH:333

Recently, Adrian Ioana proposed to study the endomorphism semigroup of a typeII1 factor. is semigroup End(M) is the semigroup of all ultraweakly continuous ∗-homomorphisms from M to itself, where we identify two endomorphisms ψ1, ψ2 if thereis a unitary u in M such that ψ1(x) = uψ2(x)u∗ for all x. In particular, Ioana raised thequestion of which semigroups appear as endomorphism semigroups of type II1 factors. Ishow that all countable semigroups appear in this way.

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Endomorphisms of Graph C*-Algebras

Wojciech Szymanski Thursday 13:30–14:20University of Southern Denmark MH:333Coauthors: Roberto Conti, University of Rome ‘LaSapienza’ and Jeong Hee Hong, Korea Maritime Uni-versity

We discuss recent progress in the study of automorphisms and, more generally, endo-morphisms of graph C*-algebras. In particular, a combinatorial approach to permutativeendomorphisms is presented and the Weyl group of a graph algebra is introduced anddiscussed. A relation between the Weyl group and shift automorphisms is indicated. especial case of the Cuntz algebras is mentioned.

Classification of Cuntz-Krieger algebras and Graph algebras

Gunnar Restorff Thursday 14:35–15:00University of the Faroe Islands MH:333

In the talk I will cover some recent progress in trying to get strong classification forpurely infinite Cuntz-Krieger algebras and graph algebras and describe some problem thatarise.

Corners of Cuntz-Krieger algebras

Sara Arklint Thursday 15:00–15:25University of Copenhagen MH:333

We provide conditions on a graph describing exactly when its associated graph C*-algebra is a Cuntz-Krieger algebra. Using this, one can show that the class of Cuntz-Krieger algebras is closed under stable isomorphism within the class of unital C*-algebras,and consequently that corners of Cuntz-Krieger algebras are Cuntz-Krieger algebras.

Gradations on Leavitt path algebras

Johan Öinert Thursday 15:40–16:05Lund University MH:333

Leavitt path algebras were introduced during the last decade and are currently receiv-ing a lot of attention from algebraists as well as analysts. ere are (at least) two naturalways to define a group gradation on a Leavitt path algebra. In this talk, I will describethese gradations and explain how one may use the graded structure to swiftly obtain con-ditions for simplicity of a (row-finite) Leavitt path algebra, and to prove the Cuntz-Kriegeruniqueness theorem.

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A non-standard hierarchical tiling

Maria Ramirez-Solano Thursday 16:05–16:30University of Copenhagen MH:333

e Bowers and Stephenson conformally regular pentagonal tiling of the plane enjoysremarkable combinatorial and geometric properties. Since it does not have finite localcomplexity in any usual sense, it is beyond the standard tiling theory. On the other hand,the tiling can be completely described by its combinatorial data that, rather automatically,has finite local complexity. With the aim to compute its K-theory, we construct the hulland C*-algebra of this tiling solely from its combinatorial data. As the tiling possesses nonatural R2 action by translation, there is no a priori reason to expect that the K-theory ofthe C*-algebra of the tiling is the same as the K-theory or cohomology of the hull of thetiling, and it would be very interesting if they were different.

Operator Theory and Complex AnalysisOrganiser(s): Olivia Constantin (Canterbury)

Dixmier trace for Toeplitz and Hankel operators on weightedFock spaces

Miroslav Englis Wednesday 13:30–13:55Academy of Sciences, Prague MH:CCoauthors: H. Bommier and E.-H. Youssfi, Marseille

We give criteria for the membership of Toeplitz operators and of products of Hankeloperators, with symbols of a certain type, in Schatten ideals and in the Dixmier class, andformulas for their Dixmier trace, on a variety of weighted Segal-Bargmann-Fock spaceson the complex plane.