Afskedslecture-slides-mfj-finalweb.math.ku.dk/~mfj/Afskedslecture-slides-mfj-final.pdfMy lecture will focus on three themes: Mathematics: Analysis on Symmetric spaces, spherical functions

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Mogens Flensted-Jensen a few dates

• Born 1942• Student 1961• Starts at UniCph 1963• Cand.scient. 1968• Ass.prof.(lektor) 1973• Professor KVL 1979• Professor UniCph 2007 (at IGM by “infusion”)• Professor UniCph 2012 (at IMF by “confusion”)• Emeritus 2012

Mogens Flensted-Jensen - Department of Mathematical Sciences

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Mathematics at KVL


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Updates:Tomas Vils Pedersen lektor 2000-Henrik L. Pedersen lektor 2002-2012Professor 2012 -

1975: Institut for Matematik og Statistik; 1991: Institut for Matematik og Fysik; 2004: Institut for Grundvidenskab (including chemistry); 2009: Institut for Grundvidenskab og Miljø2012:

2012: Institut for Matematiske Fag

Department Names


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Retirement Lecture May 3 2013

Mathematics and Research policy: A view back on activities, I was happy to take part in.

Mogens Flensted-JensenDepartment of Mathematical SciencesHomepage: http://www.math.ku.dk/~mfj/

June 1st 1979 I left KU for Landbohøjskolen


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Great celebration!

June 1st 1979 – Sept. 30th 2012


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Mathematics and Research policy

My lecture will focus on three themes: Mathematics: Analysis on Symmetric spaces, spherical

functions and the discrete spectrum. Research council work: From the national research

councils to the creation of the ERC (European Research Council).

My journey from University of Copenhagen to “Landbohøjskolen” and the “infusion” back again.

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Ordsprogenens Bog 7:29 “Gud skabtemennesket som de burde være; men de harså mange sære ting for”.

Ecclesiastes 7:29 “Lo, this only have I found, that God hath made man upright; but they have sought out many inventions.”.

Is pure mathematics useful?

Mathematics: Analysis on Symmetric spaces, spherical functions and the discrete spectrum.Børge Jessen: Selected Topics in Analysis

• I was introduced to Fourier integralsEsben Kehlet: Functional analysis

• Master thesis: Disintegration of von Neumann algebrasWerner Fenchel: Geometry and analysis

• Go to The Mittag-Leffler Institute!Sigurdur Helgason: Symmetric spaces and spherical functions

• My mathematical “fate” was establishedTom H. Koornwinder: Special functions

• The Fourier-Jacobi transformJacques Faraut: Invitation to Tunis

• New Idea: Duality between Riemannian and Non-Riemannian symmetric spaces

MIT 1976-77: • David Vogan: Minimal K-types• Toshihiko Matsuki: Closed orbits


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Børge Jessen


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Sigurdur Helgason


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Mittag-Leffler Institute1970-71 and 1995


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Mittag-Leffler Institute - Housing


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In the spring of 1975 Jacques Faraut invited me to spend one month I Tunis. One day on the bus coming back from the university, I suddenly realized a relation between “SL(2,C)” and “SL(2,R)” coming from their embedding in “SO(2,2)”. This led me to, what I later called “a duality between non-Riemannian and Riemannian symmetric spaces”.

A new idea!

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Symmetric Spacesinmathematical terms

A Symmetric Space is an affine manifold for which the geodesic reflection in any point is an affine isomorphism


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A partial duality


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Spherical Functions on a Symmetric Space G/K

General non-Riemannian Symmetric Spaces G/H

Discrete Series for Symmetric Spaces


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My D.Sc. defense 1980


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The classical addition formula for the cosine function:cos(x+y) = cos(x)cos(y) - sin(x)sin(y)

With Tom Koornwinder: The Fourier-Jacobi transform

The addition formula:φλ(akb) = φλ(a) φλ(b) + .........+ …..

A long formula:

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Travels with mathematics 1978 - 1999

Kleebach, Lyminy, Bielefeld, Oberwolfach, Strasbourg, Paris, Oslo, Les-Plain-s-Bex/Sch, Garwitz/DDR, Torino, Leiden, Amsterdam, Maryland, St. Louis, MIT, San Diego, Athens/GA, Reykjavik, Tunis, Nancy, Lyon, Bern, Utrecht, Hamburg, Tokyo, Kyoto, Hiroshima, Adelaide, Sydney, Göttingen, Main, Abijan, Dubrovnik, Srini/Tjek., Nice, Cornell, San Antonio, Stockholm, Lund, Uppsala, Lindköping, Edingburgh.

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Highlight 1: Harish-ChandraPlancherel Formula for G

Discrete seriesAsymptotic

expansionsSpherical functionsKey Paper:


of Mathematical Sciences

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Highlight 2: HelgasonGeometric Analysis on G/K

Spherical functions and Paley-Wiener theorems

Poisson transform: Helgason conjecture

Key paper:



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Highlight 3: Kashiwara et al. Solution to Helgason Conjecture for G/K

HyperfunctionsSystems of PDE’s with

regular singularities

Key paper:



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Highlight 4: ArthurPaley-Wiener Theorem for G

Ideas from Campoli-Wallach

Abstract intertwiningrelations

Analytic continuation

Key paper:J. Arthur: A Paley-Wiener theorem for real reductivegroups.Acta Math. 150 (1983), 1-90



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Highlight 5: Flensted-JensenExistence of Discrete Series for G/H

Duality between non-compact and non-Riemannian symmetric spaces

A rank conditionA simple formula for the discrete series

Key paper:

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Highlight 6: OshimaSolution to MFJconjecture for G/HPDE’s with regular singularieties

and boundary values

Key ”paper”:



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Highlight 7: Oshima-MatsukiClassification of Discrete Series for G/H

Closed orbitsBoundary relations

Key paper:

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Highlight 8: Delorme Plancherel Formula for G/H

TruncationsSchwartz space considerations

Key paper:Delorme PatrickFormule de Plancherel pour les espaces symétriquesréductifsAnn. of Math. (2) 147, no. 2, 417--452, 1998

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Highlight 9: Ban-Schlichtkrull Paley-Wiener Theorem for G/H

Spherical distributionsResidue calculusAbstract intertwining relation

Key paper:E.P. van den Ban and H. SchlichtkrullThe Paley–Wiener theorem for a reductive symmetric space, Annals of Math. 164 (2006), 879–909. May 3 2013


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Plancherel Formula for G/H

MLI November 1995

Paley-Wiener Theoremfor G/HMLI November 1995


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A few snapshots


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Japan August 1986

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Roskilde 1992 – Helgason 65 years!


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At the Shock-price ceremony for Andrew Wiles


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Drawing by Saint-Exupéry


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The Mathematics Doing mathematical research is a kind of art:

You must understand (to a certain extend) the known mathematical world (theory)

You must see some “interesting” unexplored region You must begin to explore such a region You design or discover the right “map” of the region (i.e.

formulate a hypothesis) – This is the “art” part You must prove it rigorously – This is where you need

craftsmanship and ingenuity

In this connection we, mathematicians, talk about

Beauty!

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In mathematics we talk about “beauty”

When the “art” of designing the “map” gives a result, which is

Build on easy accessible concepts Easy to conceive and understand the structure and

the content Has not been understood before Is difficult to prove rigorously

Research council work: From the national research councils to the creation of the ERC (European Research Council).

SJVF (Danish Agricultural and Veterinary Research Council)

• Chairman 1997-2003


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Abel Prize to Srinivasa S. R. Varadhan 2007Mogens Flensted-Jensen - Department of Mathematical Sciences

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Danish EU-presidency Autumn 2002 Conference October 7-8: Do we need a European Research Council?

Mogens Flensted-Jensen, Chairman, Board of the Danish Research councils Enric Banda, secretary general of ESF Sven Frøkjær, Danish Medical Research Council Knud Larsen from the ministry of Science, Technology and Innovation Pär Omling, Swedish Research Council Nina Prætorius, Danish Research Council for the Humanities Clara de la Tore, European Commission Peder Olesen Larsen, former chair of the National Danish Research Foundation Vibeke Hein Olsen and David Grønbæk of the Research Agency

ERCEG: European Research Council Expert Group 2003

Hard work 2003-2004

Dan Brändström, Director of the Bank of Sweden Tercentenary Foundation Olle Edqvist, his assistant Vibeke Hein Olsen, Danish Research Agency

Danish EU-presidency conference October 7-82002


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Great Success!

European Science Foundation November 2002


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The members of the Expert GroupProfessor Federico Mayor, ChairProfessor Mogens Flensted-Jensen, Vice ChairProfessor Norbert Kroó, Dr. Wilhelm Krull, Professor David J. McConnellProfessor Gérard MégieProfessor Helga NowotnyDr John TaylorMrs Myrsini Zorba

ERCEG: European Research Council Expert Group 2003“The Mayor group”

Professor Peter Nijkamp, observer NLMr Peter Kind, observer EC Professor Dan Brändström, Secretary

Three essential problems:• The ERC should rest its support solely on

scientific merits. • Oversubscription• Subsidiarity

Director General of DG Research, Achilleas Mitsos:• European wide competition on investigator-driven

research is an added value


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ERCEG: European Research Council Expert Group 2003


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Mayor reportDecember 2003

AutonomyFundingAccountabilityGovernanceSpecific mission

Commissionaire Philippe Busquinat Nobel Party 2003

• Europe need more basic research• I hope you can create a European

Research Council• So we can have a competition

between the best teams of research on an European level


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Frontier Research: The European ChallengeHigh-Level Expert Group ReportFunding of research through a European-wide competition:

• Added value above and beyond what can be achieved at the national level

• The single most important means to remedy Europe’s current weakness in high quality research

The main benefits of the ERC include the following:• Encouraging and supporting the finest talent• Selectivity, agility and focus• Status and visibility for research leaders• Dynamic structural effects on the European research system• Economic benefits• Societal benefits

Harris Report May 2005

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The Proposal for FP72007 – 2013EC April 2005

Co-operation 44.7 bil. Euro (4-9/Y)Ideas (ERC) 11.9 bil. Euro (1-2.5/Y)People (M-C) 7.2 bil. Euro (0.5-1.6/Y)Capacity 7.5 bil. Euro (0.6-1.6/Y

(Numbers by April 2005 – reduced somewhat later)

ERC was created in 2007 with a budget growing up to about 2 billion Euros a year

ERC 5 years celebration I Brussels March 28 2012


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ARC in Singapore 2006-20013


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ResearchCentersofExcellenceinSingapore.(Each~DKR600.000over5‐10years)

Singapore Center on Environmental Life Sciences Engineering The Centre is led by Professor Staffan Kjelleberg, Scientia Professor from the University of New South Wales, Sydney Australia

Mechanobiology Institute, Singapore The Mechanobiology Institute, Singapore is led by Professor Michael Sheetz, professor from the Department of Biological Sciences at Columbia University.

Earth Observatory of Singapore The EOS is led by Professor Kerry Sieh, a former Professor of Geology in Caltech and chaired professor in Caltech's Tectonics Observatory

Cancer Science Institute of Singapore The CSI Singapore is led by Professor Daniel Tenen from Harvard Medical School.

Centre for Quantum Technologies Headed by Professor Artur Ekert (Professor of Quantum Physics, University of Oxford),

AcademicResearchCouncilgivingadvicetoSingaporeGovernmentonResearchanduniversitypolicy.

The Nobel Party 2009


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From University of Copenhagen to Landbohøjskolen” and the “infusion” back.

• Teaching• Mathematics: Research and travel• Fagråd• IT-administration• PhD-education policy• Konsistorium• Dina• Research councils• Evaluation of Danish education (Math, Phys, Chem)• Research based public service• Vice-dean for teaching• Fusion processes• Great colleagues


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Institut for matematik og statistik 1989


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Danish Informatics Network in the Agricultural Sciences


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Mathematics is easy

Proof: LIFE is difficult!


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Mathematics is easy


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My Colleague Poul Einer Hansenand Roal Als

Interesting translation by Poul Einer:


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Mats RudemoProfessor of StatisticsA great Colleague!


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Poul Einer’sPoem to him!


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Research basedPublic-service

Mathematics at KVL


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Updates:Tomas Vils Pedersen lektor 2000-Henrik L. Pedersen lektor 2002-2012Professor 2012 -

1975: Institut for Matematik og Statistik; 1991: Institut for Matematik og Fysik; 2004: Institut for Grundvidenskab (including chemistry); 2009: Institut for Grundvidenskab og Miljø2012:

2012: Institut for Matematiske Fag

Many fusions!!


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Pointing to the future: I hope that


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the question about cuspidality for semisimple symmetric spaces G/H can be solved.

the ERC shall continuously develop as the place for “the Olympics” in European research.

the research based public‐sector service along with research based teaching will grow in quality and in mutual respect.

we, after the “infusion”, can preserve and develop the strong KVL‐spirit of being at the university not only for our own research, but also in order to assist students and researcher’s from other fields.

Thank You!


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I want to thank my many colleagues and collaborators within and outside of mathematics!

In particular I want to thank my wife, Inger, and our children, Mads and Mikala for their support and bearing with me during the years.

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Thank you very much for listening to me!

You are all most welcome to the reception on the 4th floor of the Math-buildingMogens Flensted-Jensen, Professor of Mathematics (Emeritus)Department of Mathematical SciencesUniversity of CopenhagenUniversitetsparken 5DK-2100 Copenhagen ØPhone: +45 35 32 07 80Mobile:+45 26 31 26 65E-mail: [email protected]: http://www.math.ku.dk/~mfj/


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Documents

Afskedslecture-slides-mfj-finalweb.math.ku.dk/~mfj/Afskedslecture-slides-mfj-final.pdfMy lecture will focus on three themes: Mathematics: Analysis on Symmetric spaces, spherical functions