5/2/2013 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mathematics at KVL Mogens Flensted-Jensen a few dates Updates: Tomas Vils Pedersen lektor 2000- Henrik L. Pedersen lektor 2002-2012 Professor 2012 - Retirement Lecture May 3 2013 • Born 1942 Department Names • Student 1961 1975: Institut for Matematik og Statistik; 1991: Institut for Matematik og Fysik; Mathematics and Research policy: • Starts at UniCph 1963 2004: Institut for Grundvidenskab (including chemistry); A view back on activities, I was • Cand.scient. 1968 2009: Institut for Grundvidenskab og Miljø • Ass.prof.(lektor) 1973 2012: happy to take part in. • Professor KVL 1979 • Professor UniCph 2007 (at IGM by “infusion”) • Professor UniCph 2012 (at IMF by “confusion”) Mogens Flensted-Jensen • Emeritus 2012 2012: Institut for Matematiske Fag Department of Mathematical Sciences Homepage: http://www.math.ku.dk/~mfj/ May 3 2013 May 3 2013 May 3 2013 Dias 1 Dias 2 Dias 3 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences st June 1 1979 I left KU for Landbohøjskolen June 1st 1979 – Sept. 30th 2012 Mathematics and Research policy Great celebration! 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. May 3 2013 May 3 2013 May 3 2013 Dias 4 Dias 5 Dias 6 1 5/2/2013 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mathematics: Analysis on Symmetric spaces, spherical Børge Jessen Is pure mathematics useful? functions and the discrete spectrum. Børge Jessen: Selected Topics in Analysis Ordsprogenens Bog 7:29 “Gud skabte • I was introduced to Fourier integrals mennesket som de burde være; men de har Esben Kehlet: Functional analysis så mange sære ting for”. • Master thesis: Disintegration of von Neumann algebras Werner Fenchel: Geometry and analysis • Go to The Mittag-Leffler Institute! Ecclesiastes 7:29 “Lo, this only have I found, Sigurdur Helgason: Symmetric spaces and spherical functions that God hath made man upright; but they • My mathematical “fate” was established have sought out many inventions.”. Tom H. Koornwinder: Special functions • The Fourier-Jacobi transform Jacques 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 May 3 2013 May 3 2013 May 3 2013 Dias 7 Dias 8 Dias 9 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Sigurdur Helgason Mittag-Leffler Institute Mittag-Leffler Institute - Housing 1970-71 and 1995 A new idea! 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”. May 3 2013 May 3 2013 May 3 2013 Dias 10 Dias 11 Dias 12 2 5/2/2013 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences May 3 2013 May 3 2013 May 3 2013 Dias 13 Dias 14 Dias 15 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences A partial duality Symmetric Spaces in mathematical terms A Symmetric Space is an affine manifold for which the geodesic reflection in any point is an affine isomorphism May 3 2013 May 3 2013 May 3 2013 Dias 16 Dias 17 Dias 18 3 5/2/2013 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Spherical Functions on a Symmetric Space G/K Discrete Series for Symmetric Spaces General non-Riemannian Symmetric Spaces G/H May 3 2013 May 3 2013 May 3 2013 Dias 19 Dias 20 Dias 21 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences May 3 2013 My D.Sc. defense 1980 A long formula: 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) + .........+ ….. May 3 2013 Mogens Flensted-Jensen - Department of Mathematical Sciences May 3 2013 Dias 22 Dias 23 Dias 24 4 5/2/2013 Mogens Flensted-Jensen - Department of Mathematical Sciences Highlight 1: Harish-Chandra Highlight 2: Helgason Travels with mathematics 1978 - 1999 Plancherel Formula for G Geometric Analysis on G/K Kleebach, Lyminy, Bielefeld, Oberwolfach, Discrete series Spherical functions and Strasbourg, Paris, Oslo, Les-Plain-s-Bex/Sch, Paley-Wiener Asymptotic Garwitz/DDR, Torino, Leiden, Amsterdam, theorems expansions Maryland, St. Louis, MIT, San Diego, Athens/GA, Poisson transform: Reykjavik, Tunis, Nancy, Lyon, Bern, Utrecht, Spherical functions Helgason conjecture Hamburg, Tokyo, Kyoto, Hiroshima, Adelaide, Key Paper: Key paper: Sydney, Göttingen, Main, Abijan, Dubrovnik, Srini/Tjek., Nice, Cornell, San Antonio, Stockholm, Lund, Uppsala, Lindköping, Edingburgh. May 3 2013 May 3 2013 27 May 3 2013 Dias 26 Mogens Flensted-Jensen - Department Mogens Flensted-Jensen - Department Dias 25 of Mathematical Sciences of Mathematical Sciences Highlight 3: Kashiwara et al. Highlight 4: Arthur Highlight 5: Flensted-Jensen Solution to Helgason Conjecture for G/K Paley-Wiener Theorem for G Existence of Discrete Series for G/H Ideas from Campoli- Duality between non-compact and non- Hyperfunctions Wallach Riemannian symmetric spaces Systems of PDE’s with Abstract intertwining A rank condition regular singularities relations A simple formula for the discrete series Analytic continuation Key paper: Key paper: Key paper: J. Arthur: A Paley-Wiener theorem for real reductive groups. Acta Math. 150 (1983), 1-90 May 3 2013 28 May 3 2013 29 May 3 2013 30 Mogens Flensted-Jensen - Department Mogens Flensted-Jensen - Department Mogens Flensted-Jensen - Department of Mathematical Sciences of Mathematical Sciences of Mathematical Sciences 5 5/2/2013 May 3 2013 Highlight 7: Oshima-Matsuki Highlight 6: Oshima Classification of Discrete Series for G/H Solution to MFJ Highlight 8: Delorme Plancherel Formula for G/H conjecture for G/H Closed orbits Key paper: PDE’s with regular singularieties Boundary relations and boundary values Truncations Schwartz space considerations Key ”paper”: Key paper: Delorme Patrick Formule de Plancherel pour les espaces symétriques réductifs Ann. of Math. (2) 147, no. 2, 417--452, 1998 May 3 2013 31 May 3 2013 32 Mogens Flensted-Jensen - Department Mogens Flensted-Jensen - Department Mogens Flensted-Jensen - Department of Mathematical Sciences of Mathematical Sciences of Mathematical Sciences 33 May 3 2013 Mogens Flensted-Jensen - Department of Mathematical Sciences Plancherel Formula for G/H Highlight 9: Ban-Schlichtkrull MLI November 1995 Paley-Wiener Theorem for G/H Spherical distributions Residue calculus Abstract intertwining relation Paley-Wiener Theorem for G/H MLI November 1995 Key paper: E.P. van den Ban and H. Schlichtkrull The Paley–Wiener theorem for a reductive symmetric space, Annals of Math. 164 (2006), 879–909. May 3 2013 35 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department May 3 2013 34 of Mathematical Sciences Dias 36 6 5/2/2013 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences May 3 2013 May 3 2013 May 3 2013 Dias 37 Dias 38 Dias 39 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Japan August 1986 A few snapshots May 3 2013 42 May 3 2013 May 3 2013 Mogens Flensted-Jensen - Department Dias 40 Dias 41 of Mathematical Sciences 7 5/2/2013 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences Roskilde 1992 – Helgason 65 years! Drawing by Saint-Exupéry At the Shock-price ceremony for Andrew Wiles May 3 2013 May 3 2013 May 3 2013 Dias 43 Dias 44 Dias 45 Mogens Flensted-Jensen - Department of Mathematical Sciences Mogens Flensted-Jensen - Department of Mathematical Sciences May 3 2013 Drawing by Saint-Exupéry Drawing by Saint-Exupéry 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