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Analysis, Geometry and Group Representations for Homogeneous Spaces
Groups and their homogeneous spaces are basic objects in science and to unravel their structure and that of certain classes of functions on them is of fundamental importance.
A classical example in that respect form Fourier series and integrals. Harmonic analysis on locally compact groups is the search for a non-commutative generalization of this theory.
At the conference we focused on a selected number of topics of actual interest: symmetric spaces, representation theory related to number theory, special functions and quantum groups. The goals were to discuss the various interrelations between them and to stimulate future research in these directions. Therefore we gathered reknowned specialists in these fields and young researchers to get a vivid exchange of views.
There were 52 participants from 10 different countries that attended the week program with a substantial group of young researchers.
The program consisted first of all of 15 keynote addresses of 45 minutes each followed by lively discussions. The speakers and their titles were:
1) Masato Wakayama: Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials
2) Joachim Hilgert: Wigner and Patterson-Sullivan distributions for locally symmetric spaces
3) Hideyuki Ishi: The Berezin transforms associated to homogeneous Kaehler metrics on a homogeneous bounded domain
4) Atsumu Sasaki: Visible actions on multiplicity-free spaces
5) Volker Heierman: On Shahidi's tempered L-function conjecture
6) Patrick Delorme: Constant term of Eisenstein integrals of reductive p-adic symmetric spaces
7) Hidenori Fujiwara: On the polynomial conjectures
8) Bernhard Krötz: Invariant measures on homogeneous spaces, with applications to function spaces and lattice counting
9) Erik van den Ban: On the symplectic structure of hyperbolic co-adjoint orbits
10) Taro Yoshino: Topological blow-up
11) Hiroyuki Ochiai: Positivity of an alpha determinant
12) Michael Pevzner: Spectral approach to composition formulas
13) Katsuhisa Mimachi: Connection formulas of the solutions of Fuchsian differential equations and intersection numbers of twisted cycles
14) Masatoshi Noumi: Remarks on elliptic Schur functions
15) Erik Koelink: Modular properties for quantum groups
Besides this part of the program, participants also had the possibility to give a short presentation of their work and ample use of this opportunity was made: all reserved time slots were fully booked. Their respective titles were:
1) Troels Johansen: Almost everywhere convergence of Bochner-Riesz means in Jacobi Analysis
2) Stéphanie Cupit-Foutou: Real structures on wonderful varieties
3) Ralf Gramlich: Topological split Kac-Moody groups and their buildings
4) Eitan Sayag: Distinction, Gelfand property and base change
5) Oksana Yakimova: Nilpotent Gelfand pairs and spherical transform of Schwartz functions
6) Job Kuit: Radon transformation on reductive symmetric spaces:support theorems
7) Andreas Kollross: Nonnegatively curved homogeneous metrics
8) Antonio Jose Di Scala: A geometric proof of the Karpelevich-Mostow theorem
9) Stefan Berceanu: Holomorphic discrete series representations on Siegel-Jacobi domains
10) Stefan Kolb: Braid group actions on quantum symmetric pair coideal subalgebras
There were further two discussion sessions led by the organizers containing the following contributions:
Detlev Poguntke: Synthesis properties of orbits in the unitary dual of nilpotent Lie groups.
Bas Janssens: Universal central extensions of Gauge groups
Finally, Loek Helminck organized a special session on Generalized Cartan spaces, of which he described in an overview the present state of affairs and led the discussion.
Besides that the participants told us the conference was a source of inspiration for new ideas and yielded various new cooperations, also concrete plans were developed during the conference for a future follow-ups.
The conference was financially made possible by the support of the following institutions or organizations:
1) The Lorentz Center (NWO)
2) The Japanese Science Foundation
3) The cluster “Geometry and Quantum Theory” (GQT)
4) The Mathematical Research Institute (MRI)
Finally we like to express our gratitude to the staff of the Lorentz Center, in particular Henriette Jensenius, Mieke Schutte and Corrie Kuster for their guidance, help and support at the whole process of organizing this workshop. All participants were impressed by the pleasant ambiance at the Center and the excellent support from its staff.
Gerard Helminck (University of Amsterdam)
Takaaki Nomura (Kyushu University)