July 1 (Wed)July 4 (Sat), 2015
Confirmed Speakers:
13:0014:00 Oshima
Break
14:1515:15 Matumoto
15:1516:00 Coffee Break (Fujiwara Hall)
16:0017:00 Hirai
Break
17:1518:15 Nishiyama
13:0014:00 Orsted
14:1515:15 Bianchi
15:1516:00 Coffee Break (Fujiwara Hall)
16:0017:00 Pevzner
Break
17:1518:15 Kaizuka
Conference Dinner (18:30 Bus)
13:0014:00 Vershik
14:1515:15 Bianchi
15:3016:30 Orsted
Speaker:  Gabriele Bianchi (Universita di Firenze) 
Title:  The covariogram and FourierLaplace transform in {\mathbb C}^n 
Abstract: 
The covariogram g_{K} of a convex body K in R^n is the function which
associates to each x in R^n the volume of the intersection of K with
K+x. Determining K from the knowledge of g_K is known as the covariogram
problem. It is equivalent to determining the characteristic function 1_K
of K from the modulus of its FourierLaplace transform, a particular
instance of the phase retrieval problem. We will present this problem and a recent result that shows that when K is sufficiently smooth and in any dimension n, K is determined by g_K in the class of sufficiently smooth bodies. The proof uses in an essential way a study of the asymptotic behavior at infinity of the zero set of the FourierLaplace transform of 1_K in C^n done by Toshiyuki Kobayashi. We also discuss the relevance for the covariogram problem of known determination results for the phase retrieval problem and the difficulty of finding explicit geometric conditions on K which grant that the entire FourierLaplace transform of 1_K cannot be factored as the product of nontrivial entire functions. This shows a connection between the covariogram problem and the Pompeiu problem.

Speaker:  Takeshi Hirai (½δ ) (Kyoto University) 
Title:  A review of my work on characters of semisimple Lie groups 
Abstract: 
Concentrating on the subject of characters of semisimple Lie groups, I
try to review series of my papers. The talk will contain subjects such
as

Speaker:  Koichi Kaizuka (LΛφκ) (Gakushuin University) 
Title:  Scattering theory for invariant differential operators on symmetric spaces of noncompact type and its application to unitary representations 
Abstract: 
We develop the scattering theory for invariant differential
operators on symmetric spaces of noncompact type.
We study asymptotic behavior of (joint) eigenfunctions in
a suitable Banach space. By the scattering theory,
we present three types of unitary representations of
semisimple Lie groups in an explicit form as a uniform limit of
representations on the Banach space.

Speaker:  Masatoshi Kitagawa (kμX«) (the University of Tokyo) 
Title:  On the irreducibility of U(g)^Hmodules 
Abstract: 
I will report on the irreducibility of U(g)^Hmodules arising from
branching problems.
It is wellknown that a U(g)^Kmodule Hom_K(W,V) is irreducible for any
irreducible (g, K)module V and Ktype W.
For a noncompact subgroup H, the same statement is not true in general.
In this talk, I will introduce a positive example and negative example
for the irreducibility of Hom_H(W,V).

Speaker:  Toshiyuki Kobayashi (¬Ρrs) (the University of Tokyo) 
Title:  Analysis of minimal representatinons"geometric quantization" of minimal nilpotent orbits 
Abstract: 
Minimal representations are the smallest infinite dimensional
unitary representations of reductive groups. About ten years ago, I suggested a program of "geometric analysis" with minimal representations as a motif. We have found various geometric realizations of minimal representations that interact with conformal geometry, conservative quantities of PDEs, holomorphic model (e.g. Focktype model), $L^2$model (Schr\"odingertype model), and Dolbeault cohomology models. I plan to discuss some of these models based on works with my collaborators, Hilgert, Mano, M\"ollers, and \O rsted among others. From the viewpoint of the orbit philosoply by KirillovKostant, minimal representations may be thought of as a quantization of minimal nilpotent orbits. In certain setting, we give a "geometric quantization" of minimal representations by using certain Lagrangean manifolds. Our construction includes the Schr\"odinger model of the SegalShaleWeil representation of the metaplectic group, and the commutative model of the complementary series representations of O(n,1) due to A. M. Vershik and M. I. Graev.

Speaker:  Toshihisa Kubo (vΫv) (the University of Tokyo) 
Title:  On the reducible points for scalar generalized Verma modules 
Abstract: 
In 1980's EnrightHoweWallach and Jakobsen individually classified
the reducible points for scalar generalized Verma modules induced from
parabolic subalgebras with abelian nilpotent radicals,
for which the generalized Verma modules are unitarizable.
Recently, Haian He classified all the reducible points for
such scalar generalized Verma modules. In this talk
we will discuss about classifying reducible points for
scalar generalized Verma modules induced from maximal parabolic
subalgebras
with twostep nilpotent radicals.This is a joint work in progress with
Haian He and Roger Zierau.

Speaker:  Hisayosi Matumoto (Ό{v`) (the University of Tokyo) 
Title:  Homomorphisms between scalar generalized Verma modules of ${\ mathfrak gl}(n, {\mathbb C})$ 
Abstract: 
An induced module of a complex reductive Lie algebra from a
onedimensional representation
of a parabolic subalgebra is called a scalar generalized Verma module.
In this@talk, we give a classification of homomorphisms between scalar
generalized Verma modules
of ${\mathfrak gl}(n,{\mathbb C})$. In fact such homomorphisms are
compositions of elementary
homomorphisms.

Speaker:  Kyo Nishiyama (ΌR ) (Aoyama Gakuin University) 
Title:  Double flag variety over reals: Hermitian symmetric case 
Abstract: 
Let $G$ be a reductive Lie group and $L$ its symmetric subgroup, i.e., $
L$ is open in $G^{\theta}$ for a certain involution $\theta$. Choose
parabolic subgroups $ P \subset G $ and $ Q \subset L $ respectively,
and put $ X = G/P \times L/Q $. We call $X$ a double flag variety. $L$
acts on $X$ diagonally, and $X$ is said tobe of finite type if there are
only finitely many $L$orbits. In this talk, we concentrate on the pair $ (G, L) = (Sp_{2n}(\R), GL_n(\ R)) $ and consider $ X=LGrass(\R^{2n}) \times Grass_d(\R^n) $ (product of Lagrangian Grassmannian and Grassmannian of $d$dimensional subspaces). This double flag variety is turned out to be of finite type and we discuss various interesting properties of $X$, which is not fully investigated yet. This is based on an ongoing joint work with Bent Ørsted.

Speaker:  Hiroyuki Ochiai ([V) (Kyushu University) 
Title:  Covariant differential operators and HeckmanOpdam hypergeometric systems 
Abstract: 
This is a joint work with Tomoyoshi Ibukiyama and Takako
Kuzumaki.
We consider holomorphic linear differential operators with constant
coefficients acting on Siegel modular forms, which preserve the
automorphy when restricted to a subdomain. We give a characterization
of
the symbols of such differential operators, and mention an explicit form
in terms of hypergeometric functions with respect to root systems
introduced by G.Heckman and E.Opdam.

Speaker:  Bent Ørsted (Århus University) 
Title:  Generalized Fourier transforms 
Abstract: 
In these lectures, based on joint work with Salem Ben Said and
Toshiyuki Kobayashi, we shall define a natural family of deformations
of the usual Fourier transform in Euclidian space. The main idea is
to replace the standard Laplace operator by a twoparameter family
of deformations in such a way, that it still is a member of a triple
generating the threedimensional simple Lie algebra. In particular
we shall describe

Speaker:  Michael Pevzner (Reims University) 
Title:  Symmetry breaking operators and resonance phenomena for branching laws 
Abstract: 
We shall explain the fundamental role of the Gauss hypergeometric
equation
in the explicit realization of symmetry breaking operators for reductive
pairs
and the control of multiplicities of the corresponding branching laws
for singular
parameters.

Speaker:  Anatoly Vershik (St. Petersburg State University) 
Title:  Representtions of current groups and theory of special representations 
Abstract: 
In the beginning of the 70th H. Araki gave a general scheme of the
consrutruction of the representations in the Fock space (=ItoWiener
space)
of the groups of the functions with values in Lie groups. Independently
in
the paper (1973) GelfandGraevVershik gave the first example of the
irreducible represnetations for the case of $SL(2,R)$ and he for
semisimple group of rank one — $O(n,1), U(n,1)$. Many authors work on
this direction(VGG, Ismagilov, Delorm, Guichardet et al). The main point
is
the cocycle of the group with value in the irreducibe faithful
represention.
During the last 10 year in the papers by Graev et Vershik the following
progress was obtained 1) New models ("integral model" , Poisson, Quasipoussin model instead of Fock model) of the representation of current group was constructed; 2) Systematic approach to the studying of cohomology in the special unitary representations; In particulary for the Iwasawa subgroup of semsimple groups like $U(p,q),O(p,q)$ and other solvable groups. 3) Recent attepmt to extend theory for nonunitary representations. There many open problems and link with other areas. 
© Toshiyuki Kobayashi