Eric Opdam (#1), Erik van den Ban, Patrick Delorme, Mogens FlenstedJensen, Masaki Kashiwara, Toshiyuki Kobayashi, Toshihiko Matsuki, Hisayosi Matumoto, Hiroyuki Ochiai, Yasunori Okada, Eric Opdam (#2), Toshio Oshima, Yoshiki Otobe, Hideko Sekiguchi, Jiro Sekiguchi, Nobukazu Shimeno, Gombodorj Bayarmagnai, Bernhard Krötz, Salah Mehdi, Peter Trapa, Roger Zierau, Sigurdur Helgason, Fulton Gonzalez, Angela Pasquale, Henrik Schlihitkrull, Michel Duflo, Ryosuke Kodera, Shunsuke Tsuchioka, Gert Heckman #1, Gert Heckman #2, Hiroshi Iritani, Carlos Olmos, Michael Pevzner, Daniel Sternheimer, Takaaki Nomura, Toshikazu Sunada #1, Toshikazu Sunada #2, Kyo Nishiyama,
(GCOE Lectures)  
Date and place: 

Speaker:  Eric Opdam (University of Amsterdam) 
Title:  The spectral category of Hecke algebras and applications Lecture 1: Reductive padic groups and Hecke algebras. Lecture 2: Affine Hecke algebras and harmonic analysis. Lecture 3: The spectral category and correspondences of tempered representations. Lecture 4: Example: Lusztig's unipotent representations for classical groups. 
Abstract: [ pdf ] 
Hecke algebras play an important role in the harmonic analysis
of a padic reductive group. On the other hand, their representation
theory and harmonic analysis can be described almost completely
explicitly. This makes affine Hecke algebras an ideal tool to study the
harmonic analysis of padic groups. We will illustrate this in this
series of lectures by explaining how various components of the Bernstein
center contribute to the level0 Lpackets of tempered
representations, purely from the point of view of harmonic analysis.
We define a "spectral category" of (affine) Hecke algebras. The
morphisms in this category are not algebra morphisms but are affine
morphisms between the associated tori of unramified characters, which are
compatible with respect to the socalled HarishChandra μfunctions.
We show that such a morphism generates a Plancherel measure preserving
correspondence between the tempered spectra of the two Hecke algebras
involved. We will discuss typical examples of spectral morphisms. We apply the spectral correspondences of affine Hecke algebras to level0 representations of a quasisplit simple padic group. We will concentrate on the example of the special orthogonal groups SO_{2n+1}(K). We show that all affine Hecke algebras which arise in this context admit a *unique* spectral morphism to the IwahoriMatsumoto Hecke algebra, a remarkable phenomenon that is crucial for this method. We will recover in this way Lusztig's classification of "unipotent" representations. 
(Conference in honor of Toshio Oshima's 60th birthday "Differential Equations and Symmetric Spaces")  
Date:  1316 January, 2009 
Place:  Graduate School of Mathematical Sciences, the University of Tokyo 
Speakers:  Erik van den Ban (Utrecht University) 
Patrick Delorme (University of AixMarseille II)  
Mogens FlenstedJensen (University of Copenhagen)  
Masaki Kashiwara (柏原正樹) (RIMS)  
Toshiyuki Kobayashi (小林俊行) (The University of Tokyo)  
Toshihiko Matsuki (松木敏彦) (Kyoto University)  
Hisayosi Matumoto (松本久義) (The University of Tokyo)  
Hiroyuki Ochiai (落合啓之) (Nagoya University)  
Yasunori Okada (岡田靖則) (Chiba University)  
Eric Opdam (University of Amsterdam)  
Toshio Oshima (大島利雄) (The University of Tokyo)  
Yoshiki Otobe (乙部厳己) (Shinshu University)  
Hideko Sekiguchi (関口英子) (The University of Tokyo)  
Jiro Sekiguchi (関口次郎) (Tokyo University of Agriculture and Technology)  
Nobukazu Shimeno (示野信一) (Okayama University of Science)  
Date:  February 3 (Tue), 2009, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Gombodorj Bayarmagnai (University of Tokyo) 
Title:  The (g,K)module structure of principal series and related Whittaker functions of SU(2,2) 
Abstract: [ pdf ] 
In this talk the basic object will be the principal series representataion of SU(2,2), parabolically induced by the minimal parabolic subgroup. We discuss about the (g,K)module structure on that type of principal series explicitely, and provide various integral expressions of some smooth Whittaker functions with certain Ktypes. 
(GCOE Spring School on Representation Theory)  
Date:  March 1217, 2009 
Place:  Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Bernhard Krötz (Germany) 
Title:  HarishChandra modules 
Abstract: [ pdf ] 
We plan to give a course on the various types of topological
globalizations of HarishChandra modules.
It is intended to cover the following topics:

Speaker:  Salah Mehdi (France) 
Title:  EnrightVaradarajan modules and harmonic spinors 
Abstract: [ pdf ] 
The aim of these lectures is twofold. First we would like to describe the construction of the EnrightVaradarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory. Then we shall use the EnrightVaradarajan modules to define a product for harmonic spinors on homogeneous spaces. 
Speaker:  Peter Trapa (USA) 
Title:  Special unipotent representations of real reductive groups 
Abstract: [ pdf ] 
These lectures are aimed at beginning graduate students
interested in the representation theory of real Lie groups. A familiarity
with the theory of compact Lie groups and the basics of HarishChandra
modules will be assumed. The goal of the lecture series is to give an
exposition (with many examples) of the algebraic and geometric theory of
special unipotent representations. These representations are of
considerable interest; in particular, they are predicted to be the
building blocks of all representation which can contribute to spaces of
automorphic forms. They admit many beautiful characterizations, but their
construction and unitarizability still remain mysterious.
The following topics are planned:

Speaker:  Roger Zierau (USA) 
Title:  Dirac Cohomology 
Abstract: [ pdf ] 
Dirac operators have played an important role in
representation theory. An early example is the construction of
discrete series representations as spaces of L^{2} harmonic
spinors on symmetric spaces G/K. More recently a very natural
Dirac operator has been discovered by Kostant; it is referred to
as the cubic Dirac operator. There are algebraic and geometric
versions. Suppose G/H is a reductive homogeneous space and
$\mathfrak g = \mathfrak h + \mathfrak q$. Let S_{\mathfrak q} be the
restriction of the spin representation of SO(\mathfrak q) to
H ⊂ SO(\mathfrak q). The algebraic cubic Dirac operator is
an Hhomomorphism \mathcal D: V \otimes S_{\mathfrak q} → V \otimes
S_{\mathfrak q}, where V is an $\mathfrak g$module. The
geometric geometric version is a differential operator acting on
smooth sections of vector bundles of spinors on G/H. The
algebraic cubic Dirac operator leads to a notion of Dirac
cohomology, generalizing $\mathfrak n$cohomology.
The lectures will roughly contain the following.

Contact:  Toshio Oshima [ Email ] and Toshiyuki Kobayashi [ Email ] 
Workshop on Integral Geometry and Group Representations  
Date:  August 5 (Wed)10 (Mon), 2009 
Place:  Tambara Institute of Mathematical Sciences, The University of Tokyo (東京大学玉原国際セミナーハウス) 
Invited speakers include:
Mike Eastwood, Sigurdur Helgason, Angela Pasquale and Henrik SchlichtkrullOrganizers: Fulton B. Gonzalez， Tomoyuki Kakehi, Toshiyuki Kobayashi and Toshio Oshima  
MiniConference "Integral Geometry and Representation Theory" [ pdf ]  
Date:  August 12 (Wed), 2009 
Place:  Room 002, Graduate School of Mathematical Sciences, the University of Tokyo 
10:0011:00  
Speaker:  Sigurdur Helgason (MIT) 
Title:  Radon transforms and some applications 
11:2012:20  
Speaker:  Fulton Gonzalez (Tufts University) 
Title:  Multitemporal wave equations: mean value solutions 
14:0015:00  
Speaker:  Angela Pasquale (Universite Metz) 
Title:  Analytic continuation of the resolvent of the Laplacian in the Euclidean setting 
Abstract:  We discuss the analytic continuation of the resolvent of the Laplace operator on symmetric spaces of the Euclidean type and some generalizations to the rational Dunkl setting. 
15:3016:30  
Speaker:  Henrik Schlihitkrull (Univ. of Copenhagen) 
Title:  Decay of smooth vectors for regular representation 
Abstract:  Let G/H be a homogeneous space of a Lie group, and consider the regular representation L of G on E=L^p(G/H). A smooth vector for L is a function f in E such that g mapsto L(g) f is smooth, G to E. We investigate circumstances under which all such functions decay at infinity (jt with B. Krötz). 
(GCOE Lectures)  
Date:  October 7 (Wed) & 9 (Fri), 2009, 16:3017:30 
Place:  Room 128, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Michel Duflo (Paris 7) 
Title:  Lecture 1. Representations of classical Lie superalgebras Lecture 2. Associated varieties for Representations of classical Lie superalgebras 
Abstract: [ pdf ] 
(Lecture 1) In this lecture, I'll survey classical topics on finite dimensional representations of classical Lie superalgebras, in particular the notion of the degree of atypicality.
(Lecture 2) 
Date:  October 13 (Tue), 2009, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Ryosuke Kodera (小寺諒介) (University of Tokyo) 
Title:  Extensions between finitedimensional simple modules over a generalized current Lie algebra 
Abstract: [ pdf ] 
$\mathfrak{g}$を$\mathbb{C}$上の有限次元半単純Lie代数,$A$を有限生成可換$\mathbb {C}$代数とする. テンソル積$A \otimes \mathfrak{g}$に自然にLie代数の構造を与えたものを一般化されたカレントLie代数と呼ぶ. 一般化されたカレントLie代数の任意の2つの有限次元既約表現に対して,その1次のExt群を完全に決定することができたので,その結果について発表する. 
Date:  October 15 (Thu), 2009, 16:3018:00 
Place:  Room 122, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Shunsuke Tsuchioka (土岡俊介) (RIMS, Kyoto University) 
Title:  HeckeClifford superalgebras and crystals of type $D^{(2)}_{l}$ 
Abstract: [ pdf ] 
It is known that we can sometimes describe the representation theory of "Hecke algebra" by "Lie theory". Famous examples that involve the Lie theory of type $A^{(1)}_n$ are LascouxLeclercThibon's interpretation of Kleshchev's modular branching rule for the symmetric groups and Ariki's theorem generalizing LascouxLeclercThibon's conjecture for the IwahoriHecke algebras of type A. Brundan and Kleshchev showed that some parts of the representation theory of the affine HeckeClifford superalgebras and its finitedimensional "cyclotomic" quotients are controlled by the Lie theory of type $A^{(2)}_{2l}$ when the quantum parameter $q$ is a primitive $(2l+1)$th root of unity. In this talk, we show that similar theorems hold when $q$ is a primitive $4l$th root of unity by replacing the Lie theory of type $A^{(2)}_{2l}$ with that of type $D^{(2)}_{l}$. 
Date:  November 4 (Wed), 2009, 16:3018:00 
Place:  Room 128, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Gert Heckman (IMAPP, Faculty of Science, Radboud University Nijmegen) 
Title:  Birational hyperbolic geometry 
Abstract: [ pdf ] 
We study compactifications for complex ball quotients. We first recall the SatakeBaileyBorel compactification and the Mumford resolution. Then we discuss compactifications of ball quotients minus a totally geodesic divisor. These compactifications turn up for a suitable class of period maps (related to the lecture of the speaker on friday on "Geometric structures"). 
IPMU workshop "Quantizations, integrable systems and representation theory"  
Date:  November 5 (Thu)6 (Fri), 2009 
Place:  Seminar Room at IPMU Prefab. B, The University of Tokyo (Kashiwa Campus) 
Invited speakers:  Gert Heckman (IMAPP, Faculty of Science, Radboud University Nijmegen) Hiroshi Iritani (Kyushu University) Carlos Olmos (National University of Cordoba, Argentina) Michael Pevzner (Univ. de Reims) Daniel Sternheimer* (Univ. de Bourgogne) *to be confirmed 
Organizers:  Martin Guest, Toshiyuki Kobayashi, Toshitake Kohno 
Tentative Program:  November 5 10:3012:00 Pevzner, Composition formulas seen through representation theory I 13:3015:00 Olmos, Submanifolds and holonomy 15:0015:30 Tea 15:3017:00 Heckman, Complex hyperbolic structures Evening workshop dinner November 6 10:3012:00 Pevzner, Composition formulas seen through representation theory II 13:3015:00 Iritani, Quantization in semiinfinite Hodge theory 15:0015:30 Tea 15:3017:00 Sternheimer* 
（集中講義：数理科学特別講義 I）[ レポート問題 ]  
Date:  December 7 (Mon)11 (Fri), 2009, 14:4016:40 
Place:  Room 123, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Takaaki Nomura (野村隆昭) (Kyushu University) 
Title:  等質錐と等質ジーゲル領域 
Abstract: [ pdf ] 
本講義は，E. Cartanの問題「$n \geqq 4$ のとき，$\C^n$に非対称な等質有界領域が存在するか」に肯定的な解答を与えた等質ジーゲル領域（$\C$の上半平面の高次元化），及び等質開凸錐に関するものである．私や名古屋大学の伊師英之氏，金沢大学の甲斐千舟氏の近年の結果（共同あるいは私や彼ら自身の単独研究），特に対称領域の特徴付けに関する結果の解説を中心に講義をするが，そこで用いられる基本的な概念や代数的構造物については，例と共に詳しく述べる．定理についても，完全な証明を与えることより，むしろ例を通して理解するというような方針で進めたい． 講義内容についてのキーワードをいくつか箇条書きにすると...

（集中講義：数理科学特別講義 IX）  
Date:  December 14 (Mon)18 (Fri), 2009, 14:4016:40 
Place:  Room 123, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Toshikazu Sunada (砂田利一) (Meiji University) 
Title:  Quantum walks in view of discrete geometric analysis 
Abstract: [ pdf ] 
This lecture treats quantum walks in view of “geometry of unitary operators”.
Ideas in discrete geometric analysis, developed to solve various problems in analysis
on graphs, are effectively employed to give new insight to the theory which has been
attracting computer scientists and physicists over the past decade. The notion of quantum walks is a “quantum” version of classical random walks, which is, as indicated by its name, closely related to quantum mechanics. Unlike the case of classical walks depending on imaginary random control by an external device such as the flip of a coin or the cast of a dice, randomness of quantum walks is directly linked to the probabilistic nature of physical states in the quantum system concerned. Though a protoidea of quantum walks is already seen in the celebrated theory of path integrals initiated by R. P. Feynman, its intense study has rather a short history, compared with that of classical walks which has been developed and applied to various disciplines for more than a century. Indeed it is in the pioneer work by Y. Aharonov, L. Davidovich, and N. Zagury that the term “quantum (random) walk” was coined for the first time (1993). Since then, several setups for the theory have been proposed, mainly aiming at the design of fast algorithms by means of quantum computing. In this lecture, I take up the simplest formulation among them, and discuss some fundamental aspects of quantum walks. Especially, I discuss periodic quantum walks on crystal lattices, and establish local limit formulae under a certain condition. A (discretetime) quantum walk is simply defined to be a pair (U; E) of a unitary operator U acting in a Hilbert space H and a complete orthonormal basis E = fexj x 2 V g of H, where the set of indices V is supposed to be countable. A connection with quantum mechanics is made by regarding E as the set of pure (eigen) states associated with an observable, and thinking of Unex (n 2 Z) as the time evolution of the state ex. Then the quantity pn(x; y) := jhUnex; eyij2 is the probability that the state ey is observed at time n in this evolutional system, and hence we obtain a family of probabilities (probability mass functions) fpn(x; ¢)g1n=1 on V . This is a quantum analogue of nstep transition probability for classical walks. One of main themes in the study of quantum walks is, as in the classical case, asymptotic behaviors of pn(x; y) as n goes to infinity, which turns out to be quite a bit different from the classical case. The abstract setup above is entirely within the scope of operator theory in Hilbert spaces, thereby, at the first sight, not seeming to invent any new aspects at all. But a simple geometric view opens up new horizons, which lead us to a rich and varied theory of of quantum walks. 
Date:  December 15 (Tue), 2009, 17:0018:00 
Place:  Room 056, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Toshikazu Sunada (砂田利一) (Meiji University) 
Title:  Open Problems in Discrete Geometric Analysis 
Abstract: [ pdf ] 
Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups. 
Date:  December 22 (Tue), 2009, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Kyo Nishiyama (西山 享) (Aoyama Gakuin University) 
Title:  既約表現の隨伴多様体は余次元 1 で連結か？—証明の破綻とその背景 
Abstract: [ pdf ] 
既約 HarishChandra $ (g, K) $ 加群の原始イデアルの隨伴多様体が既約であって、ただ一つの冪零隨伴軌道 $ O^G $ の閉包になることはよく知られている(Joseph, Borho)。 一方、HC加群の隨伴多様体は必ずしも既約でないが、その既約成分は $ O^G $ の $ K $等質ラグランジュ部分多様体の閉包になる。 それらの既約成分は余次元1で連結であることをいくつかの集会で報告したが、その証明には初等的な誤りがあった。セミナーでは、証明の元になった Vogan の定理の紹介 (もちろん間違っていない) と、それを拡張する際になぜ証明が破綻するかについてお話しする。(今のところ証明修復の目処は立っていない。) 
© Toshiyuki Kobayashi