GCOEレクチャーズ

過去の記録 ~06/15次回の予定今後の予定 06/16~


過去の記録

2010年06月01日(火)

16:30-18:00   数理科学研究科棟(駒場) 126号室
Birgit Speh 氏 (Cornel University)
Introduction to the cohomology of locally symmetric spaces
(ENGLISH)
[ 講演概要 ]
I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\\Gamma =K \\backslash G / \\Gamma $.
If $X_\\Gamma $ is cocompact this cohomology can be expressed as the $(g,K)$-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2010年02月18日(木)

10:30-17:00   数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (Pars Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces III
[ 講演概要 ]
In this course I will focus on recent advances
on our understanding of discrete subgroups of Lie groups.

I will first survey how ideas from semisimple algebraic groups,
ergodic theory and representation theory help us to understand properties of these discrete subgroups.

I will then focus on a joint work with Jean-Francois Quint
studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:

We fix two integral matrices A and B of size d, of determinant 1,
and such that no finite union of vector subspaces is invariant by A and B.
We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
Yves Benoist 氏 (Paris Sud) 15:00-16:00
Discrete groups acting on homogeneous spaces IV

2010年02月17日(水)

10:30-16:00   数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (Paris Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces I
[ 講演概要 ]
In this course I will focus on recent advances
on our understanding of discrete subgroups of Lie groups.

I will first survey how ideas from semisimple algebraic groups,
ergodic theory and representation theory help us to understand properties of these discrete subgroups.

I will then focus on a joint work with Jean-Francois Quint
studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:

We fix two integral matrices A and B of size d, of determinant 1,
and such that no finite union of vector subspaces is invariant by A and B.
We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
Yves Benoist 氏 (Paris Sud) 15:00-16:00
Discrete groups acting on homogeneous spaces II

2010年01月28日(木)

16:30-17:30   数理科学研究科棟(駒場) 999号室
Charles Fefferman 氏 (Princeton University)
Extension of Functions and Interpolation of Data
[ 講演概要 ]
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.

Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?

Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?

What can be said about the above problems for function spaces other than $C^m(\\mathbf{R}^n)$?

2010年01月27日(水)

14:40-16:10   数理科学研究科棟(駒場) 002号室
Charles Fefferman 氏 (Princeton University)
Extension of Functions and Interpolation of Data
[ 講演概要 ]
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.

Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?

Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?

What can be said about the above problems for function spaces other than $C^m(\\mathbf{R}^n)$?

2010年01月25日(月)

14:40-16:10   数理科学研究科棟(駒場) 002号室
Charles Fefferman 氏 (Princeton University)
Extension of Functions and Interpolation of Data
[ 講演概要 ]
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.

Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?

Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?

What can be said about the above problems for function spaces other than $C^m(\\mathbf{R}^n)$?

2009年10月21日(水)

15:30-17:00   数理科学研究科棟(駒場) 122号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Mini course on the gradient models, Ⅲ: Non convex potentials at high temperature
[ 講演概要 ]
In the non convex case, the situation is much more complicated. In fact Biskup and Kotecky describe a non convex model with several ergodic components. We investigate a model with non convex interaction for which unicity of the ergodic component, scaling limits and large deviations can be proved at sufficiently high temperature. We show how integration can generate strictly convex potential, more precisely that marginal measure of the even sites satisfies the random walk representation. This is a joint work with Codina Cotar and Nicolas Petrelis.

2009年10月14日(水)

15:30-17:00   数理科学研究科棟(駒場) 128号室
Claudio Landim 氏 (IMPA, Brazil)
Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅳ

2009年10月14日(水)

13:30-15:00   数理科学研究科棟(駒場) 128号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Mini course on the gradient models, Ⅱ: Convex interaction potential
[ 講演概要 ]
Much is known for strictly convex interactions, which under rescaling behave much like the harmonic model. In particular the unicity of the ergodic component have been established by Funaki and Spohn, and the scaling limit to the gradient of the continuous gaussian free field by Naddaf and Spencer. The results are based on special analytical and probabilistic tools such as the Brascamp-Lieb inequality and the Hellfer-Sj\\"osstrand random walk representation. These techniques rely on the strict convexity of the interaction potential.

2009年10月09日(金)

16:30-17:30   数理科学研究科棟(駒場) 128号室
Duflo氏による講義 2講目
Michel Duflo 氏 (Paris 7)
Associated varieties for Representations of classical Lie
super-algebras
[ 講演概要 ]
In this lecture, I'll discuss the notion of "Associated
varieties for Representations of classical Lie super-algebras (joint work with Vera Serganova)" and the relation with the degree of atypicality. This is related to a conjecture of Kac and Wakimoto.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2009年10月07日(水)

16:30-17:30   数理科学研究科棟(駒場) 128号室
Duflo氏による一講目
Michel Duflo 氏 (Paris 7)
Representations of classical Lie super-algebras

[ 講演概要 ]
In this lecture, I'll survey classical topics on finite dimensional representations of classical Lie super-algebras, in particular the notion of the degree of atypicality.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2009年10月05日(月)

15:30-17:00   数理科学研究科棟(駒場) 128号室
Claudio Landim 氏 (IMPA, Brazil)
Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅲ

2009年10月05日(月)

13:30-15:00   数理科学研究科棟(駒場) 128号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Mini course on the gradient models, I: Effective gradient models, definitions and examples
[ 講演概要 ]
We describe a phase separation in $R^{d+1}$ by an effective interface model with basis in $Z^d$ and height in $R$. We assume that the interaction potential depends only on the discrete gradient and that the a priori measure is the product Lebesgue measure. Note that this is an unbounded massless model with continuous symmetry and this implies that the interface is delocalized for the infinite model in lower lattice dimensions $d=1,2$. Instead of looking at the distribution of the height of the interface itself, we consider the measure on the height differences the so called gradient Gibbs measure, which exists in any dimensions. The gradient field must satisfy the loop condition, that is the sum of the gradient along any closed loop is zero, this implies a long range interaction with a slow decay of the correlations. We are interested in characterizing the ergodic components of this gradient field, in the decay of correlations, large deviations and continuous scaling limits. As an example we consider the harmonic or discrete gaussian free field with quadratic interactions.

2009年09月30日(水)

15:30-17:00   数理科学研究科棟(駒場) 123号室
Claudio Landim 氏 (IMPA, Brazil)
Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅱ

2009年09月28日(月)

15:30-17:00   数理科学研究科棟(駒場) 123号室
Claudio Landim 氏 (IMPA, Brazil)
Macroscopic fluctuation theory for nonequilibrium stationary states, I
[ 講演概要 ]
We present a review of recent work on the statistical mechanics of nonequilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.

2009年07月30日(木)

11:00-15:45   数理科学研究科棟(駒場) 002号室
東京大学グローバルCOE事業の一環として,サマースクール『非可積分系におけるソリトンの振舞いと安定性』を開催します. チュートリアル形式の講義ですので,非専門家や若手を含む,多くの�
水町 徹 氏 (九州大学) 11:00-12:00
長波長近似モデルと孤立波の安定性Ⅱ
Frank Merle 氏 (Cergy Pontoise 大学/IHES) 13:30-14:30
Dynamics of solitons in non-integrable systemsⅤ
Frank Merle 氏 (Cergy Pontoise 大学/IHES) 14:45-15:45
Dynamics of solitons in non-integrable systemsⅥ
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_001.html

2009年07月29日(水)

11:00-17:15   数理科学研究科棟(駒場) 002号室
東京大学グローバルCOE事業の一環として,サマースクール『非可積分系におけるソリトンの振舞いと安定性』を開催します. チュートリアル形式の講義ですので,非専門家や若手を含む,多くの�
水町 徹 氏 (京都大学) 11:00-12:00
長波長近似モデルと孤立波の安定性Ⅰ
[ 講演概要 ]
KdV方程式をはじめとする長波長近似の非線形分散型方程式は,水面波の運動やプラズマ中のイオンの運動を記述することで知られている. KdV方程式のソリトン解は安定的に伝播することが知られていたが,近年変分法に基づいたアプローチで非可積分系のモデルの場合にもソリトン解とよく似た解が安定的に存在することが証明された.第1回目の講演ではに変分原理に基づいた安定性の結果について概説し,次にFermi-Pasta-Ulam格子やある種の流体のbidirectional modelなど変分原理から安定性がうまく説明できないモデルの場合について述べる.
Frank Merle 氏 (Cergy Pontoise 大学/IHES) 13:30-14:30
Dynamics of solitons in non-integrable systemsⅢ
Frank Merle 氏 (Cergy Pontoise 大学/IHES) 14:45-15:45
Dynamics of solitons in non-integrable systemsⅣ
中西 賢次 氏 (九州大学) 16:15-17:15
シュレディンガー写像及び熱流における調和写像の漸近安定性と振動現象についてⅡ
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_001.html

2009年07月28日(火)

13:30-17:15   数理科学研究科棟(駒場) 002号室
東京大学グローバルCOE事業の一環として,サマースクール『非可積分系におけるソリトンの振舞いと安定性』を開催します. チュートリアル形式の講義ですので,非専門家や若手を含む,多くの�
Frank Merle 氏 (Cergy Pontoise 大学/IHES) 13:30-14:30
Dynamics of solitons in non-integrable systemsⅠ
[ 講演概要 ]
完全可積分系であるKdV方程式においては,多重ソリトン解の構造はすでに詳しく解明されており,ソリトンどうしが衝突した後,各ソリトンの形状がすぐに元通りに復元するなどの性質もよく知られている.しかし方程式中の指数を変えて得られる一般化KdV方程式の場合は,非可積分系であるため,多重ソリトン解の便利な表示式は存在せず,ソリトンどうしの衝突後に何が起こるのか,理論的には未解明であった.Merle氏は,最近Yvon Martel氏と共同でこの問題を解決し,衝突後にわずかな欠損が生じるもののソリトンの形状が見事に復元することを証明するとともに,大きなソリトンが微小なソリトンと衝突した際に生じる位相(phase)のズレに関して, KdV方程式の場合と全く違う現象が起こることも明らかにした.
Frank Merle 氏 (Cergy Pontoise 大学/IHES) 14:45-15:45
Dynamics of solitons in non-integrable systemsⅡ
中西 賢次 氏 (京都大学) 16:15-17:15
シュレディンガー写像及び熱流における調和写像の漸近安定性と振動現象についてⅠ
[ 講演概要 ]
平面から球面への調和写像をシュレディンガーや熱流で時間発展させたときの漸近安定性を回転対称下で調べる.この問題は,調和写像の写像度が低いほど摂動部との空間遠方相互作用が大きくなる所が難しく,実際写像度2の熱流では初期摂動に応じて非自明な時間漸近挙動が現れる.この講演では,非線形シュディンガー方程式の場合をモデルとして比較しながら、漸近安定性を示す一般的な手続きとそこからの変更点,必要となる線形評価などについて解説する.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_001.html

2009年03月25日(水)

16:00-17:30   数理科学研究科棟(駒場) 128号室
Mark Gross 氏 (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations II
[ 講演概要 ]
The second half of the lecture.

2009年03月24日(火)

16:00-17:30   数理科学研究科棟(駒場) 128号室
Mark Gross 氏 (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations I
[ 講演概要 ]
I will discuss the SYZ conjecture which attempts to explain mirror symmetry via the existence of dual torus fibrations on mirror pairs of Calabi-Yau manifolds. After reviewing some older work on this subject, I will explain how it leads to an algebro-geometric version of this conjecture and will discuss recent work with Bernd Siebert. This recent work gives a mirror construction along with far more detailed information about the B-model side of mirror symmetry, leading to new mirror symmetry predictions.

2009年03月17日(火)

10:00-17:30   数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Roger Zierau 氏 (Oklahoma State University) 11:00-12:00
Dirac Cohomology
Salah Mehdi 氏 (Metz University) 13:30-14:30
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz
(Max Planck Institute) 15:00-16:00
Harish-Chandra modules
Peter Trapa 氏 (Utah) 16:30-17:30
Special unipotent representations of real reductive groups

2009年03月16日(月)

10:00-16:20   数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Bernhard Krötz
(Max Planck Institute) 10:00-11:00
Harish-Chandra modules
[ 講演概要 ]
We plan to give a course on the various types of topological globalizations of Harish-Chandra modules. It is intended to cover the following topics:

1.Topological representation theory on various types of locally convex vector spaces.

2.Basic algebraic theory of Harish-Chandra modules

3. Unique globalization versus lower bounds for matrix coefficients

4. Dirac type sequences for representations

5. Deformation theory of Harish-Chandra modules
The new material presented was obtained in collaboration with Joseph Bernstein and Henrik Schlichtkrull. A first reference is the recent preprint "Smooth Frechet Globalizations of Harish-Chandra Modules" by J. Bernstein and myself, downloadable at arXiv:0812.1684v1.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#kroetz
Peter Trapa 氏 (Utah) 11:15-12:15
Special unipotent representations of real reductive groups
[ 講演概要 ]
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 Harish-Chandra 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:

1.Algebraic definition of special unipotent representations and examples.

2.Localization and duality for Harish-Chandra modules.

3. Geometric definition of special unipotent representations.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#trapa
Roger Zierau 氏 (Oklahoma State University) 13:30-14:30
Dirac Cohomology
[ 講演概要 ]
Dirac operators have played an important role in representation theory. An early example is the construction of discrete series representations as spaces of L2 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 H-homomorphism \\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.

1.Construction of the spin representations of \\widetilde{SO}(n).

2.The algebraic cubic Dirac operator \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q will be defined and some properties, including a formula for the square, will be given.

3. Of special interest is the case when H=K, a maximal compact subgroup of G and V is a unitarizable $(\\mathfrak g,K)$-module. This case will be discussed.

4.The Dirac cohomology of a finite dimensional representation will be computed. We will see how this is related to $\\mathfrak n$-cohomology of V.

5. The relationship between the algebraic and geometric cubic Dirac operators will be described. A couple of open questions will then be discussed.

The lectures will be fairly elementary.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#zierau
Salah Mehdi 氏 (Metz University) 15:20-16:20
Enright-Varadarajan modules and harmonic spinors
[ 講演概要 ]
The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan 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 Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#mehdi

2009年03月14日(土)

09:00-14:00   数理科学研究科棟(駒場) 123号室
Roger Zierau 氏 (Oklahoma State University) 09:00-10:00
Dirac cohomology
Salah Mehdi 氏 (Metz University) 10:15-11:15
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz 氏 (Max Planck Institute) 11:45-12:45
Harish-Chandra modules
Peter Trapa 氏 (Utah University) 13:00-14:00
Special unipotent representations of real reductive groups

2009年03月13日(金)

09:30-16:30   数理科学研究科棟(駒場) 123号室
Salah Mehdi 氏 (Metz) 09:30-10:30
Enright-Varadarajan modules and harmonic spinors
[ 講演概要 ]
The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan 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 Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
Peter Trapa 氏 (Utah) 11:00-12:00
Special unipotent representations of real reductive groups
Bernhard Krötz
(Max Planck Institute) 13:30-14:30
Harish-Chandra modules
Roger Zierau 氏 (Oklahoma State University) 15:00-16:00
Dirac Cohomology

2009年03月12日(木)

09:30-14:30   数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Roger Zierau 氏 (Oklahoma State University) 09:30-10:30
Dirac Cohomology
[ 講演概要 ]
Dirac operators have played an important role in representation theory. An early example is the construction of discrete series representations as spaces of L2 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 H-homomorphism \\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.

1.Construction of the spin representations of \\widetilde{SO}(n).

2.The algebraic cubic Dirac operator \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q will be defined and some properties, including a formula for the square, will be given.

3. Of special interest is the case when H=K, a maximal compact subgroup of G and V is a unitarizable $(\\mathfrak g,K)$-module. This case will be discussed.

4.The Dirac cohomology of a finite dimensional representation will be computed. We will see how this is related to $\\mathfrak n$-cohomology of V.

5. The relationship between the algebraic and geometric cubic Dirac operators will be described. A couple of open questions will then be discussed.

The lectures will be fairly elementary.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Bernhard Krötz 氏 (Max Planck) 11:00-12:00
Harish-Chandra modules
[ 講演概要 ]
We plan to give a course on the various types of topological globalizations of Harish-Chandra modules. It is intended to cover the following topics:

1.Topological representation theory on various types of locally convex vector spaces.

2.Basic algebraic theory of Harish-Chandra modules

3. Unique globalization versus lower bounds for matrix coefficients

4. Dirac type sequences for representations

5. Deformation theory of Harish-Chandra modules
The new material presented was obtained in collaboration with Joseph Bernstein and Henrik Schlichtkrull. A first reference is the recent preprint "Smooth Frechet Globalizations of Harish-Chandra Modules" by J. Bernstein and myself, downloadable at arXiv:0812.1684v1.
Peter Trapa 氏 (Utah大学) 13:30-14:30
Special unipotent representations of real reductive groups
[ 講演概要 ]
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 Harish-Chandra 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:

1.Algebraic definition of special unipotent representations and examples.

2.Localization and duality for Harish-Chandra modules.
3. Geometric definition of special unipotent representations.

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