GCOEレクチャーズ

過去の記録 ~05/21次回の予定今後の予定 05/22~


過去の記録

2009年02月13日(金)

15:00-16:00   数理科学研究科棟(駒場) 370号室
大学院生を対象に、3回の講演を実施します。講演ごとに曜日、時間、場所が異なりますのでご注意ください。
又、各回ともなるべく独立になるようにします。

Vladimir Romanov 氏 (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第3講
[ 講演概要 ]
For a linear second-order hyperbolic equation with variable coefficients the fundamental solution for the Cauchy problem is considered. An asymptotic expansion of this solution in a neighborhood of the characteristic cone is introduced and explicit formulae for coefficients of this expansion are derived. Similar questions are discussed for the elasticity equations related to an inhomogeneous isotropic medium.

2009年02月06日(金)

15:00-16:00   数理科学研究科棟(駒場) 370号室
大学院生を対象に、3回の講演を実施します。講演ごとに曜日、時間、場所が異なりますのでご注意ください。
又、各回ともなるべく独立になるようにします。

Vladimir Romanov 氏 (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第2講
[ 講演概要 ]
For a linear second-order hyperbolic equation with variable coefficients the fundamental solution for the Cauchy problem is considered. An asymptotic expansion of this solution in a neighborhood of the characteristic cone is introduced and explicit formulae for coefficients of this expansion are derived. Similar questions are discussed for the elasticity equations related to an inhomogeneous isotropic medium.

2009年01月26日(月)

17:15-18:15   数理科学研究科棟(駒場) 470号室
大学院生を対象に、3回の講演を実施します。講演ごとに曜日、時間、場所が異なりますのでご注意ください。
又、各回ともなるべく独立になるようにします。

Vladimir Romanov 氏 (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第1講
[ 講演概要 ]
For a linear second-order hyperbolic equation with variable coefficients the fundamental solution for the Cauchy problem is considered. An asymptotic expansion of this solution in a neighborhood of the characteristic cone is introduced and explicit formulae for coefficients of this expansion are derived. Similar questions are discussed for the elasticity equations related to an inhomogeneous isotropic medium.

2009年01月23日(金)

17:00-18:00   数理科学研究科棟(駒場) 370号室
Eric Opdam 氏 (University of Amsterdam )
The spectral category of Hecke algebras and applications 第4講 Example: Lusztig's unipotent representations for classical groups.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

2009年01月22日(木)

17:00-18:00   数理科学研究科棟(駒場) 370号室
Eric Opdam 氏 (University of Amsterdam)
The spectral category of Hecke algebras and applications 第3講 The spectral category and correspondences of tempered representations.

[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

2009年01月09日(金)

17:00-18:00   数理科学研究科棟(駒場) 123号室
Eric Opdam 氏 (University of Amsterdam)
The spectral category of Hecke algebras and applications 第2講 Affine Hecke algebras and harmonic analysis.


[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

2009年01月08日(木)

17:00-18:00   数理科学研究科棟(駒場) 123号室
大学院生・若手研究者を対象とした第3回GCOEレクチャーズ(4回連続講演)です。
Eric Opdam 氏 (University of Amsterdam)
The spectral category of Hecke algebras and applications
第1講: Reductive p-adic groups and Hecke algebras
[ 講演概要 ]
Hecke algebras play an important role in the harmonic analysis of a p-adic 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 p-adic groups. We will illustrate this in this series of lectures by explaining how various components of the Bernstein center contribute to the level-0 L-packets 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 so-called Harish-Chandra μ-functions. 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 level-0 representations of a quasi-split simple p-adic 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 Iwahori-Matsumoto Hecke algebra, a remarkable phenomenon that is crucial for this method. We will recover in this way Lusztig's classification of "unipotent" representations.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

2008年11月28日(金)

14:40-16:10   数理科学研究科棟(駒場) 002号室
Andrei Pajitnov 氏 (Univ. de Nantes)
Circle-valued Morse theory
, Lecture 2

2008年11月26日(水)

14:40-16:10   数理科学研究科棟(駒場) 002号室
Andrei Pajitnov 氏 (Univ. de Nantes)
Circle-valued Morse theory, Lecture 1
[ 講演概要 ]
Morse theory of circle-valued functions, initiated by S. P. Novikov in 1980-1982 is now a rapidly developing domain with applications and connections to many other fields of geometry and topology such as dynamical systems, Lagrangian intersections,
knots and links in three-dimensional sphere.

We will start with the basics of the theory, discuss the construction of the Novikov complex, relations with the dynamical zeta functions, and the knot theory. We will conclude with a list of the open problems of the theory.

2008年10月27日(月)

16:30-17:30   数理科学研究科棟(駒場) 128号室
Joachim Hilgert 氏 (Paderborn University)


Holomorphic extensions of highest weight representations to Olshanskii semigroups


[ 講演概要 ]
In this lecture I will present a proof of Olshanskii's Theorem, which says that
for a simple group of Hermitean type unitarizable highest weight
representations can be holomorphically extended to contractive representations
of a complex semigroup containing the group in its boundary.

2008年10月17日(金)

15:00-16:00   数理科学研究科棟(駒場) 118号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーズです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その4 Applications and open problems

[ 講演概要 ]
In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krötz-Stanton), random matrices (Huckleberry-Püttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

2008年10月16日(木)

15:00-16:00   数理科学研究科棟(駒場) 123号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーズです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その3 Highest weight representations
[ 講演概要 ]
In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

2008年10月15日(水)

15:00-16:00   数理科学研究科棟(駒場) 122号室
大学院生・若手研究者を対象とした第1回GCOEレクチャーです。
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations その2 Geometric background
[ 講演概要 ]
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert

2008年10月14日(火)

15:00-16:00   数理科学研究科棟(駒場) 118号室
Joachim Hilgert 氏 (Paderborn University)
Holomorphic extensions of unitary representations" その1 "Overview and Examples"
[ 講演概要 ]
In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert

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