過去の記録

GCOEセミナー

14:50-15:40 数理科学研究科棟(駒場) 122号室
O. Iliev 氏 (フラウンホーファー産業数学研究所、ドイツ)
Flow and material simulation for industrial purposes

2010年02月17日(水)

GCOEレクチャーズ

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

統計数学セミナー

15:00-16:10 数理科学研究科棟(駒場) 128号室
清智也氏 (東京大学情報理工学系研究科)
勾配写像で表される球面上の確率分布族

[ 講演概要 ]
球面上の確率分布族は、方向統計学において重要である。本講演では、コスト凸関数 (c-凸関数)と呼ばれる関数とその勾配写像を用いて、球面上の分布族を構成する。コスト凸関数とは、最適輸送理論の分野で導入された概念であり、ユークリッド空間における凸関数をリーマン多様体の場合へ拡張させたものである。提案する分布族の性質をいくつか示し、簡単な方向データの解析例を示す。

[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/14.html

2010年02月16日(火)

トポロジー火曜セミナー

17:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: 17:00 - 17:30 コモンルーム
Dieter Kotschick 氏 (Univ. M\"unchen)
Characteristic numbers of algebraic varieties

[ 講演概要 ]
The Chern numbers of n-dimensional smooth projective varieties span a vector space whose dimension is the number of partitions of n. This vector space has many natural subspaces, some of which are quite small, for example the subspace spanned by Hirzebruch--Todd numbers, the subspace of topologically invariant combinations of Chern numbers, the subspace determined by the Hodge numbers, and the subspace of Chern numbers that can be bounded in terms of Betti numbers. I shall explain the relation between these subspaces, and characterize them in several ways. This leads in particular to the solution of a long-standing open problem originally formulated by Hirzebruch in the 1950s.