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Lie群論・表現論セミナー
過去の記録 ～05/22｜次回の予定｜今後の予定 05/23～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 小林俊行 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html |
2010年02月19日(金)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (Orsay)
Discrete groups acting on homogeneous spaces V
Yves Benoist 氏 (Orsay)
Discrete groups acting on homogeneous spaces V
[ 講演概要 ]
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.
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.
