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Lie Groups and Representation Theory Seminar 2019

List of speakers:
Takaaki Nomura, Yves Benoist #1, Yves Benoist #2,
集中講義 intensive lectures (901-57 数理科学特別講義Ⅲ/0505115 数理科学続論C (理学部) 共通講義)
Date: June 17 (Mon)-21 (Fri), 2019
Place: Room 123, Graduate School of Mathematical Sciences, the University of Tokyo
Speaker: Takaaki Nomura 野村隆昭 (九州大学名誉教授/大阪市立大学数学研究所特別研究員)
Title: 球面調和函数と群の表現
Abstract:
球面調和函数は,数学をはじめ,物理学や工学等,様々な分野で現れる重要な函数である.$\mathbb{R}^3$における2次元球面の場合は,ルジャンドル多項式を用いて,3次元回転群の表現論とともに詳しく論じられ,扱っている著書や文献も数多くある.
本講義では,次元を一般にした場合の球面調和函数について,古典的理論から群の表現論や非可換調和解析等の現代的視点までを一貫した形で概説する予定である.
集中講義 intensive lectures (数理科学特論VIII)
Date: Oct 3, 10, 17, 24, 31, Nov 7, 14, 21, 28, 2019, 13:00-14:45
Place: Room 128, Graduate School of Mathematical Sciences, the University of Tokyo
Speaker: Yves Benoist (CNRS, Université Paris-Sud)
Title: Kleinian groups
Abstract:
Kleinian groups are discrete groups of isometries of the hyperbolic space. We will study both subgroups of finite and infinite covolume. Here are a few aspects that we will discuss:
- The hyperbolic space, its boundary and its isometries.
- Construction of discrete subgroups and lattices.
- Limit set, convex cocompact subgroups and autosimilar fractal sets.
- Hausdorff dimension, critical exponent and spectrum of the Laplacian.
談話会 Colloquium
Date: Oct 25, 2019, 15:30-16:30
Place: Room 123, Graduate School of Mathematical Sciences, the University of Tokyo
Speaker: Yves Benoist (CNRS, Université Paris-Sud)
Title: Arithmeticity of discrete subgroups
Abstract:
By a theorem of Borel and Harish-Chandra, an arithmetic group in a semisimple Lie group is a lattice. Conversely, by a celebrated theorem of Margulis, in a higher rank semisimple Lie group G any irreducible lattice is an arithmetic group.

The aim of this lecture is to survey an arithmeticity criterium for discrete subgroups which are not assumed to be lattices. This criterium, obtained with Miquel, generalizes works of Selberg and Hee Oh and solves a conjecture of Margulis. It says: a discrete irreducible Zariski-dense subgroup of G that intersects cocompactly at least one horospherical subgroup of G is an arithmetic group.

© Toshiyuki Kobayashi