2009年度 組合せ数学セミナー†
第2回 2010年 2月10日(水)†
- 題名: Cellular automata and groups: dynamical aspects of infinite groups
- 時間: 15:00～16:30
- 場所: 伊都キャンパス 数理棟 1階 122番教室
- 講師: Tullio Ceccherini-Silberstein (University of Sannio)
- 概要:
In this talk I would like to introduce the audience to the theory of
cellular automata and groups focusing on some dynamical aspects of infinite groups
(amenability, residual finiteness, local finiteness, periodicity,
surjunctivity and soficity).
As an application, we shall also describe a solution to the
Kaplansky conjecture on the stable finiteness of groups rings
(with coefficients in any field) for the class of sofic groups.
第1回 2010年 2月 9日(火)†
- 題名: On the Okounkov-Vershik approach to the representation theory of the symmetric groups
- 時間: 15:00～16:30
- 場所: 伊都キャンパス 数理棟 1階 122番教室
- 講師: Tullio Ceccherini-Silberstein (University of Sannio)
- 概要:
In this talk, I would like to describe the representation theory
of the symmetric groups along the new lines developed by several authors,
in particular by A.M. Vershik, G.I. Olshanskii and A. Okounkov.
The tools/ingredients of this new approach are either completely new,
or were not fully understood in their whole importance by previous
authors. I'll try to analyze such tools/ingredients which consist of:
(i) the algebras of conjugacy-invariant functions, the algebras of bi-$K$-invariant functions,
the Gelfand pairs and their spherical
functions;
(ii) the Gelfand-Tsetlin algebras and their corresponding bases;
(iii) the branching diagrams, the associated posets and the content of a tableau;
(iv) the Young-Jucys-Murphy elements and their spectral analysis;
(v) the characters of the symmetric group viewed as spherical functions.
