Nigel Higson教授 スーパーグローバルコース数学特別講義

Nigel Higson教授(Kyoto University / Pennsylvania State University)によるスーパーグローバルコース数学特別講義を下記の要領で行います。

日 時
2017年4月14日(金)〜5月26日(金) *5月5日を除く毎週金曜日
4月14日(金) 10:00〜12:00
4月21日(金) 10:00〜12:00
4月28日(金) 10:00〜12:00 / 14:00〜16:00
5月12日(金) 10:00〜12:00 / 14:00〜16:00
5月19日(金) 10:00〜12:00
5月26日(金) 10:00〜12:00
場 所
京都大学理学部3号館 127大会議室
題 目
The Noncommutative Geometry of Tempered Representations
概 要
The purpose of these lectures is to study the tempered dual of a real reductive group as a noncommutative topological space.
The unitary dual of a locally compact group may be identified with the spectrum of its group C*-algebra. The C*-algebra point of view equips the unitary dual with a topology, and it also associates to every unitary representation of the group, irreducible or not, a closed subset of the dual. In the case of a real reductive group, the tempered dual is the closed set associated to the regular representation.
The tempered dual may also be thought of as the spectrum of the so-called reduced C*-algebra. Following standard practice in C*-algebra theory and noncommutative geometry, we shall interpret the problem of studying the tempered dual as a noncommutative topological space as the problem of studying the reduced C*-algebra up to Morita equivalence.
The extra effort that is required to study the tempered dual in this more elaborate way, and not just a set, is rewarded in spectacular fashion by a beautiful isomorphism statement in K-theory that was conjectured by Connes and Kasparov, and later proved by Wassermann and Lafforgue. I shall describe a proof of the Connes-Kasparov isomorphism for real reductive groups that mostly follows the approach outlined by Wassermann but also uses ideas introduced by Vincent Lafforgue, together with new index-theory calculations that extend Lafforgue's ideas.
言 語
備 考