Top Global Course Special Lectures by Prof. Nigel Higson
Top Global Course Special Lectures by Prof. Nigel Higson (Kyoto / Pennsylvania State University) will take place as follows:
 Course Title
 Top Global Course Special Lectures 3
 Date & Time
 April 14  May 26, 2017 (Every Friday except May 5.)

Friday, April 14, 10:0012:00
Friday, April 21, 10:0012:00
Friday, April 28, 10:0012:00 / 14:0016:00
Friday, May 12, 10:0012:00 / 14:0016:00
Friday, May 19, 10:0012:00
Friday, may 26, 10:0012:00  *Please see the poster for further details.
 Venue
 127 Conference room, Faculty of Science Bldg. #3, Kyoto University
 Title
 The Noncommutative Geometry of Tempered Representations
 Abstract

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 socalled 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 Ktheory that was conjectured by Connes and Kasparov, and later proved by Wassermann and Lafforgue. I shall describe a proof of the ConnesKasparov isomorphism for real reductive groups that mostly follows the approach outlined by Wassermann but also uses ideas introduced by Vincent Lafforgue, together with new indextheory calculations that extend Lafforgue's ideas.
Please note that anyone in the front rows of the room can be captured by a video camera.