# LMS-INI- Bath Summer School on K-Theory & Representation Theory

VIRTUAL#### 19/07/2021 - 23/07/2021

**Organisers:**

Dr. Haluk Şengün, University of Sheffield

Prof. Roger Plymen, University of Manchester

Prof. Nigel Higson, PennState University

Funding: core funding from the Isaac Newton Institute (INI)

Sponsor: Institute for Mathematical Innovation (IMI)

#### EVENT OVERVIEW

This is the summer school part of the LMS-INI-Bath Symposium on K-theory and Representation Theory (which will take place in July 2022). In this summer school, we will cover material that is foundational to the upcoming symposium, namely, representation theory of real and p-adic Lie groups, the theory of C*-algebras and operator K-theory, and finally the method of "Dirac Induction" which brings the above together by employing Dirac operators in the study of representations.

## Videos:

K-Theory and representation Theory Summer School: Aubert L1 video

K-Theory & Representation Theory Summer School: Aubert L2 video

K-Theory & Representation Theory Summer School: Aubert L3 video

K-Theory & Representation Theory Summer School: Wang L1 video

K-Theory & Representation theory Summer School: Wang L2 video

K-Theory & Representation Theory Summer School: Wang L3 video

K-theory & Representation Theory Summer School: Mesland L1 video

K-Theory & Representation Theory Summer School : Mesland L2 video

K-Theory & Representation Theory Summer School: Mesland L3 video

K Theory & Representation Theory Summer School: Hochs L1 video

K Theory & Representation Theory Summer School: Hochs L2 video

K Theory & Representation Theory Summer School: Hochs L3 video

## EVENT DOWNLOADS

## Organising Committee

## Lecturers List

#### Peter Hochs (Nijmegen)

Title: An introduction to the representation theory of Lie groups

Abstract:

We will cover the basic theory of the representations of real Lie groups, with the main goal of giving an overview the classification of (almost all) tempered representations of real linear semisimple Lie groups. We will pay special attention to the discrete series representations. The case of SL(2) over the reals will be exposed in detail.

#### Bram Mesland (Leiden)

Title: An introduction to (group) C*-algebras & K-theory

Abstract:

We will cover aspects of the theory of C*-algebras, focusing mainly on group C*-algebras and operator K-theory. The main goal will be to provide a description of K-theory of reduced group C*-algebra of semisimple real Lie groups.

#### Hang Wang (Shanghai)

Title: Dirac operators and Representation Theory

Abstract:

We will introduce Dirac operators in the setting of symmetric spaces associated to semisimple real Lie groups. The construction of discrete series representations using Dirac operators will be presented. Finally, we will cast the construction in the language of operator K-theory.

#### Anne-Marie Aubert (Paris)

Title: An introduction to the representation theory of p-adic groups

Abstract:

These lectures will cover the foundations of the theory, finishing with the Bernstein parametrisation of the tempered dual. The case of SL(2) over the p-adic numbers will be studied in detail.