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.
Lecture Series 1
Lecturer: 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.
Lecture Series 2
Lecturer: 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, paying special attention to discrete series representations. The case of SL(2) over the reals will be exposed in detail.
Lecture Series 3
Lecturer: Bram Mesland (Leiden)
Title: An introduction to the theory of (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 SL(2) over the reals.
Lecture Series 4
Lecturer: Hang Wang (Shanghai)
Title: Dirac operators and Representation Theory
Abstract: We will introduce the Dirac operators in the setting of symmetric spaces associated to semisimple real Lie groups. The construction of discrete series representations using the Dirac operators will be presented. Finally, we will cast the construction in the language of operator K-theory.
Participation is FREE for everyone. However you are required to register.