Summer school on Representation theory of finite and p-adic groups
Time:09:00:29/08/2016 to 16:30:01/09/2016
Venue/Location: C2-714
Purpose: Representation theory plays a central role in modern mathematics. As Gelfand once spoke with a point of humour, all mathematics is representation theory. This summer school aims to cover some basic foundation of representation theory. It should be accessible to PhD students in mathematics and advanced undergraduate student with strong background in algebra and geometry.
Content:Morning (9:00-11:30) and Afternoon (14:00 - 16:30) lectures everyday
Participants: Open to researchers, graduate and advanced undergraduate students
1) Deligne-Lusztig theory (Pham Huu Tiep)
Abstract:
Linear algebraic groups and their finite counterparts -- finite groups of Lie type -- play an important role in mathematics, particularly in group theory and number theory.
By the classification theorem of finite simple groups (CFSG), the majority of finite non-abelian simple groups arise from finite groups of Lie type. One of the most fundamental achievements in the area is the Deligne-Lusztig theory of complex representations of finite groups of Lie type. Together, the CFSG and the Deligne-Lusztig theory have made it possible to resolve many problems arising from important applications outside of group theory, particularly in number theory and algebraic geometry.
The goal of these lectures is to introduce the audience to some basic ideas of the Deligne-Lusztig theory.
2) Characters of finite and compact groups (Ngo Bao Chau)
Abstract:
This is an introductory course to representation theory of finite and compact groups with emphasis on characters. We will use Barry Simon's book as a basic reference for this school.