Topics in Representation Theory

Speaker

朱永昌 Zhu Yongchang

Professor of YMSC

Time

Tues. & Thur., 10:40 am-12:15,

Sept. 16-Dec. 18, 2025

Venue

B725, Shuangqing Complex Building A

Description

This course is divided into two parts. The first part covers basic concepts in representation theory, including an introduction to representations of Lie groups and p-adic groups, with a focus on Heisenberg groups and Weil representations of symplectic groups. We will also explore infinite-dimensional groups and the generalization of Weil representations to infinite-dimensional symplectic groups, as well as the algebraic structures that arise in infinite-dimensional Lie theory, such as vertex operator algebras.

The second part of the course will address several front-line research topics, including the explicit construction of automorphic forms on loop groups, the study of positivity structures, and the beta-gamma systems associated with representations of modular groups and their applications.

Prerequisite:

Lie groups, Lie algebras, some simple algebraic geometry

Target Audience:

Undergraduate students, Graduate students

Teaching Language: English