Introduction to Geometric Langlands Theory

任课教师 Speaker:Lin Chen
时间 Time:Tues. & Thur., 13:30-15:05, Sept. 19-Dec. 19, 2023
地点 Venue:Classroom B627, Tsinghua University Shuangqing Complex Building A(清华大学双清综合楼A座B627教室); Zoom Meeting ID: 271 534 5558 Passcode: YMSC


1. Sept. 29-Oct.6:Mid-Autumn Festival and National Day Holidays, No lectures.

2. The lectures on Oct. 10 and Oct. 12 will be canceled. From Oct.17, the venue for Tuesdays will be changed to Lecture Hall C548, Shuangqing Complex Building A.

3. The lectures on Dec. 12 and Dec. 14 will be delivered only online.  Zoom Meeting ID: 271 534 5558 Passcode: YMSC

4. The lecture on Dec. 14 is adjusted to Dec. 19, Lecture Hall C548, Shuangqing Complex Building A. Zoom Meeting ID: 271 534 5558 Passcode: YMSC


We will give an introduction course to the research field called Geometric Langlands Theory (GLT).

Roughly speaking, GLT is the analogue of the classical Number-theoretical Langlands Theory under the function field analogy, but the mathematical structures studied in GLT are often “1-categorical level higher” than its number-theoretical counterpart. Typical such structures include: sheaves on the moduli stack of G-torsors or \check{G}-local systems, categorical representations of the loop group LG, sheaves on the Iwahori-Hecke double quotient, e.t.c..

We will introduce the main results and conjectures, as well as the guiding philosophy in this field. The goal is to provide enough preparation for people interested in this field to read new research papers.


Basic algebraic geometry, category theory, representation theory


Quantization of Hitchin’s integrable system and Hecke eigensheaves (by A. Beilinson and V. Drinfeld)

Singular support of coherent sheaves and the Geometric Langlands Conjecture (by D. Arinkin and D. Gaitsgory)

An informal introduction to categorical representation theory and the local Geometric Langlands Program (by G. Dhillon)



Dr. Lin Chen is an assistent professor at Yau Mathematical Sciences Center. He obtained his Ph.D. in Mathematics from Harvard University in 2021. Dr. Chen’s research interests center around the Geometric Langlands Program. He is also interested in geometric representation theory, higher category theory and derived algebraic geometry.