Introduction to Geometric Langlands Theory

Description:

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.

Prerequisite:

Basic algebra geometry; Group theory, information theory, quantum mechanics (preferable)

Biography:

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.