It has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum filed theory.  This course will at first give a motivated introduction to the Langlands Program, including its geometric reformulation, addressed primarily to physicists.  Then I will describe the connections between the Langlands Program and two-dimensional conformal field theory, which give us important insights into the physical implications of the Langlands duality.

E-mail：yyuan@tsinghua.edu.cn 

teaching materials：/uploads/file/2020/20200508/20200508175144_24652.rar

Linear Algebra, Commutative Algebra, Lie Algebra.

1, E. Frenkel, “Lectures on the Langlands Program and cinformal field theory”.

2, E. Witten, “Gauge theory and the geometric Langlands Program”, notes of a talk at the Third Simons Workshop, SUNY at Stony Brook, August 2005.

3, A. Belavin, A. Polyakov and A. Zamolodchikov, “Infinite conformal symmetries in two-dimensional quantum field theory”, Nucl. Phys. B241 (1984) 333-380.