Critical limit of CFT and classical limit geometric Langlands

by Duong Dinh (MPIM)

Tuesday 16 Apr 2024, 14:00 → 16:00 Europe/Berlin

More than 30 years ago, Beilinson and Drinfeld used techniques inspired by 
conformal field theories to construct a natural quantization of the Hitchin integrable systems,
which is a key ingredient in their approach to the geometric Langlands correspondence. For G = SL_2, I will start by explaining the role of conformal field theories in this construction, such as how the eigenfunctions of quantum Hitchin Hamiltonians can appear as limits at 
critical level of solutions to the Knizhnik–Zamolodchikov equations. I will then construct a 
symplectomorphism from the cotangent of the moduli spaces of pairs (bundle, subbundle) 
to certain symmetric product of the cotangent of the base curve, and explain how this can 
be considered as a classical limit of the geometric Langlands correspondence.