A q-deformation of the geometric Langlands correspondence
Prof.Pavel SAFRONOV(Université de Genève & IHES)
Amphithéâtre Léon Motchane (IHES)
Amphithéâtre Léon Motchane
35, route de Chartres, F-91440 Bures-sur-Yvette (France)
The geometric Langlands correspondence was introduced by Beilinson and Drinfeld as a tool to solve quantum Hitchin systems such as the Gaudin model. The correspondence can be understood following Kapustin and Witten as arising from S-duality in a topologically twisted 4-dimensional super Yang-Mills theory. In this talk I will describe a multiplicative deformation of the Hitchin system and explain a conjectural statement of the corresponding q-deformed correspondence. I will also give some motivations for the statement from the theory of higher deformation quantization and a deformed setup of Kapustin and Witten.