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Math-Physics Joint Seminar

Tuesday, May 1, 2018 - 4:30pm

Philsang Yoo



University of Pennsylvania


The geometric Langlands program arose in the 1980's as an analogue of the Langlands program for algebraic curves, but only recently were Arinkin and Gaitsgory (2012) able to formulate a plausible categorical version of the conjecture, introducing the notion of singular supports for coherent sheaves. A few years earlier, Kapustin and Witten (2006) placed a version of the categorical conjecture in a physical context, but their work didn't capture the algebro-geometric nature of the conjecture nor did it address the subtleties Arinkin and Gaitsgory had to overcome. After setting up a rigorous mathematical model for Kapustin and Witten's theory, we identify the physics of the Arinkin--Gaitsgory formulation of the conjecture. Moreover, from the physical interpretation, we suggest some curious factorization structure in the geometric Langlands theory. This is based on a joint work with Chris Elliott

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