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The notion of singular support for coherent sheaves was introduced by Arinkin and Gaitsgory in order to carefully state the geometric Langlands conjecture. This is a conjectural equivalence of categories of sheaves on certain moduli spaces: in order to make the conjecture reasonable one needs to restrict to sheaves which satisfy a certain "singular support condition". In this talk I'll explain how to think about this singular support condition from the point of view of boundary conditions in twisted N=4 gauge theory. Specifically, Arinkin and Gaitsgory's singular support condition arises by considering only those boundary conditions which are compatible with a natural choice of vacuum state. By allowing this vacuum state to move away from this natural choice we see aspects of a rich additional structure for the geometric Langlands correspondence. This work is joint with Philsang Yoo.

Collection/Series:

Event Type:

Seminar

Scientific Area(s):

Speaker(s):

Event Date:

Monday, May 15, 2017 - 14:00 to 15:30

Location:

Space Room

Room #:

400

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