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Title:
Applications of 3d N=4 theories in geometric representation theory
Speaker:
Abstract:
I will discuss a few constructions and predictions to have come out of a recent study of boundary conditions in 3d N=4 gauge theories with Bullimore, Hilburn, and Gaiotto. A major goal the study was to obtain a physical explanation/understanding of symplectic duality (in the sense of Braden-Licata-Proudfoot-Webster), which I will touch upon briefly. Another result, which I will explain in greater detail, is an action of certain quantum algebras on the equivariant cohomology of vortex moduli spaces, generalizing work of Braverman-Feigin-Finkelberg-Rybnikov. If time allows, I also hope to mention the symplectic duals of Nakajima's Hecke correspondences, and some recent work of Gaiotto on applications to the geometric Langlands program.
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