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# Andrey Smirnov, Special Colloquium

## December 1, 2017 @ 4:00 pm - 5:00 pm

**Title:** *Symplectic resolutions and representation theory.*

**Abstract:** It was recently realized that the enumerative geometry of a special type of symplectic varieties (known as the symplectic resolutions) is governed by the representation theory of certain Kac-Moody type algebras. I will start this talk with several elementary examples of this correspondence. In particular, I will discuss the relation between quantum cohomology and quantum K-theory of cotangent bundles to Grassmannians and representation theory of sl(2). I then outline generalizations to other symplectic resolutions and discuss some recent results and open problems in the field. I will also go over several applications of these ideas to combinatorics, theory of special functions, differential (and q-difference) equations and mathematical physics.