Quantum Groups from Cohomological Donaldson-Thomas Theory

Shivang Jindal (University of Edinburgh)

Tuesday 15th October 15:00-16:00 Maths 311B

Abstract

In 2012, Schiffmann and Vasserot considered a Hall algebra type construction on the cohomology of moduli of sheaves supported on points on a plane and used it to prove AGT conjecture. However, due to the singular nature of the moduli of representations of pre-projective algebra, these algebras are very hard to study and are often highly nontrivial. In this talk, my goal is to give an introduction to this idea of building algebras out of moduli spaces and explain how one can use tools from Cohomological Donaldson-Thomas theory to study these algebras. In particular, I will explain how for the case of cyclic quiver, this algebra turns out to be universal enveloping algebra of an appropriate half of degenerated Lie algebra of matrix differential operators on torus, while its deformation turns out be an explicit integral form of affine Yangian of gl(n). 

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