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Asaf Horev: Geometric representation theory and factorization homology on surfaces

Time: Wed 2019-11-13 11.00 - 12.00

Location: Kräftriket, house 6, room 306 (Cramér-rum)

Participating: Asaf Horev, Stockholms universitet

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The purpose of this talk is to give an exposition to quantum character varieties, following Ben-Zvi, Brochier and Jordan's papers arXiv:1501.04652  and arXiv:1606.04769 .

Ben-Zvi-Brochier-Jordan use factorisation homology to construct a 2D topological field theory (TFT) associated to a braided tensor category \(\mathcal{A}\), which assigns to each surface a category. For \(\mathcal{A}\) the category of representations of a quantum group \(G\) this TFT is used to constructs quantum character varieties, which encode the moduli of \(G\)-local systems on an oriented surface. Quantum character varieties recover some well known constructions in quantum group theory: for an annulus it recovers the reflection equation algebra, for a punctured torus it recovers the algebra of quantum differential operators, and for the torus the TFT recovers the category if quantum \(\mathcal{D}\)-modules. 

In this talk I will sketch the main construction of BZ-B-J and indicate how it explains some well known actions of mapping class groups and surface braid groups on the above algebras.