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SUMMARY:Generalized Character Varieties and Quantization via Factorization
  Homology
DTSTART:20220301T101500
DTEND:20220301T111500
DTSTAMP:20260407T035408Z
UID:e9db8dceb8dfa4fd719cb64afb02756a023381c367b9bbbc557a89b3
CATEGORIES:Conferences - Seminars
DESCRIPTION:Corina Keller\, Université Montpellier\nFactorization homolog
 y is a local-to-global invariant which "integrates" disk algebras in symme
 tric monoidal higher categories over manifolds. In this talk I will focus 
 on a particular instance of factorization homology on surfaces where the i
 nput algebraic data is a braided monoidal category. If one takes the repre
 sentation category of a quantum group as an input\, it was shown by Ben-Zv
 i\, Brochier and Jordan (BZBJ) that categorical factorization homology qua
 ntizes the category of quasi-coherent sheaves on the moduli space of G-loc
 al systems. I will discuss two applications of the factorization homology 
 approach for quantizing (generalized) character varieties. First\, I will 
 explain how to compute categorical factorization homology on surfaces with
  principal D-bundles decorations\, for D a finite group. The main example 
 comes from an action of Dynkin diagram automorphisms on representation cat
 egories of quantum groups. We will see that in this case factorization hom
 ology gives rise to a quantization of Out(G)-twisted character varieties (
 This is based on joint work with Lukas Müller). In a second part we will 
 consider surfaces that are decorated with marked points. It was shown by B
 ZBJ that the algebraic data governing marked points are braided module cat
 egories and I will discuss an example related to the theory of dynamical q
 uantum groups.
LOCATION:MA A3 30 https://plan.epfl.ch/?room==MA%20A3%2030
STATUS:CONFIRMED
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