Video URL

https://pirsa.org/16050052

Gluing in factorization homology via quantum Hamiltonian reduction

Jordan, D. (2016). Gluing in factorization homology via quantum Hamiltonian reduction. Perimeter Institute for Theoretical Physics. https://pirsa.org/16050052

Jordan, Daniel. Gluing in factorization homology via quantum Hamiltonian reduction. Perimeter Institute for Theoretical Physics, May. 26, 2016, https://pirsa.org/16050052 

          @misc{ scivideos_PIRSA:16050052,
            doi = {10.48660/16050052},
            url = {https://pirsa.org/16050052},
            author = {Jordan, Daniel},
            keywords = {Mathematical physics},
            language = {en},
            title = {Gluing in factorization homology via quantum Hamiltonian reduction},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2016},
            month = {may},
            note = {PIRSA:16050052 see, \url{https://scivideos.org/pirsa/16050052}}
          }

Daniel Jordan

DOI 10.48660/16050052
Source Repository PIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Topological factorization homology is an invariant of manifolds which enjoys a hybrid of the structures in topological field theory, and in singular homology.  These invariants are especially interesting when we restrict attention to the factorization homology of surfaces, with coefficients in braided tensor categories.  In this talk, I would like to explain a technique, related to Beck monadicity, which allows us to compute these abstractly defined categories, as modules for explicitly computable, and in many cases well-known, algebras.

 

The algebras produced in this way for the annulus and punctured torus are the so-called ``reflection equation algebra" and "quantum differential equation algebra", respectively.  When we close up punctures, a variation on the our formalism naturally reproduces the framework of quantum Hamiltonian reduction, and leads to simultaneous deformations of categories D(g/G) of character sheaves on g, on the one hand, and categories QC(Ch_G(T^2)), of quasi-coherent sheaves on the character variety of T^2, on the other.  We call these deformations "quantum character varieties", and they form the two-dimensional part of a four dimensional TFT related to Kapustin-Witten's geometric Langlands TFT, or "topologically twisted N=4 SYM".