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Cluster quantization from factorization homology

[Moved Online] Tensor categories and topological quantum field theories March 16, 2020 - March 20, 2020

March 16, 2020 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): David Jordan (University of Edinburgh)
  • cluster

  • skein

  • TFT

  • parabolic induction

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification



Character varieties are moduli spaces of representations of fundamental groups of manifolds. In dimensions 2 and 3 these exhibit symplectic and Lagrangian structures respectively, and it is an important question in 3d and 4d TQFT to quantize these structures functorially. In the 90's and 00's, three quantization schemes were proposed: via so-called Alekseev-Grosse-Schomerus algebras, via skein theory, and via Fock-Goncharov cluster quantizations. The AGS and FG constructions were intrinsically algebraic, but lacked the desired topological functoriality, while the skein construction is intrinsically topological but algebraically inaccessible. It is by now understood how to obtain AGS algebras and skein theory in the context of factorization homology, in particular how to unify the two quantizations. In this talk I will explain joint work with Ian Le, Gus Schrader and Sasha Shapiro which constructs Fock-Goncharov cluster quantizations from factorization homology. An interesting new ingredient is that of parabolic induction domain walls labeling line defects on the surface.

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H.264 Video 917_28177_8230_2-Jordan.mp4
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