Homotopy quantum groups
Organizers
Speaker
David Reutter
Time
Wednesday, June 25, 2025 3:00 PM - 4:30 PM
Venue
A3-3-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
The SymTFT paradigm in physics suggests to describe the symmetries of a D=(d+1)-dimensional quantum field theory as the data of a (D+1)-dimensional bulk topological quantum field theory with a D-dimensional topological boundary theory, termed a `quiche' by Freed, Moore and Teleman. In this way, quiches generalize (higher categorical) groups and hence topological spaces (considered up to homotopy).
In this talk, I will describe how one may assign to a quiche a list of `homotopy quantum groups' — Hopf algebras in a certain braided category associated to the quiche — which generalize the homotopy groups of a topological space. I will argue that for d>=3 (and sufficiently finite topological field theories valued in linear categories), these homotopy quantum groups are in fact (classical) abelian groups. I will explain how these groups can be computed for quiches arising from (higher) fusion categories.
This is based on joint work in progress with Theo Johnson-Freyd.
In this talk, I will describe how one may assign to a quiche a list of `homotopy quantum groups' — Hopf algebras in a certain braided category associated to the quiche — which generalize the homotopy groups of a topological space. I will argue that for d>=3 (and sufficiently finite topological field theories valued in linear categories), these homotopy quantum groups are in fact (classical) abelian groups. I will explain how these groups can be computed for quiches arising from (higher) fusion categories.
This is based on joint work in progress with Theo Johnson-Freyd.