Homotopy quantum groups
演讲者
David Reutter
时间
2025年06月25日 15:00 至 16:30
地点
A3-3-301
线上
Zoom 242 742 6089
(BIMSA)
摘要
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.
演讲者介绍
David Reutter is a mathematician leading the Emmy Noether Research Group at the University of Hamburg, where he investigates topological quantum field theory beyond three dimensions. His research focuses on higher category theory, low-dimensional topology, homotopy theory, and quantum algebra, particularly in relation to fusion categories and TQFTs. After earning his PhD at Oxford under Jamie Vicary, he held postdoctoral positions at the Max Planck Institute for Mathematics and MSRI. He is known for his contributions to fusion 2-categories, semisimple 4D TQFTs, and the categorification of algebraic structures.