Topology, Algebraic Geometry, and Dynamics Seminar (TADS): The unitary cobordism hypothesis

Speaker: Luuk Stehouwer, Dalhousie University

Title: The unitary cobordism hypothesis

Abstract: The cobordism hypothesis classifies extended topological quantum field theories (TQFTs) in terms of algebraic information in the target category. One of the core principles in quantum field theory - unitarity - says that state spaces are not just vector spaces, but Hilbert spaces. Recently in joint work with many others, we have defined unitarity for extended TQFTs, inspired by Freed and Hopkins. Our main technical tool is a higher-categorical version of dagger categories; categories $C$ equipped with a strict anti-involution $\dagger: C \to C^{op}$ which is the identity on objects. I explain joint work in progress with Theo Johnson-Freyd, Cameron Krulewski and Lukas Müller in which we prove a version of the cobordism hypothesis for unitary TQFTs. I will illustrate the situation in low-dimensional concrete examples.

Date/Time: March 21, 1:30pm

Location: Exploratory Hall, Room 4208