260024 VU 3-dimensional functorial field theories (2022S)

This course is an introduction to examples of functorial field theories in three spacetime dimensions, meant for both theoretical physicists and mathematicians interested in the subject. After a self-contained yet steep review of the necessary tools from category theory, the first two thirds of the course will be on topological quantum field theories of Reshetikhin-Turaev type; in the last third we will study how to include spin in such theories. The course is organised jointly with Lorant Szegedy.

In physics, Reshetikhin-Turaev theories are related to the quantisation of Chern-Simons gauge theories. Mathematically the main ingredients of the theory are modular fusion categories and surgery theory, both of which will be introduced in the course. Among the applications that can be discussed are knot invariants like the Jones polynomial and the relation to 2-dimensional conformal field theory.

The course will be held in seminar style with ample room for discussions. A detailed plan, including an extended introduction and precise pointers to textbooks, will be presented in the first session. Every other session will be divided into up to 90 minutes of presentation (mostly by students) and at least 45 minutes of discussion.

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Depending on the status of the pandemic, the course will be held on-site or online. We hope and plan to be on-site, responsibly with regards to publich health. More information will be available in early March.