260081 VU Topological quantum field theory 2 (2023S)

This course is a continuation of the introduction to an axiomatic, functorial approach to topological quantum field theory (TQFT) of the winter term 2022/23. Familiarity with parts of that course (on symmetric monoidal functors and duality) will be assumed, but new participants will be provided a set of written lecture notes for the previous course. (If students express interest, an optional review sessions will be offered in the beginning of March.)

The course will introduce the notions of state sum models, sigma models and Landau-Ginzburg models, explain how they are examples of closed TQFTs, and how they relate to other parts of theoretical physics and mathematics. Depending on the preferences of the audience, later parts of the course will either focus on 3-dimensional TQFTs and their application to topological quantum computation, or on the theory of TQFTs that describe boundary conditions and more general "defects", as well as their application to full, non-topological QFTs.