Representation Theory and Mathematical Physics Seminar: Premodular categories and 4-dimensional topological field theories

Seminar | November 7 | 4-5 p.m. | 891 Evans Hall

 Alexander Kirillov Jr., Stony Brook University

 Department of Mathematics

The notion of topological field theory was formalized by Michael Atiyah; it is a purely mathematical notion inspired by physics. In particular, such a theory gives invariants of closed \(d\)-manifolds.

Examples of 3-dimensional topological field theories have been well studied, most notably Reshetikhin–Turaev and Turaev–Viro theories. However, in dimension 4, situation is much less understood.

In this talk, we give an overview of one construction of a 4-dimensional topological field theory based on the notion of pre-modular category; in particular, we give computation of invariants which such a theory would associate to some 2-dimensional surfaces.