USask PIMS Geometry and Physics (GAP) Seminar: Matthew B. Young

Chern-Simons theory, as introduced by Witten, is a three dimensional quantum gauge theory associated to a compact simple Lie group and a level. The mathematical model of this theory as a topological quantum field theory was introduced by Reshetikhin and Turaev and is at the core of modern quantum topology. The goal of this talk is to explain a non-semisimple modification of the construction of Reshetikhin and Turaev which realizes Chern-Simons theory with gauge supergroup U(1 \vert 1), as studied in the physics literature by Rozansky-Saleur and Mikhaylov. In particular, I'll motivate and explain various relative modular structures on the category of representations of the quantum group of \mathfrak{gl}(1 \vert 1) which should be seen as non-semisimple analogues of modular tensor categories associated to the quantum representation theory of a simple Lie algebra at a root of unity. Based on joint work with Nathan Geer.