Friday, March 12, 2021
03/12/2021 - 1:00pm
In this talk I'll explain joint work with Gunningham and Safronov which proves of a conjecture of Witten, asserting that the skein module of a closed oriented 3-manifold is finite-dimensional. The proof ties together techniques from topological field theory, geometric representation theory, and deformation quantization. The results hold not just for the Kauffman bracket skein module but for the $G$-skein theory of an arbitrary reductive group $G$, for generic parameters $q$. Time permitting I'll formulate a (conjectural) instance of geometric Langlands duality involving these dimensions, and indicated a few cases where the conjecture is confirmed.