S-duality and Lie Super-algebras

Explore a series of conjectural statements providing geometric realization of categories of finite-dimensional representations of quantum simple Lie super-algebras with invariant symmetric bilinear forms in this lecture. Delve into the motivation behind these conjectures from S-duality in mathematical physics, with a focus on those formulated by D. Gaiotto for classical Lie super-algebras. Examine the connection to local quantum geometric Langlands correspondence and its relation to the "relative Langlands duality" of Ben Zvi, Sakellaridis, and Venkatesh. Investigate proven cases of these conjectures based on works by Braverman, Finkelberg, Ginzburg, Travkin, and Yang. Gain insights into advanced topics in mathematical physics and representation theory throughout this comprehensive talk.