Title: Skein theory and the geometric Langlands program.Abstract: Â Skein modules are certain families of vector spaces spanned by embedded links or graphs in a 3-manifold M, modulo certain local relations. They can be thought of both as an obstruction to defining a polynomial invariant of knots in M and as an invariant of the 3-manifold […]
Title: Kapustin-Witten (KW) and Kapustin-Rozanksy-Witten (KRS) theory path to knot homologyAbstract: My talk is based on the joint project with Lev Rozansky. As a motivation, I will interpret KRS theory as KW theory with defects. Then I will explain how we rigorously construct 3D TQFT, which is a KRS theory with targets Hilbert scheme of […]
Title: Bulk-edge correspondence and an alternative proof of Bott periodicity theorem via Quot schemesAbstract: The study of topological matter is one example of the application of algebraic topology in physics. The bulk-edge correspondence, which asserts that the bulk index of a topological matter coincides with its edge index, has been formulated mathematically in various forms […]
Title: Decategorified Heegaard Floer theory and actions of both E and FAbstract: I will outline a relative of decategorified bordered sutured Heegaard Floer homology in which the vector spaces assigned to surfaces S with corners have actions of the full psl(1|1) (with both E and F) for smooth circles in the boundary of S, and […]
Title: Highly Connected 7-manifolds, Non-negative Curvature and the Linking FormAbstract: Closed manifolds admitting non-negative sectional curvature are not very well understood and it is, at present, quite difficult to obtain examples with interesting topology. Â All known examples depend in some way on two basic facts: First, compact Lie groups admit a bi-invariant metric (hence, non-negative […]