Title:  Symplectic annular Khovanov homology for symmetric knots 

Speaker:  Sriram Raghunath

Abstract: When a knot diagram is symmetric, it induces an action on the Khovanov chain complex of the knot. We can analyze the equivariant cohomology of the chain complex with this action to understand relationships between the Khovanov homology of the original knot and the Khovanov homology of the quotient knot. Stoffregen and Zhang have studied the extension of this action to the Khovanov homotopy type and applied Smith theory to prove results about periodic knots, while Lipshitz and Sarkar have used the same technique to understand the Khovanov homology of strongly invertible knots. 

Seidel and Smith have defined a symplectic reformulation of combinatorial Khovanov homology, and they have used localization techniques in Floer theory to study the symplectic Khovanov homology of 2-periodic knots. In our work, we define an annular version of symplectic Khovanov homology, and apply this theory to understand the symplectic Khovanov homology of 2-periodic and strongly invertible knots. This is joint work with Kristen Hendricks and Cheuk Yu Mak.