Splicing map for positroid varieties -- Combinatorics seminar

I will introduce the splicing map, a map that decomposes top-dimensional positroid varieties into a product of two top-dimensional varieties in a way that preserves the overall dimension. We can represent this map using the associated cluster structures, interpreting it as an isomorphism generated by fixing a subset of cluster variables and applying a cluster quasi-equivalence. The development of the splicing map is inspired by the connection Galashin and Lam established between the torus-equivariant homology of $\Pi_{k,n}^\circ$ and the Khovanov-Rozansky homology $HHH$ of the torus link $T(k,n-k)$. This is joint work with Eugene Gorsky. If time permits, I may briefly discuss the splicing map for non-top dimensional positroids which is joint work with Eugene Gorsky, Jose Simental, and Soyeon Kim.