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Presented By: Combinatorics Seminar - Department of Mathematics

Splicing map for positroid varieties -- Combinatorics seminar

Tonie Scroggin, UC Davis

The quiver of G(3,8) and its image under splicing The quiver of G(3,8) and its image under splicing
The quiver of G(3,8) and its image under splicing
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.
The quiver of G(3,8) and its image under splicing The quiver of G(3,8) and its image under splicing
The quiver of G(3,8) and its image under splicing

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