Speaker:  Melissa Sherman-Bennett  (MIT)

Title:  Cluster structure on braid varieties from 3D plabic graphs

Abstract:  

Braid varieties are smooth irreducible affine varieties associated to any positive braid.  Their cohomology is expected to contain information about the Khovanov-Rozansky homology of a related link.  Special cases of braid varieties include Richardson varieties, double Bruhat cells, and double Bott-Samelson cells.  Cluster algebras are a class of commutative rings with a rich combinatorial structure, introduced by Fomin and Zelevinsky.  I'll discuss joint work with P. Galashin, T. Lam and D. Speyer in which we show the coordinate rings of braid varieties are cluster algebras.  Seeds for these cluster algebras come from "3D plabic graphs", which are bicolored graphs embedded in a 3-dimensional ball and generalized postnikov's plabic graphs for positroid varieties.