Department of Mathematics - Master Calendar

Title: Delta-matroids and toric degenerations in the maximal orthogonal Grassmannian OG(n,2n+1) 

Abstract: Let Z be a general point of the Grassmannian Gr(k,n), which has an action by T = (C*)^n.  Berget and Fink proved a formula via equivariant localization that expresses the cohomology class of the torus orbit closure of Z as a sum of products of Schubert classes, indexed by partitions. In a previous work, Lian gave a new proof of the formula by constructing an explicit toric degeneration of the general orbit closure in Gr(k,n) into a union of Richardson varieties, whose moment map images form a polyhedral decomposition of that of the general orbit closure. With C. Lian, we apply this strategy to deduce a formula in the case of the maximal orthogonal Grassmannian OG(n,2n+1). I will explain the general strategy, focusing on the case of Gr(k,n), and highlight the additional difficulties in its application to OG(n,2n+1).