Victoria Schleis (Durham University):

Abstract: We study the geometry of initial degenerations of homogeneous subvarieties of (multi-)projective space using polyhedral geometry. In 2017, Corey characterized initial degenerations of the Grassmannian through limits of strata in a matroid stratification of the Grassmannian corresponding to the weight vector of the initial degeneration. Since then, similar results have been proven for the flag variety and Spinor varieties. In my talk, I will discuss recent work in progress extending this study beyond specific examples to homogeneous subvarieties of (multi)-projective space. The talk is based on joint work in progress with George Balla, Dan Corey, and Igor Mahklin.