Standard Monomials for Positroid Varieties

Watch a 57-minute mathematics seminar lecture exploring the combinatorial study of positroid varieties through Gröbner bases, following Hodge's influential approach from the 1940s. Delve into an explicit combinatorial description of standard monomials and Gröbner bases of positroid varieties under Hodge degeneration, introduced by Knutson-Lam-Speyer in 2013. Learn how these varieties provide an advantageous stratification of the Grassmannian and discover the connections between cyclic and reflectional symmetry of positroid varieties and combinatorial operations on semistandard Young tableaux. Explore a formula for computing characters of cyclic Demazure modules through a recurrence on Hilbert series of positroid varieties, addressing a question posed by Lam. The research presented represents collaborative work with Ayah Almousa and Shiliang Gao.