Geometry Seminar
Date: October 11, 2019
Time: 4:00PM - 5:00PM
Location: BLOC 628
Speaker: Taylor Brysiewicz, Texas A&M University
Title: The degree of Stiefel manifolds and spaces of Parseval frames.
Abstract: The (k, n)-th Stiefel manifold is the space of k×n matrices M with the property that M*M^T=Id. Equivalently, this is the space of Parseval n-frames for k-dimensional space. The polynomial equations characterizing the Stiefel manifold define an embedded affine algebraic variety. We will sketch our proof of a formula for its degree using aspects of representation theory, Gelfand-Tsetlin polytopes, and the combinatorics of non-intersecting lattice paths. [joint work with Fulvio Gesmundo]