## 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]