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Texas A&M University

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]