QLunch:Varieties of sum of powers, Stiefel manifolds and their degrees

Speaker: Fulvio Gesmundo from QMATH

Title: Varieties of sum of powers, Stiefel manifolds and their degrees

Abstract: Varieties of sum of powers parameterize decompositions of a given homogeneous polynomial as sum of powers of linear forms: they have been studied since the nineteenth century and they are notoriously a difficult object to understand. Given a homogeneous polynomial, we introduce an alternative variety that records similar information as the variety of sum of powers, and we observe that in the case of quadratic forms this object is identified with the Stiefel manifold. I will present some recent work, joint with T. Brysiewicz, where we studied this algebraic variety and in particular we computed its degree.