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Workshop

Stable and Hurwitz slices, a degree principle and a generalized Grace-Walsh-Szegő theorem

  • Sebastian Debus (TU Chemnitz, Germany)
E1 05 (Leibniz-Saal)

Abstract

We consider affine varieties defined by multivariate complex symmetric polynomials and address the question whether such a variety contains a point with only few distinct real and imaginary coordinates. We present a degree principle for half-planes and a weak generalization of Grace-Walsh-Szegő’s coincidence theorem to symmetric polynomials that are not necessarily multiaffine but which can be expressed in few elementary symmetric polynomials. The results are derived from studying linear slices of the set of univariate stable polynomials with respect to a closed half-plane using Vieta’s formulas. Similarly, we study affine slices of the set of weakly Hurwitz polynomials.

This is joint work with Cordian Riener and Robin Schabert

conference
29.07.24 02.08.24

MEGA 2024

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Felix-Klein-Hörsaal

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Christian Lehn

Ruhr-Universität Bochum

Irem Portakal

Max Planck Institute for Mathematics in the Sciences

Rainer Sinn

Universität Leipzig

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Simon Telen

Max Planck Institute for Mathematics in the Sciences

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