Combinatorics Seminar - Sebastian Debus (Otto-von-Guericke University Magdeburg)

16:15-18:00

Speaker: Sebastian Debus

Title: The wonderful geometry of the Vandermonde map

Abstract: In this talk we consider the geometry of the image of the Vandermonde map consisting of the first d power sums restricted on the probability simplex. The images form an increasing chain in the number of variables. We describe the image for finite n and at infinity, and prove that it has the combinatorial structure of a cyclic polytope.
We relate the image to the study of copositive symmetric forms and prove undecidability of verifying nonnegativity of trace polynomials whose domain are all symmetric matrices of all sizes.

This is joint work with Jose Acevedo, Greg Blekherman and Cordian Riener.