Time: 14:00 -- 16: 00, April 11, 2025

Venue: Room 612, A6, Institute of Mathematics-VAST

Abstract: We study non-negativity of convex polynomials by employing critical value polynomials and Descartes' rule of signs. The main result shows that, under a genericity condition, a lower-bounded polynomial $p$ is non-negative if and only if the number of sign changes of the coefficients of the critical value polynomial of $-p$ is even. Based on the proof, we propose a method to symbolically check whether such a polynomial $p$ is non-negative or not.

The talk is based on joint work with Akiko Takeda (the University of Tokyo).