# Graph Density Inequalities, Sums of Squares and Tropicalization

Date: Thu, Feb 11, 2021

Location: Zoom, PIMS, University of Victoria

Conference: PIMS-UVic Discrete Math Seminar

Subject: Mathematics

Class: Scientific

### Abstract:

Establishing inequalities among graph densities is a central pursuit in extremal graph theory. One way to certify the nonnegativity of a graph density expression is to write it as a sum of squares or as a rational sum of squares. In this talk, we will explore how one does so and we will then identify simple conditions under which a graph density expression cannot be a sum of squares or a rational sum of squares. Tropicalization will play a key role for the latter, and will turn out to be an interesting object in itself. This is joint work with Greg Blekherman, Mohit Singh, and Rekha Thomas.