## PIMS-UVic Discrete Math Seminar: Annie Raymond

- Date: 02/11/2021
- Time: 10:00

Online

Graph Density Inequalities, Sums of Squares and Tropicalization [video]

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.

This seminar took place via zoom and a recording is available on mathtube.org.