# Computer Science/Discrete Mathematics Seminar I

## Graph Density Inequalities, Sums of Squares and Tropicalization

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.

This is joint work with Greg Blekherman, Mohit Singh, and Rekha Thomas.

### Date & Time

February 01, 2021 | 11:15am – 12:15pm

### Location

Remote Access - see Zoom link below### Speakers

Annie Raymond

### Speaker Affiliation

University of Massachusetts Amherst