At the intersection of Ramsey and Turán

Ramsey and Turán numbers are both central quantities in graph theory. Both maximize some quantity — the number of edges (Turán) or independence number (Ramsey) — over n-vertex graphs containing no copy of a fixed forbidden subgraph. In this talk, I'll tell you about a quantity that combines the two notions and what we know about it.

This talk will feature high-dimensional spheres, the regularity lemma, and perhaps even an integral!