UVictoria Discrete Math Seminar: Hung-Hsun Hans Yu

In this talk, I will talk about applications of the entropy method and a tool that we call the mixture bound. To demonstrate how the mixture bound can be applied, I will show how one can prove Lovász’s version of the Kruskal–Katona theorem. I will also present some recent results on the rainbow triangle problem, which asks to determine the maximum number of rainbow triangles in a 3-edge-colored simple graph with a given number of edges. Time permitting, I will briefly mention how the mixture bound can be applied to obtain Turán-type results as well. This talk is based on joint work with Ting-Wei Chao and Maya Sankar.