Discrete Math Literature Seminar

Speaker: Ramón García
Title: Solution of uniform Turán’s Tetrahedron Problem by Kielak, Král’, Lamaison, Liu, Shu, and Wu.
Abstract: Turán’s tetrahedron problem, posed in 1941, is one of the best-known open problems in extremal combinatorics. A related version asks what happens when the edges of a hypergraph are required to be spread uniformly throughout the vertex set. In this talk, I will discuss a recent paper by Kielak, Král’, Lamaison, Liu, Shu, and Wu that solves this uniform version. They show that the exact threshold is (1/2), confirming a construction of Rödl from 1986. I will give an overview of the problem, the main result, and some of the ideas behind the proof. If time permits, we will also discuss a proof by Matija Bucić.