Georgia Institute of Technology College of Sciences

A semialgebraic hypergraph is a hypergraph whose edges can be described by a system of polynomial inequalities. Semialgebraic hypergraphs appear in many problems in discrete geometry. There has been growing interest in semialgebraic hypergraphs since the discovery that they satisfy strong regularity lemmas, where between most parts, the hypergraph is either complete or empty. In this talk, I will talk about an optimal regularity lemma along these lines and several applications. Based on joint work with Jonathan Tidor.