Dhruv Mubayi: Hypergraph Eigenvalues and Quasirandomness

Since the foundational results of Thomason and Chung-Graham-Wilson on quasirandom graphs over 20 years ago, there has been a lot of effort by many researchers to extend the theory to hypergraphs. I will present some of this history, and then describe our recent results that provide such a generalization. One key new aspect in the theory is a systematic study of hypergraph eigenvalues first introduced by Friedman and Wigderson. This leads to the study of various extremal questions on hypergraphs, for example, spectral Turan-type problems and spectral packing problems. I will present recent work on both these topics that generalize various results in graph theory like Turan's theorem and the Hajnal-Szemeredi theorem. This is joint work with Peter Keevash and John Lenz.