Speaker: Nick Cook  (Duke University)

Title: Large deviations and regularity method for sparse random hypergraphs

Abstract: The "infamous upper tail" problem for subgraph counts in Erdős–Rényi graphs has received considerable attention since it was popularized by Janson and Rucinski, and has connections with questions in graph limit theory and statistical physics. I will survey work in this area and discuss a new approach for the more general setting of hypergraphs, based on an extension of the regularity method to sparse hypergraphs. In particular, we develop a sparse counting lemma and decomposition theorem for tensors under a novel class of norms that generalize the matrix cut norm. Based on joint work with Amir Dembo and Huy Tuan Pham.