Intersections of Hypergraphs: Discrepancy and Anticoncentration

This lecture explores the discrepancy of hypergraph pairs, a concept introduced by Bollobás and Scott in 2010 that measures how uniformly and independently hypergraph edges are distributed. Learn about the speaker's research extending previous results by presenting counterexamples to the Bollobás-Scott conjecture for all k > 2, while demonstrating that for k values between 3 and 14, any collection of three k-uniform hypergraphs of moderate density always contains a pair with large discrepancy. The talk also addresses a related result resolving the dense case of a conjecture on edge statistics of hypergraphs. Professor Tuan Tran from the University of Science and Technology of China presents this research based on joint work with Diep Luong and Yang Dilong, drawing on his expertise in extremal and probabilistic combinatorics.