Benjamin Sudakov

Tuan Tran

Tuesday, March 18, 2025 5:05 PM - 6:15 PM

Online

Zoom 787 662 9899 (BIMSA)

The discrepancy of a pair of hypergraphs, introduced by Bollobás and Scott (2010), measures how uniformly and independently their edges are distributed. Building on results by Erdős and Spencer, Bollobás and Scott conjectured that any pair of k-uniform hypergraphs of moderate density should have a large discrepancy. While Bollobás and Scott confirmed this for $k=2$, they later found a counterexample for $k=3$. In this talk, we extend their result by presenting a counterexample for all $k>2$. Additionally, we show that for $k=3,4,\ldots,14$, any collection of three $k$-uniform hypergraphs of moderate density always contains a pair with large discrepancy. We also discuss a related result that resolves the dense case of a conjecture by Kwan, Sudakov, and the speaker on edge statistics of hypergraphs.

This talk is based on joint work with Diep Luong and Yang Dilong.

Tuan Tran is an Associate Professor of Mathematics at University of Science and Technology of China. He received his PhD from Free University of Berlin, under the supervision of Tibor Szabo. Before joining USTC, he held postdoctoral positions at Institute for Basic Science (Korea), ETH Zurich, and Czech Academy of Sciences.His main research interests are Extremal, Probabilistic and Additive Combinatorics.