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Research seminar in Discrete Mathematics
Intersections of hypergraphs: discrepancy and anticoncentration
Intersections of hypergraphs: discrepancy and anticoncentration
Organizer
Benjamin Sudakov
Speaker
Tuan Tran
Time
Tuesday, March 18, 2025 5:05 PM - 6:15 PM
Venue
Online
Online
Zoom 787 662 9899
(BIMSA)
Abstract
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.
This talk is based on joint work with Diep Luong and Yang Dilong.
Speaker Intro
Tuan Tran is a professor at the University of Science and Technology of China (USTC). He earned his Ph.D. from the Free University of Berlin in 2015 under the supervision of Tibor Szabó. His research focuses on extremal and probabilistic combinatorics.