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Research seminar in Discrete Mathematics
Research seminar in Discrete Mathematics
A d-degree generalization of the Erdős-Ko-Rado Theorem
A d-degree generalization of the Erdős-Ko-Rado Theorem
Organizers
Jie Ma
, Benjamin Sudakov
Speaker
Hao Huang
Time
Tuesday, October 28, 2025 5:05 PM - 6:15 PM
Venue
Online
Online
Zoom 787 662 9899
(BIMSA)
Abstract
Perhaps the most well-known theorem in extremal combinatorics, the Erdős-Ko-Rado (EKR) Theorem asserts that for n>=2k, an intersecting family of k-subsets of {1, ..., n} contains at most n-1 \choose k-1 sets. In 2017, Yi Zhao and I established a degree version of the EKR Theorem, showing that when n>=2k+1, the least popular element of the ground set is contained in at most n-2 \choose k-2 sets of such a family. In this talk, I will present a further generalization of these results to the setting of minimum d-degree, improving a result of Kupavskii. This is a joint work with Yi Zhang (BUPT).
Speaker Intro
Hao Huang is currently an Associate Professor at the National University of Singapore. Prior to joining NUS, he was a tenure-track Assistant Professor in the Department of Mathematics at Emory University from 2015 to 2021, and was tenured there in 2021. From 2012 to 2015, he held postdoctoral positions at the Institute for Advanced Study in Princeton, DIMACS at Rutgers University, and the Institute for Mathematics and its Applications at the University of Minnesota. He completed his B.S. degree in the School of Mathematical Sciences at Peking University in 2007. He received his Ph.D. in June 2012 from the Department of Mathematics at UCLA, where he was advised by Professor Benny Sudakov.