Student Probability and Mathematical Physics Seminar

---

The Erdős-Ko-Rado theorem and its randomized variants

Speaker: Austen Mazenko, CIMS

Location: Warren Weaver Hall 201

Date: Tuesday, February 24, 2026, 12:30 p.m.

Synopsis:

The Erdős-Ko-Rado theorem on maximal intersecting k-families of sets is a cornerstone of extremal combinatorics. We will outline a recent simple proof of the stability of Erdős-Ko-Rado due to Bulavka and Woodroofe. Next, we'll consider Balogh, Bohman, and Mubayi's findings on the regimes of random hyper graphs where the Erdős-Ko-Rado theorem remains true, while also remarking on recent strengthenings of their main results. Finally, we'll introduce a similar result by Bollobás, Narayanan, and Raigorodskii which considers the problem for hypergraphs under a natural but different randomization scheme.