Mathematical Sciences Department Colloquium
Bob Krueger, Carnegie Mellon
Friday, January 31
10:00 - 11:00 am
Stratton 207
Title: Sparse random analogues of classical combinatorial theorems
Abstract: A successful trend in modern extremal/probabilistic combinatorics is the investigation of how well classical theorems, like those of Ramsey, Turán, and Szemerédi, hold in sparse random contexts. Graph and hypergraph container methods have played a fundamental role in improving our knowledge of various sparse structures. I will present an overview of this area, including some joint work with Jozsef Balogh and Haoran Luo on a random version of the Erdős-Ko-Rado Theorem and Sperner's Theorem. If time permits, I will also talk about some ongoing work on a random version of Ramsey's Theorem.