The asymptotics of $r(4,t)$

Combinatorics Seminar
Friday, October 27, 2023 - 3:15pm for 1 hour (actually 50 minutes)
Skiles 308
Sam Mattheus – Vrije Universiteit Brussel –
Tom Kelly

I will give an overview of recent work, joint with Jacques Verstraete, where we gave an improved lower bound for the off-diagonal Ramsey number $r(4,t)$, solving a long-standing conjecture of Erd\H{o}s. Our proof has a strong non-probabilistic component, in contrast to previous work. This approach was generalized in further work with David Conlon, Dhruv Mubayi and Jacques Verstraete to off-diagonal Ramsey numbers $r(H,t)$ for any fixed graph $H$. We will go over of the main ideas of these proofs and indicate some open problems.