MATH Seminar

Title: The asymptotics of $r(4,t)$
Seminar: Combinatorics
Speaker: Sam Mattheus of UVB
Contact: Liana Yepremyan,
Date: 2023-10-25 at 4:00PM
Venue: MSC E406
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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.

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