We improve the upper bound for diagonal Ramsey numbers to R(k+1,k+1) ≤ exp(-c(log k)2)(2k)!/(k!)2 for k ≥ 3. To do so, we build on a quasirandomness and induction framework for Ramsey numbers introduced by Thomason and extended by Conlon, demonstrating optimal ‘effective quasirandomness’ results about convergence of graphs. This optimality represents a natural barrier to improvement.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
