We improve the upper bound for diagonal Ramsey numbers to
for . 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.
"Diagonal Ramsey via effective quasirandomness." Duke Math. J. 172 (3) 545 - 567, 15 February 2023. https://doi.org/10.1215/00127094-2022-0048