  We improve the upper bound for diagonal Ramsey numbers to
\[R(k+1,k+1)\le\exp(-c(\log k)^2)\binom{2k}{k}\] for $k\ge 3$. 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.
