General Events - Department of Mathematics

Speaker: Marcelo Campos

Title: An exponential improvement for diagonal Ramsey

Abstract: The Ramsey number R(k) is the minimum natural n such that every red-blue colouring of the edges of the complete graph K_n on n vertices contains a monochromatic copy of K_k. In this talk I will present a recent result that shows R(k) < (4 - c)^k for some constant c > 0. This is the first exponential improvement over the upper bound of Erdős and Szekeres, proved in 1935. 

This is joint work with Simon Griffiths, Robert Morris and Julian Sahasrabudhe.