Exponential improvements in Ramsey theory

Abstract: The Ramsey number r(t) is the smallest natural number n such that every two-colouring of the edges of $K_n$ contains a monochromatic copy of $K_t$. It has been known for over seventy years that the Ramsey number lies between $\left(\sqrt{2}\right)^t$ and $4^t$, but improving either bound by an exponential factor remains a difficult open problem. In this lecture, we discuss several related problems where such an exponential improvement has been achieved.

This talk reflects joint work with many co-authors, including Asaf Ferber, Jacob Fox, Andrey Grinshpun, Xiaoyu He and Yuval Wigderson.

combinatoricsprobability

Audience: researchers in the topic

Extremal and probabilistic combinatorics webinar

Series comments: We've added a password: concatenate the 6 first prime numbers (hence obtaining an 8-digit password).