Ramsey numbers of books and quasirandomness

Perhaps the biggest open problem in graph Ramsey theory is to determine the asymptotic growth rate of the Ramsey numbers of the clique . For this problem, the lower and upper bounds of 2^{r/2} and 4^r, respectively, have remained essentially unchanged for over 70 years. One promising approach towards improving the upper bound comes from the so-called book graphs, whose Ramsey numbers are known to have strong connections to the classical Ramsey numbers of cliques. In this talk, I will present several recent results about these Ramsey numbers of books and their relation to the theory of quasirandom graphs. This is joint work with David Conlon and Jacob Fox.