Xiaoyu He, Princeton University

Abstract

The vast majority of natural Ramsey numbers studied to date have polynomial or exponential growth rates. We give a hypergraph Ramsey number - perhaps the simplest of its kind - with an unusual intermediate growth rate. Namely, let S_n be the 3-uniform star (with n+1 vertices and (n choose 2) edges) and let K_4 be the complete 3-uniform hypergraph on 4 vertices. We show  2^{c(log n)^2} < r(K_4, S_n) < 2^{n^{2/3+o(1)}}.

Based on joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Andrew Suk, and Jacques Verstraete.

See: https://sites.google.com/view/rutgersdmseminar