Speaker:  Yuval Wigderson  (Stanford University)

Title:  Size Ramsey numbers

Abstract: 

The size Ramsey number of a graph H is the minimum number of edges in a graph G with the property that no matter how we two-color the edges of G, we can find a monochromatic copy of H. This notion was introduced in 1978 by Erd˝os, Faudree, Rousseau, and Schelp, and despite more than four decades of work, there is a lot that is still unknown; notably, of the four questions that conclude the Erd˝os-Faudree-Rousseau-Schelp paper, only one had been resolved as of last year. In this talk, I’ll discuss recent work in which we resolve approx.  2.5 of the three remaining questions, using a variety of new combinatorial and probabilistic constructions.

Based on joint work with David Conlon and Jacob Fox.