Sam Spiro, Rutgers University

Abstract

Let ex(n,F) denote the maximum number of edges that an F-free graph can have.  One of the few ways we know how to get general lower bounds on ex(n,F) is to us random graphs, but the usual Gnp construction typically doesn't do very well.  In this talk we discuss how you can do better by considering random graphs based off of polynomials over finite fields.  In particular, we discuss Bukh and Conlon's breakthrough regarding the rational exponents conjecture.