Speaker: Dr. Brandon Hanson, Assistant Professor at University of Maine

Title: “Around the Sum-Product problem”

Abstract:  In the early 80's Erdos and Szemeredi posed the following problem. Suppose A is a finite set of integers, and form their sum- and product-sets, A+A={a+b:a,b∈ A} and A⋅ A={ab:a,b∈ A}. Must one of the two sets be nearly as large as possible? Since then, progress has been made by adopting tools from several areas -- geometry, Fourier analysis, information theory, etc. We will survey some known results, applications, and challenges that arise in the study of their problem.