Mathematics Seminar - 02/28/20

Feb 28 3:00 pm
Speaker

Dr. Thai Haong Le, University of Mississippi

Title

Structures in difference sets

Physical Location

Allen Hall 411

Abstract: A general principle says that if A is a subset of a group G and A is large in a certain sense, then we expect the difference set A - A = {a - a’: a, a’ ∈ A } to contain nice structures. For example, a classical theorem of Steinhaus says that if A is a subset of positive Lebesgue measure of ℝ, then A - A contains an open interval around 0. If A is a subset of positive density of a vector space ?pn over a finite field ?p, then we expect A - A to contain a large subspace. I will talk about various manifestations of this principle in analysis, number theory and combinatorics. These include joint works with P.-Y. Bienvenu and Z. Ge.