Discretized Sum-Product and Geometric Measure Theory

Abstract: In this talk, I will first briefly review the history of sum-product estimates in the setting of finite fields and mention the applications of sum-product type problems. Then I will start introducing the celebrated result of Bourgain about the discretized sum-product estimates and the applications to geometric measure theory problems. Finally I will talk about our recent results about expanding polynomials in terms of Hausdorff dimension and discuss their sum-product phenomena.

Mathematics

Audience: researchers in the topic

Trends in Mathematical Research