Analysis and PDE Seminar: Quantitative additive energy estimates for regular sets and connections to discretized sum-product theorems

Seminar | September 10 | 4:10-5 p.m. | 740 Evans Hall

 Laura Cladek, UCLA

 Department of Mathematics

We prove new quantitative additive energy estimates for a large class of porous measures which include, for example, all Hausdorff measures of Ahlfors-David subsets of the real line of dimension strictly between 0 and 1. We are able to obtain improved quantitative results over existing additive energy bounds for Ahlfors-David sets by avoiding the use of inverse theorems in additive combinatorics and instead opting for a more direct approach which involves the use of concentration of measure inequalities. We discuss some connections with Bourgain's sum-product theorem.