### Quantitative additive energy estimates for regular sets and connections to discretized sum-product theorems

- Series
- Analysis Seminar
- Time
- Wednesday, March 28, 2018 - 13:55 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Laura Cladek – UCLA – lauratcladek@gmail.com

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.