Geometric Energies: Between Combinatorial Geometry and Additive Combinatorics

Adam Sheffer, Baruch College/CUNY

April 10, 2018

We will discuss the rise of geometric variants of the concept of Additive energy. In recent years such variants are becoming more common in the study of Combinatorial Geometry problems. We will survey this development and then focus on a recent work with Cosmin Pohoata. This work studies geometric variants of additive higher moment energies, and uses those to derive new bounds for several problems in Combinatorial Geometry.