Adam Sheffer

Monday, May 14 at 9:00 AM

Abstract

Additive Combinatorics is an active research field combining combinatorics, number theory, and harmonic analysis. In recent years, a variety of results in Combinatorial Geometry have been obtained by using ideas from Additive Combinatorics. For example, the concept of additive energy turned out to be very useful for several types of geometric problems. In this talk we will introduce basic concepts from Additive Combinatorics, and then show how these are used to derive geometric results. No prior knowledge of the subject is necessary. The talk will also go over related natural problems that were not seriously studied yet (since these problems originate from very recent works). Moreover, there are likely to be various additional Combinatorial Geometry problems that can be studied using similar tools from Additive Combinatorics. This makes this topic well suited for collaborations without requiring a large amount of background.