UAlberta-PIMS Mathematics and Statistics Colloquium: Artem Zvavitch

In this talk, we will discuss several inequalities in convex geometry inspired by sumset estimates in additive combinatorics and inequalities in information theory. We begin by investigating sharp constants in convex geometry analogues of Plünnecke-Ruzsa-type inequalities, specifically determining the best constant $c_n$ such that $$ |A||A+B+C| \le c_n |A+B||A+C|, $$ for any compact convex sets $A,B,C \subset {\mathbb R}^n$, where $+$ we denotes the Minkowski sum and $|A|$ represents the volume of $A$.

Furthermore, we will explore connections between these inequalities and various results in convex geometry, including inequalities involving mixed volumes and Loomis-Whitney-type es.