Exponential decay of intersection volume and applications

Abstract

When two balls in a discrete metric space have small intersection? We give some natural conditions to guarantee an exponential decay on the volume of such intersections. Our proof is conceptually simple, making use of concentration of measure on a “slice”. We will discuss a couple of applications of this volume estimate in coding theory, and mention some recent developments on kissing numbers/spherical codes. This is based on joint work with Irene Gil Fernadez, Jaehoon Kim, Oleg Pikhurko and Tuan Tran.

Speaker Intro

Hong Liu is the head of the Extremal Combinatorics and Probability Group (ECOPRO) and a distinguished research fellow at the Institute for Basic Science (IBS). Previously, he was a faculty at the Mathematics Institute at University of Warwick. He was awarded the UK Research and Innovation Future Leaders Fellowship in 2019. Before that, he was a Leverhulme Early Career Fellow, working with Oleg Pikhurko. Hong got his Ph.D. in 2015 at University of Illinois at Urbana Champaign, advised by József Balogh. His primary research interests are extremal and probabilistic combinatorics.