Sharp stability for the Brunn-Minkowski inequality for arbitrary sets | Research seminar in Discrete Mathematics

Abstract

The Brunn-Minkowski inequality states that for (open) sets A and B in Rd, we have4 + B|1/d > |A|l/d + |B|l/d. Equality holds if and only if A and B are convex and homotheticsets in R". In this talk, we present a sharp stability result for the Brunn-Minkowski inequality.concluding a long line of research on this problem, We show that if we are close to eauality in theBrunn-Minkowski ineguality, then A and B are close to being homothetic and convex, establishingthe exact dependency between the three notions of closeness.This is based on joint work withAlessio Figalli and Peter van Hintum.

Speaker IntroMarius Tiba completed his PhD under the supervision of Bla Bollobs at the University ofCambridge in 2021. From 2022, has been a Titchmarsh research fellow at the MathematicalInstitute, University of Oxford. His research focuses on combinatorics and its connections withmetric geometry, analysis and combinatorial number theory.