Beijing Institute of Mathematical Sciences and Applications

Benjamin Sudakov

Marius Tiba

Tuesday, April 23, 2024 5:05 PM - 6:15 PM

Online

Zoom 787 662 9899 (BIMSA)

The Brunn-Minkowski inequality states that for (open) sets $A$ and $B$ in $R^d$, we have $|A+B|^{1/d} \geq |A|^{1/d}+|B|^{1/d}$. Equality holds if and only if $A$ and $B$ are convex and homothetic sets in $R^d$. 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 equality in the Brunn-Minkowski inequality, then $A$ and $B$ are close to being homothetic and convex, establishing the exact dependency between the three notions of closeness. This is based on joint work with Alessio Figalli and Peter van Hintum.

Marius Tiba completed his PhD under the supervision of Béla Bollobás at the University of Cambridge in 2021. From 2022, has been a Titchmarsh research fellow at the Mathematical Institute, University of Oxford. His research focuses on combinatorics and its connections with metric geometry, analysis and combinatorial number theory.