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SUMMARY:A Combinatorial Perspective on Geometric Inequalities
DTSTART:20240118T093000
DTEND:20240118T103000
DTSTAMP:20260407T195412Z
UID:0a27e99c94491ae118d3043c0181fa6a3914cf84bf716a978b13e2b9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr Marius TIBA - University of Oxford\nSeminar in Mathematics\
 n\nThe Brunn-Minkowski inequality is an important result in convex geometr
 y and analysis\, closely related to the isoperimetric inequality. It state
 s that for (open) sets A and B in $\\mathbb{R}^d$\, we have $|A+B|^{1/d} \
 \geq |A|^{1/d}+|B|^{1/d}$. Here $A+B=\\{x+y : x \\in A\, y \\in B\\}$. Equ
 ality holds if and only if $A$ and $B$ are convex and homothetic sets (one
  is a dilation of the other) in $\\mathbb{R}^d$. The stability of the Brun
 n-Minkowski inequality is the principle that if we are \\emph{close} to eq
 uality\, then A and B must be \\emph{close} to being convex and homothetic
 . In this talk\, we present a sharp stability result for the Brunn-Minkow
 ski inequality\, establishing the exact dependency between the two notions
  of closeness\, thus concluding a long line of research on this problem. W
 e shall also discuss sharp stability results for discrete analogues of the
  Brunn-Minkowski inequality. These are motivated by the fundamental \\emph
 {inverse sumset problem} in additive combinatorics: if the size of $A+B$ i
 s \\emph{small}\, what can we say about the structure of the sets $A$ and 
 $B$? This talk is mostly based on joint work with Alessio Figalli and Pete
 r van Hintum.\n 
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021 https://epfl.zoom
 .us/j/68264128421
STATUS:CONFIRMED
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