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SUMMARY:Amanda Montejano (Mexico)
DTSTART:20260716T173000Z
DTEND:20260716T175500Z
DTSTAMP:20260710T111745Z
UID:CANT2026/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/50/
 ">Discrete Brunn–Minkowski inequalities</a>\nby Amanda Montejano (Mexico
 ) as part of Combinatorial and additive number theory seminar (CANT 2026)\
 n\nLecture held in Science Center in the CUNY Graduate Center (4th floor).
 \n\nAbstract\nThe Brunn–Minkowski inequality is a cornerstone of convex 
 geometry\, with deep connections to several areas of mathematics. In recen
 t years\, there has been growing interest in developing discrete versions 
 of this inequality. Attempts to formulate a discrete version of the Brunn
 –Minkowski inequality naturally lead to problems in additive combinatori
 cs\, particularly those involving lower bounds and structural aspects of f
 inite sumsets in ${\\mathbb R}^d$ or ${\\mathbb Z}^d$. In the continuous s
 etting\, a refinement due to Bonnesen incorporates the $(d-1)$-dimensional
  volume of projections onto a hyperplane\, yielding sharper bounds that ca
 pture geometric structure. A discrete counterpart of this refinement is cu
 rrently known only in dimension two\, due to Grynkiewicz and Serra. In thi
 s paper\, we explore extensions of this result to higher dimensions. In pa
 rticular\, we introduce a framework for deriving discrete Brunn–Minkowsk
 i-type inequalities in arbitrary dimension that incorporate projection dat
 a of the underlying sets. This is a joint work with Oriol Serra and Luis M
 ontejano.\n
LOCATION:https://researchseminars.org/talk/CANT2026/50/
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