2025 CMS Winter Meeting

Toronto, Dec 5 - 8, 2025

Abstracts        

Recent progress in convex and discrete geometry
Org: Ferenc Fodor (University of Szeged, Hungary and University of Calgary, Canada) and Alina Stancu (Concordia University, Canada)

GERGELY AMBRUS, University of Szeged, Hungary

KAROLY BEZDEK, University of Calgary

TED BISZTRICZKY, University Calgary

DMITRY FAIFMAN, University of Montreal

PAVLOS KALANTZOPOULOS, University of Waterloo

DYLAN LANGHARST, Carnegie Mellon University
Grünbaum’s inequality for probability measures  [PDF]

Given a convex body $K$ in $\mathbb{R}^n$, a natural question is: if one partitions the body into two pieces along its barycenter, how small can each piece be? By “partition along its barycenter”, we mean intersecting $K$ with a half-space whose boundary is a hyperplane containing said barycenter. Grünbaum showed that the volume of each piece is at least $\left(\frac{n}{n+1}\right)^n$ times the total volume of K. Furthermore, this constant is sharp: there is equality if and only if $K$ is a cone, which means there exists a $(n - 1)$-dimensional convex body $L$ and a vector $b$, such that $K$ has face $L$ and vertex $b$ (i.e. $K$ is the convex hull of $b$ and $L$). \

In this work, which is joint with M. Fradelizi, J. Liu, F. Marin Sola, and S. Tang, we are interested in generalizing Grünbaum’s inequality to other measures. Our main results are a sharp inequality for the Gaussian measure and a sharp inequality for s-concave probability measures. The characterization of the equality case is of particular interest. Along the way, we discover new facts about the equality case of the Borell-Brascamp-Lieb inequality.

SERGII MYROSHNYCHENKO, University of the Fraser Valley

LAM NGUYEN, Memorial University of Newfoundland

DEBORAH OLIVEROS, UNAM Queretaro, Mexico

DMITRY RYABOGIN, Kent State University

EGON SCHULTE, Northeastern University

KATERYNA TATARKO, University of Waterloo

VIKTOR VIGH, University of Szeged, Hungary

BEATRICE-HELEN VRITSIOU, University of Alberta

ELISABETH WERNER, Case Western Reserve University

JIE XIAO, Memorial University of Newfoundland


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