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SUMMARY:Arnau Padrol (Sorbonne Université)
DTSTART:20211014T141500Z
DTEND:20211014T160000Z
DTSTAMP:20260422T065511Z
UID:CJCS/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/32/">Th
 e convex dimension of hypergraphs and the hypersimplicial Van  Kampen-Flor
 es Theorem</a>\nby Arnau Padrol (Sorbonne Université) as part of Copenhag
 en-Jerusalem Combinatorics Seminar\n\n\nAbstract\nI will present joint wor
 k with Leonardo Martínez-Sandoval on the \nhypersimplicial generalization
  of the linear van Kampen-Flores theorem: \nfor each n\, k and i we determ
 ine onto which dimensions can the \n(n\,k)-hypersimplex be linearly projec
 ted while preserving its \ni-skeleton. This is motivated by the study of t
 he convex dimensions of \nhypergraphs. The convex dimension of a k-uniform
  hypergraph is the \nsmallest dimension d for which there is an injective 
 mapping of its \nvertices into R^d such that the set of k-barycenters of a
 ll hyperedges \nis in convex position. Our results completely determine th
 e convex \ndimension of complete k-uniform hypergraphs. This settles an op
 en \nquestion by Halman\, Onn and Rothblum\, who solved the problem for \n
 complete graphs. We also provide lower and upper bounds for the extremal \
 nproblem of estimating the maximal number of hyperedges of k-uniform \nhyp
 ergraphs on n vertices with convex dimension d.\n
LOCATION:https://researchseminars.org/talk/CJCS/32/
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