Séminaires : Séminaire Francilien de Géométrie Algorithmique et Combinatoire

Equipe(s) : co,
Responsables :Arnaud de Mesmay, Alfredo Hubard et Arnau Padrol
Email des responsables : arnau.padrol@imj-prg.fr
Salle :
Adresse :IHP
Description

Le Séminaire de Géométrie Algorithmique et Combinatoire vise à regrouper des exposés dans ce domaine au sens le plus large, et dans les disciplines connexes en mathématiques et informatique. Il est ouvert à tous les chercheurs et étudiants intéressés. Les exposés sont destinés à un public large.

Orateur(s) Zuzana Patáková - ,
Titre On Radon and fractional Helly theorems
Date20/05/2021
Horaire14:00 à 15:00
Diffusion
RésumeRadon theorem plays a basic role in many results of combinatorial convexity. It says that any set of d+2 points in R^d can be split into two parts so that their convex hulls intersect. It implies Helly theorem and as shown recently also its more robust version, so-called fractional Helly theorem. By standard techniques this consequently yields an existence of weak epsilon nets and a (p,q)-theorem. We will show that we can obtain these results even without assuming convexity, replacing it with very weak topological conditions. More precisely, given an intersection-closed family F of subsets of R^d, we will measure the complexity of F by the supremum of the first d/2 Betti numbers over all elements of F. We show that bounded complexity of F guarantees versions of all the results mentioned above. Based on joint work with Xavier Goaoc and Andreas Holmsen.
Salle
AdresseZOOM ID: 787 498 6280
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