Séminaire LIGM - Illuminating a convex body

Le prochain séminaire de l'équipe A3SI du LIGM (unité mixte de recherche de l'Université Paris Est) aura lieu le jeudi 17 novembre de 13h30 à 14h30 à ESIEE Paris (salle 260).

Illuminating a convex body
Márton Naszódi
EPFL (Suisse), Eötvös University (Hongrie)

Abstract: A light source p in the d-dimensional real space illuminates a boundary point b of a convex body K, if the ray emanating from b in the direction pb intersects the interior of K. As is easy to see, the minimum number of light sources needed so that each boundary point is illuminated is the same as the minimum number of translates of the interior of K that cover K.

A famous open problem in discrete geometry is the Boltjanskii-Hadwiger conjecture, according to which, for every convex body, this number is at most 2^d. In this introductory talk, we will discuss different approaches to the problem, and its relationship with other questions.