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Séminaire A3SI - Márton Naszódi
Séminaire A3SI - Márton Naszódi
17-nov.-2016 13:30
Il y a: 1 year

Illuminating a convex body

Márton Naszódi - EPFL (Suisse), Eötvös University (Hongrie)

ESIEE building (room 260, see - 13h30-14h30

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.

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