# Mathematical Sciences Research Institute

Home » GFA Postdoc Seminar: On illumination conjecture and the local maximality of the cube

# Seminar

GFA Postdoc Seminar: On illumination conjecture and the local maximality of the cube December 08, 2017 (11:30 AM PST - 12:15 PM PST)
Parent Program: Geometric Functional Analysis and Applications MSRI: Simons Auditorium
Speaker(s) Galyna Livshyts (Georgia Institute of Technology)
Description No Description
Video
The celebrated Levy-Hadwiger illumination conjecture states that the boundary of every convex body in \mathbb{R}^n can be illuminated by at most $2^n$ light sources. The worst case scenario is conjectured to be the cube; moreover, it is believed that the cube is the only convex body for which the bound of $2^n$ is attained. We shall discuss some general history and basic facts around the illumination conjecture. We shall also prove that all the convex bodies in the Banach-Mazur neighborhood of the cube can be illuminated by at most $2^n-1$ light sources, thereby concluding the strict local maximality of the cube for the illumination problem. This is a joint work with K. Tikhomirov.