Séminaire de Mathématique

Some geometric aspects of the theory of convex polytopes

by Prof. Karim ADIPRASITO (IHES)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane

IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description
: I will discuss some examples where differential geometry, topology and combinatorics of polyhedra can benefit from each other, and review some tools that make this possible. In particular, I will focus on the following two topics -- the Hirsch conjecture, concerned with bounding the running time of the simplex algorithm, and an application of CAT(1)-geometry to this problem. -- two problems of Legendre--Steinitz and Perles--Shephard concerning realization spaces of polytopes, and their solution based on solving discrete PDEs. All notions will be introduced in the talk; I intend to make a friendly introduction to the theory, so non-experts are welcome.
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