Séminaire de Mathématique

Some geometric aspects of the theory of convex polytopes

by Prof. Karim ADIPRASITO (IHES)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
: 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.