Some geometric aspects of the theory of convex polytopes

par Prof. Karim ADIPRASITO (IHES)

mercredi 9 oct. 2013, 11:00 → 12:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

: 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.