Some geometric aspects of the theory of convex polytopes
Amphithéâtre Léon Motchane (IHES)
Amphithéâtre Léon Motchane
Le Bois Marie
35, route de Chartres
: 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.