Séminaires : Séminaire Francilien de Géométrie Algorithmique et Combinatoire

Equipe(s) : co,
Responsables :Arnaud de Mesmay, Alfredo Hubard et Arnau Padrol
Email des responsables : arnau.padrol@imj-prg.fr
Salle :
Adresse :Big Blue Button

Le Séminaire de Géométrie Algorithmique et Combinatoire vise à regrouper des exposés dans ce domaine au sens le plus large, et dans les disciplines connexes en mathématiques et informatique. Il est ouvert à tous les chercheurs et étudiants intéressés. Les exposés sont destinés à un public large.

Orateur(s) Raman Sanyal - ,
Titre Inscribable polytopes, routed trajectories, and reflection arrangements.
Horaire14:00 à 15:00
RésumeSteiner posed the question if any 3-dimensional polytope had a realization with vertices on a sphere. Steinitz constructed the first counter examples and Rivin gave a complete answer to Steiner's question. In dimensions 4 and up, the Universality Theorem indicates that certifying inscribability is difficult if not hopeless. In this talk, I will address the following refined question: Given a polytope P, is there a continuous deformation of P to an inscribed polytope that keeps corresponding faces parallel? In other words, is there an inscribed polytope P’ that is normally equivalent (or strongly isomorphic) to P? This question has strong ties to deformations of Delaunay subdivisions and ideal hyperbolic polyhedra and its study reveals a rich interplay of algebra, geometry, and combinatorics. In the first part of the talk, I will discuss relations to routed trajectories of particles and reflection groupoids and show that that the question is polynomial time decidable. In the second part of the talk, we will focus on class of zonotopes, that is, polytopes representing hyperplane arrangements. It turns out that inscribable zonotopes are rare and intimately related to reflection groups and Grünbaum's quest for simplicial arrangements. This is based on joint work with Sebastian Manecke.
AdresseBig Blue Button