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.

Pendant la period de crise sanitaire on reprend les activités en distanciel un jeudi par mois à 14h.

Pour recevoir les annonces de ce séminaire, envoyer un message à arnau padrol imj-prg fr.

La liste des exposés passés est disponible ici.

28 janvier 2021

14h Raman Sanyal Goethe-Universität Frankfurt

Inscribable polytopes, routed trajectories, and reflection arrangements.

Steiner 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 Gr\"unbaum's quest for simplicial arrangements. This is based on joint work with Sebastian Manecke.

Lien réunion Zoom

ID de réunion : 787 498 6280. Code secret : NJEy2h

25 févriere 2021

14h Duncan Dauvergne Princeton University

The Archimedean limit of random sorting networks

Consider a list of n particles labelled in increasing order. A sorting network is a way of sorting this list into decreasing order by swapping adjacent particles, using as few swaps as possible. Simulations of large-n uniform random sorting networks reveal a surprising and beautiful global structure involving sinusoidal particle trajectories, a semicircle law, and a theorem of Archimedes. Based on these simulations, Angel, Holroyd, Romik, and Virag made a series of conjectures about the limiting behaviour of sorting networks. In this talk, I will discuss how to use the local structure and combinatorics of random sorting networks to prove these conjectures.

Lien réunion Zoom

ID de réunion : 787 498 6280. Code secret : NJEy2h

Le séminaire bénéficie du soutien de l'Institut Henri Poincaré.

Le comité d'organisation est constitué de Alfredo Hubard, Arnaud de Mesmay et Arnau Padrol.