École Doctorale Mathématiques et STIC

Cours Doctoral - 2018 - Discrete topology and geometry, and applications

Discrete topology and geometry, and applications

  • Il s'agit d'un cours M2 de 12 heures à l'interface Math/Info
  • Ce cours aura lieu de fin mai à fin juin 2018
  • Premier cours le jeudi 24 mai 2018
  • ENPC Cité Descartes, bâtiment Coriolis, 1° étage, salle F 108
  • Ce cours est assuré par Xavier Goac et Frédéric Meunier

Topic : This course will cover some discrete theorems in topology (Sperner and Tucker) and geometry (Helly and Carathéodory) as well as several of their applications. We will illustrate how these theorems offer elementary gateways to a diversity of results in game theory and fair division, in graph theory, in optimization and in geometric data analysis.

Ressource : The lecture will build on the survey The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tvergerg by De Lorea, Goac, Meunier and Mustafa.

Pre-requisite : We will assume a general background in mathematics (continuity, vector spaces etc...)