Discrete topology and geometry, and applications
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...)