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CIRM – Centre International de Rencontres Mathématiques

Combinatorial statements, such as theorems of Caratheodory, Radon, Helly, Sperner, Tucker, Ky Fan, etc., are fundamental results of combinatorial (algebraic) topology, accessible to non-specialists, which are immediately applicable to mathematical economics, data science, game theory, graph theory, mathematical optimization, computational geometry, and other fields. The aim of our project is to study the “Ky Fan correspondence » between the topology of triangulated spherical bundles and combinatorics of generalized labelings (coloring) of the associated simplicial complexes. Guided by the review of De Loera et. al. (Bull. Amer. Math. Soc., 2019) we explore the consequences of this correspondence for the envy-free and fair division problem, Tverberg-type theorems, and other related problems of topological combinatorics.

CIRM – Centre International de Rencontres Mathématiques

Friezes, introduced 50 years ago by Coxeter, are patterns of integers defined by a simple, local condition. They consist of a finite (or infinite) number of rows written in a lattice, starting with a row of 0s and a row of 1s and satisfying a local SL2-rule: for any four neighbours a, b, c, d forming a diamond we require ad − bc = 1. Since the discovery of links to cluster algebras of type A, a plethora of generalisations have been studied in the last decades. With this workshop, we will provide a platform to establish new links between friezes and research areas in geometry, algebra and combinatorics.

Géométrie et topologie,    Algèbre