Projet ANR CHARMS

Clusters, Homological Algebra, Representations and Mirror Symmetry

Le projet ANR CHARMS vise à exploiter les interactions entre la symétrie miroir homologique, la théorie des représentations de carquois et la géométrie combinatoire et polyédrale, qui ont été notamment révélées par la théorie des algèbres amassées.

In his address at the ICM in 1994, M. Kontsevich stated his Homological Mirror Symmetry Conjecture. This conjecture relates two categories, one from symplectic geometry (the Fukaya category), the other from algebraic geometry (the category of coherent sheaves), via an equivalence of suitably defined derived categories. The conjecture remains wide open to this day.

This project aims at exploiting interactions between homological mirror symmetry, representation theory of quivers, combinatorial models and polyhedral geometry, brought to light in part by the theory of cluster algebras. The vast knowledge on cluster algebras acquired in the past twenty years opens new directions of research in each of these fields.

Le projet regroupe 14 chercheurs sur quatre pôles (Paris, Amiens, Leicester et Montréal).