Séminaires : Séminaire d'Algèbre

 In their geometric approach to cluster theory, Fock–Goncharov and Gross–Hacking–Keel construct cluster varieties beginning with a seed datum. This consists of a lattice which contains various distinguished sublattices, has a preferred basis, and carries a partially defined bilinear form. A process of mutation allows one to construct more such seed data, and birational gluing maps between the tori dual to the lattices, leading to two cluster varieties known as A and X. By enhancing the initial data to a cluster ensemble, in which the bilinear form is extended to the whole lattice, one also obtains a map from A to X. In this talk, based on joint work with Jan Grabowski, I will explain how one can obtain a seed datum, and in many cases a full cluster ensemble, from each cluster-tilting subcategory of an appropriate 2-Calabi–Yau category. Furthermore, I will explain how the seed data of different cluster-tilting subcategories are related, generalising the relationship between a seed datum and its mutations.

This talk will take place in hybrid mode at the Institut Henri Poincaré.