Séminaires : Séminaire d'Algèbre

In his study of combinatorial features of cluster categories and cluster-tilted algebras, Ringel introduced an analogue of additive functions of stable translation quivers called cluster-additive functions.
In this talk, we will define cluster-additive functions associated to any acyclic mutation matrix, relate them to tropical points of the cluster X-variety, and realise their values as certain compatibility degrees between functions on the cluster A-variety associated to the Langlands dual mutation matrix (in accordance with the philosophy of Fock-Goncharov). This is based on joint work with Peigen Cao and Jiang-Hua Lu.

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