Abstract : Cluster algebras without coefficients admit (additive) categorifications given by certain 2-Calabi-Yau triangulated categories. Relative Calabi-Yau structures in the sense of Toën and Brav-Dyckerhoff appear when one tries to extend the theory to cluster algebras with coefficients. In the context of cluster algebras associated with marked surfaces, Merlin Christ has constructed the corresponding categorifications. We will report on a slightly different approach starting from an ice quiver with potential. The talk is based on work by Yilin Wu in his thesis and more recent joint work with him.

Keywords : cluster algebra; dg category