Categorification of cluster algebras of type B and C through symmetric quivers and their representations

After recalling the combinatorial description of their cluster complex, we will state a cluster expansion formula for cluster algebras of type B and C in terms of cluster variables of type A. Then, we will explain how to associate a symmetric quiver with relations Q to any seed of a cluster algebra of type B and C. Under this correspondence, cluster variables of type B (resp. C) correspond to orthogonal (resp. symplectic) indecomposable representations of Q. Finally, we will give a categorical interpretation of the cluster expansion formula in the case of acyclic quivers.