Event Details

Speaker: Azzurra Ciliberti (Ruhr University Bochum)

Title: Cluster algebras of type B and C: from Combinatorics to Representation Theory

Abstract: The goal of this talk is to provide an accessible overview of cluster algebras of type B and C, and their link to Representation Theory.

I will begin with the combinatorial definitions of cluster algebras of type A, B and C, described via triangulations of a regular polygon. Using this framework, I will show that cluster variables of type B and C can be expressed in terms of cluster variables of type A.

Next, I will illustrate in an example that each cluster variable of type B and C can be obtained as the perfect matching Laurent polynomial of a certain planar graph.

Finally, I will present a construction that associates a symmetric quiver to every cluster algebra of type B and C, establishing a correspondence between cluster variables and symmetric indecomposable representations of the quiver.