“Cluster algebras of type B and C: from Combinatorics to Representation Theory”
Martedì 23 Settembre 2025, ore 17:00 - Aula 2BC60 - Azzurra Ciliberti (Ruhr-Universität Bochum)
Abstract
The aim of this talk is to give an accessible overview of the main results of my PhD thesis.
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 correspondences between cluster variables and symmetric indecomposable representations of the quiver.
