Geometry and Topology Seminar: Geometric realizations of quiver mutations.
20 October 2016 13:00 in CM221
A quiver is a weighted oriented graph, a mutation of a quiver is a
simple combinatorial transformation arising in the theory of cluster
algebras. In this talk we connect mutations of quivers to reflection
groups acting on linear spaces and to groups generated by point
symmetries in the hyperbolic plane. We show that any mutation class of
rank 3 quivers admits a geometric presentation via such a group and
that the properties of this presentation are controlled by the Markov
constant p^2+q^2+r^2-pqr, where p,q,r are the weights of the arrows in
the quiver. This is a joint work with Pavel Tumarkin.