Pavel Tumarkin (Durham University) – Cluster algebras, marked surfaces, and extended affine Weyl groups

Abstract: With (almost) every finite mutation class of quivers we associate two groups: an extended affine Weyl group of type A or D, and a certain quotient of a Coxeter group which behaves nicely with respect to mutations (in most cases, the latter can also be obtained as a quotient of certain surface braid group). I will discuss a connection between these groups and a (still conjectural) characterization of mutation-finite quivers in terms of positive semidefinite symmetric matrices. The talk is based on joint works (some still in progress) with Anna Felikson, John Lawson and Michael Shapiro.