School of Mathematics, Statistics and Physics

Seminar Item

Pure Maths (Algebra and Geometry) - Anna Felikson (Durham)

Quiver mutations, reflection groups and curves on punctured disc

Date/Time: Monday 26 October, 1.30pm - Algebra and Geometry Seminar

Venue: Zoom

Abstract: Mutations of quivers were introduced by Fomin and Zelevinsky in 2002 in the context of cluster algebras. For some classes of quivers, mutations can be realised using geometric or combinatorial models. We will discuss a construction of a geometric model for all acyclic quivers. The construction is based on the geometry of reflection groups acting in quadratic spaces. As an application, we show an easy and explicit way to characterise real Schur roots (i.e. dimension vectors of indecomposable rigid representations of Q over the path algebra kQ), which proves a recent conjecture of K.-H. Lee and K. Lee for a large class of acyclic quivers. This work is joint with Pavel Tumarkin.