Speaker: Kyungyong Lee, University of Nebraska

Title: A conjectural description for real Schur roots of acyclic quivers

Abstract: Let $Q$ be an acyclic quiver. The dimension vectors of indecomposable rigid representations are called real Schur roots. We give a conjectural description for real Schur roots of $Q$ using non-self-intersecting paths on Riemann surfaces, and prove it for certain quivers of finite types and for the quivers with three or less vertices and multiple arrows between every pair of vertices. Each of such paths gives rise to a reflection of the Weyl group of the corresponding Kac--Moody algebra and determines a real Schur root uniquely. This is joint work with Kyu-Hwan Lee.