Robert Marsh: Braid groups and quiver mutation

Joint work with Joseph Grant. We give a presentation of an Artin braid group of type ADE for any quiver which is mutation equivalent to a Dynkin quiver of the same type. We show how these presentations can be understood geometrically in types A and D using triangulated surfaces. These presentations also have a categorical interpretation in which the generators act as spherical twists at simple modules on derived categories of Ginzburg dg-algebras.