  We describe presentations of braid groups of type ADE and show how these
presentations are compatible with mutation of quivers, building on work of
Barot and Marsh for Coxeter groups. In types A and D these presentations can be
understood geometrically using triangulated surfaces. We then give a
categorical interpretation of the presentations, with the new generators acting
as spherical twists at simple modules on derived categories of Ginzburg
dg-algebras of quivers with potential.
