Quivers with potentials and their mutations

Jerzy Weyman

This is a report on a joint work with Derksen and Zelevinsky. We introduce mutations of quivers with potential and their representations, in the spirit of decorated representations of Marsh, Reineke and Zelevinsky. We also define a numerical mutation invariant of reprsentations of quivers with potential and use it to prove some conjectures of Fomin and Zelevinsky on g-vectors and F-polynomials.