  Motivated by string-theoretic arguments Manschot, Pioline and Sen discovered
a new remarkable formula for the Poincare polynomial of a smooth compact moduli
space of stable quiver representations which effectively reduces to the abelian
case (i.e. thin dimension vectors). We first prove a motivic generalization of
this formula, valid for arbitrary quivers, dimension vectors and stabilities.
In the case of complete bipartite quivers we use the refined GW/Kronecker
correspondence between Euler characteristics of quiver moduli and Gromov-Witten
invariants to identify the MPS formula for Euler characteristics with a
standard degeneration formula in Gromov-Witten theory. Finally we combine the
MPS formula with localization techniques, obtaining a new formula for quiver
Euler characteristics as a sum over trees, and constructing many examples of
explicit correspondences between quiver representations and tropical curves.
