  BPS quivers for N=2 SU(N) gauge theories are derived via geometric
engineering from derived categories of toric Calabi-Yau threefolds. While the
outcome is in agreement of previous low energy constructions, the geometric
approach leads to several new results. An absence of walls conjecture is
formulated for all values of N, relating the field theory BPS spectrum to large
radius D-brane bound states. Supporting evidence is presented as explicit
computations of BPS degeneracies in some examples. These computations also
prove the existence of BPS states of arbitrarily high spin and infinitely many
marginal stability walls at weak coupling. Moreover, framed quiver models for
framed BPS states are naturally derived from this formalism, as well as a
mathematical formulation of framed and unframed BPS degeneracies in terms of
motivic and cohomological Donaldson-Thomas invariants. We verify the
conjectured absence of BPS states with "exotic" SU(2)_R quantum numbers using
motivic DT invariants. This application is based in particular on a complete
recursive algorithm which determine the unframed BPS spectrum at any point on
the Coulomb branch in terms of noncommutative Donaldson-Thomas invariants for
framed quiver representations.
