  Quiver theories arising on D3-branes at orbifold and del Pezzo singularities
are studied using mirror symmetry. We show that the quivers for the orbifold
theories are given by the soliton spectrum of massive 2d N=2 theory with
weighted projective spaces as target. For the theories obtained from the del
Pezzo singularities we show that the geometry of the mirror manifold gives
quiver theories related to each other by Picard-Lefschetz transformations, a
subset of which are simple Seiberg duals. We also address how one indeed
derives Seiberg duality on the matter content from such geometrical transitions
and how one could go beyond and obtain certain ``fractional Seiberg duals.''
Moreover, from the mirror geometry for the del Pezzos arise certain Diophantine
equations which classify all quivers related by Picard-Lefschetz. Some of these
Diophantine equations can also be obtained from the classification results of
Cecotti-Vafa for the 2d N=2 theories.
