  We study a supersymmetric partition function of topological vortices in 3d
N=4,3 gauge theories on R^2 x S^1, and use it to explore Seiberg-like dualities
with Fayet-Iliopoulos deformations. We provide a detailed support of these
dualities and also clarify the roles of vortices. The N=4 partition function
confirms the proposed Seiberg duality and suggests nontrivial extensions,
presumably at novel IR fixed points with enhanced symmetries. The N=3 theories
with nonzero Chern-Simons term also have non-topological vortices in the
partially broken phases, which are essential for the Seiberg duality invariance
of the spectrum. We use our partition function to confirm some properties of
non-topological vortices via Seiberg duality in a simple case.
