  We show that there are two different dualities of two dimensional gauge
theories with N=(2,2) supersymmetry. One is basically a consequence of 3d
mirror symmetry. The non-linear sigma model with Calabi-Yau target space on the
Higgs branch of the gauge theory is mapped into an equivalent non-linear sigma
model on the Coulomb branch of the dual theory, realizing a T-dual target space
with torsion. The second duality is genuine to two dimensions. In addition to
swapping Higgs and Coulomb branch it trades twisted for untwisted multiplets,
implying a sign flip of the left moving U(1)_R charge. Succesive application of
both dualities leads to geometric mirror symmetry for the target space
Calabi-Yau.
