  Using mirror symmetry, we show that Chern-Simons theory on certain manifolds
such as lens spaces reduces to a novel class of Hermitian matrix models, where
the measure is that of unitary matrix models. We show that this agrees with the
more conventional canonical quantization of Chern-Simons theory. Moreover,
large N dualities in this context lead to computation of all genus A-model
topological amplitudes on toric Calabi-Yau manifolds in terms of matrix
integrals. In the context of type IIA superstring compactifications on these
Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2
manifolds) this leads to engineering and solving F-terms for N=1 supersymmetric
gauge theories with superpotentials involving certain multi-trace operators.
