UC Riverside

The central idea in weak mirror symmetry is relating a complex manifold and a symplectic manifold by comparing their induced differential Gerstenhaber algebras (DGAs). If they are quasi-isomorphic, we say the complex and symplectic manifold form a weak mirror pair. Complex and symplectic manifold live in a larger category of generalized complex manifolds. We can use the deformation theory of generalized complex geometry to deform some complex manifolds into symplectic manifolds. It is then natural to ask when the undeformed object and the deformed one form a weak mirror pair. This thesis provides a sufficient condition for when a complex manifold can be deformed to form a weak mirror pair. We also use this condition to determine when complex symplectic algebras can be deformed to provide a weak mirror pair.