Enumerative Problems in Algebraic Geometry

I am working on enumerative problems in algebraic geometry, with a connection to mirror symmetry. In particular I aim to understand the formal properties and behaviour of logarithmic Gromov-Witten invariants and the related quantum cohomology ring. I have approached this using a modification of logarithmic deformation theory. These invariants have been used in the construction of mirror by Gross and Siebert, and I have also been working to understand their program.