Joint Los Angeles Topology Seminar (1/2)

In this talk, I will review recent joint work with Alexander Ritter on semiprojective toric manifolds. These are non-compact toric manifolds, defined as GIT/Kahler quotients of torus actions on a vector spaces, and as such, are symplectic C*-manifolds, defined in our previous work. As a particular instance of that work, the quantum and symplectic cohomology of these toric manifolds are well defined, moreover we can compute them explicitly. We prove that symplectic cohomology of a semiprojective toric manifold is isomorphic to the Jacobian ring of its superpotential, thereby establishing the closed-string mirror symmetry statement for these manifolds.