Mark Gross

Abstract:   Mirror symmetry was a phenomenon first discovered in string theory around 1990, which predicted that two very distinct sorts of calculations on two different "mirror" manifolds would give the same answer. On one hand, one can compute Gromov-Witten invariants, invariants which essentially count numbers of holomorphic maps of the Riemann sphere into a symplectic manifold. On the other hand, one can integrate certain differential forms over cycles on a different manifold. A great deal of research has been devoted to understanding why this works.

In this talk, I will give a very simple example of mirror symmetry which is nonetheless a new phenomenon, in which both sides of the story can be completely explained. This is joint work with Bernd Siebert and Rahul Pandharipande.