Chennai Mathematical Institute


3:30 pm, Seminar Hall
Gromov-Witten Theory and Virtual Fundamental Classes

Mohan Swaminathan
Princeton University.


Given a closed symplectic manifold or a smooth projective variety, it is useful to study (pseudo-)holomorphic curves in it. These curves occur in finite dimensional moduli spaces, and intersection theory on these moduli spaces gives rise to Gromov-Witten (GW) theory, which is a symplectic invariant. The central ingredient of the intersection theory is the "virtual fundamental class" (VFC), which is a substitute for the ordinary fundamental class when the moduli space is not a smooth manifold (or orbifold) of the expected dimension. After a short introduction to GW invariants, we will describe a relatively recent construction of VFCs, in the symplectic setting, due to Pardon (2015). If time permits, we will also outline earlier constructions in the algebro-geometric setting due to Li-Tian (1996) and Behrend-Fantechi (1996).