Title: A natural Gromov-Witten virtual fundamental class

Abstract: The moduli space of pseudo-holomorphic maps into closed symplectic manifolds carries several natural structures which induce relations between the Gromov-Witten invariants. The moduli space comes in several flavors, including the orbifold version (for a finite group actions) and a relative version (relative a symplectic normal crossing divisor).

In this talk, based on joint work with Tom Parker, we discuss how these different structures on the moduli space interact to induce a unique virtual fundamental class that satisfies certain naturality conditions. This allows one to reduce the construction of the virtual fundamental class to one involving only Gromov-type perturbations (after introducing stabilizing divisors and twisted G-structures). This approach can also be used to define a Real version of Gromov-Witten invariants for closed symplectic manifolds with anti-symplectic involutions.