# Virtual neighbourhood technique and its applications

 Princeton/IAS Symplectic Geometry Seminar Topic: Virtual neighbourhood technique and its applications Speaker: Bai-Ling Wang Affiliation: Australian National University Date: Friday, March 28 Time/Room: 1:30pm - 2:30pm/Fine 322, Princeton University

In this talk, I will explain the recent joint work with Bohui Chen and Anmin Li on virtual neighborhood techniques for a Fredholm system $(B, E, S)$, where $E$ is a Banach vector bundle over a Banach manifold $B$ with a Fredholm section. Using the notion of virtual manifold theory developed by Chen and Tian, we associate a virtual system for the moduli space $M=S^{-1}(0)$. As an application, we will show that the moduli space of stable maps in a closed symplectic manifold admits an orbifold virtual system with a canonical orientation in cohomology or in K-theory.