Joint Los Angeles Topology Seminar

Moduli spaces of pseudo-holomorphic curves in symplectic topology do not usually give rise to integral fundamental classes because of the existence of automorphisms. Nevertheless, in joint work with Guanbo Xu, following proposals of Fukaya-Ono and Parker, we constructed integer-valued counts from these moduli spaces in certain generality, including the setting of Gromov-Witten invariants and Hamiltonian Floer theory. In this talk, I will give an overview of our construction, and present concrete applications of these invariants including quantitative existence results of Hamiltonian periodic orbits and topology of Hamiltonian fibrations.