Integer-Valued Gromov-Witten Type Invariants - Guangbo Xu

Explore the concept of integer-valued Gromov-Witten type invariants in this advanced mathematics lecture presented by Guangbo Xu from Texas A&M University. Delve into a rigorous definition of these invariants in genus zero for symplectic manifolds, based on recent joint work with Shaoyun Bai. Examine the evolution of Gromov-Witten invariants from rational-valued to potentially integer-valued, addressing the challenges posed by curves with nontrivial automorphism groups. Investigate Fukaya and Ono's 1997 proposal for counting curves with trivial automorphism groups, and understand how this method utilizes both orientation and stable complex structure on moduli spaces. Follow the speaker through topics including classical form, finite dimensional reduction, singlevalued perturbation, normalized polynomial perturbation, topology, local perturbations, and applications, culminating in a discussion of the newly defined invariants and concluding remarks.