Integer-Valued Gromov-Witten Type Invariants - Guangbo Xu
Offered By: Institute for Advanced Study via YouTube
Course Description
Overview
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.
Syllabus
Introduction
Classical form
Finite dimensional reduction
Singlevalued perturbation
Normalized polynomial perturbation
Topology
Local perturbations
Application
Invariants
Remarks
Taught by
Institute for Advanced Study
Related Courses
Introduction to Contact Geometry by Dheeraj KulkarniInternational Centre for Theoretical Sciences via YouTube Real Gromov-Witten Theory
International Mathematical Union via YouTube MTC and Twisted Hilbert Spaces
ICTP Mathematics via YouTube Donaldson-Thomas and Gromov-Witten Invariants - Part 17
IMSA via YouTube Donaldson-Thomas and Gromov-Witten Invariants - Part 16
IMSA via YouTube