20241203 Cisca Kalmijn

In this talk we work towards a symplectic approach to Gromov--Witten invariants, which we do by investigating pseudoholomorphic curves. Examining the relevant moduli space, we find it is a manifold under suitable assumptions. We ensure compactness by extending the moduli space of pseudoholomorphic curves to the moduli space of stable maps, which incorporate the limiting behaviour of “bubbling”. If time permits, we look at these stable maps to find a notion of convergence, Gromov convergence, that gives us compactness for the moduli space used in the definition of Gromov--Witten invariants.

In part II we use these moduli spaces to define the Gromov--Witten invariants.