Speaker: Amanda Hirschi (Cambridge University)

Title: From Six to Four

Abstract:

I will discuss joint work with Luya Wang on the other direction of the Donaldson 4-6 problem. Specifically, we show that any two simply-connected symplectic 4-manifolds, whose products with S^2 are deformation equivalent, have the same Gromov-Witten invariants. The proof relies on a generalisation of the product formula of Hirschi-Swaminathan to include gravitational descendants, as well as using classical invariants to constrain the action of diffeomorphisms on cohomology. I will give a gentle introduction to all the ingredients from Gromov-Witten theory we need.