Thomas

The KKV conjecture

I will survey the proof of the Katz-Klemm-Vafa conjecture. This expresses the Gromov-Witten theory of K3 surfaces (and K3-fibred 3-folds in fibre classes) in terms of modular forms. It gives the first non-toric geometry in dimension greater than 1 where Gromov-Witten theory is exactly solved in all genera. This is joint work with Rahul Pandharipande.