Title: Counting curves on quintic threefolds
Abstract: Gromov-Witten invariants are a way of counting holomorphic curves on a complex manifold X. Their development was spurred by predictions from physicists, and work in topological field theory has still an important influence on the subject. While one of the major intial examples to be studied is the case when X is a quintic threefold, the computation of its Gromov-Witten invariants is still an open problem. I will talk about the history of this problem including recent progress in works with Q. Chen, S. Guo and Y. Ruan.