Clemens’ conjecture states that the number of rational curves in a generic quintic threefold is finite. In this talk I will give an overview of this conjecture and in particular its relation to Gromov-Witten invariants and String theory. If time allows, I will talk about my recent article arXiv:2202.08677, in which I prove that if it is false then certain periods of rational curves in such a quintic threefold must vanish. The method is based on a generalization of a proof of Max Noether’s theorem using infinitesimal variation of Hodge structures and its reformulation in terms of integrals and Gauss-Manin connection.
