On higher genus Gromov-Witten invariants of quintic threefolds
The Gromov-Witten invariants of a smooth variety X are virtual counts
of algebraic curves in X. In the case that X is a Calabi-Yau threefold,
there is significant interest from string theorists in computing these
invariants, and many results and open questions about Gromov-Witten
invariants are motivated from physics. In my talk, I will survey some
recent developments in the case of the (in some sense) most simplest
Calabi-Yau threefolds: quintic hypersurfaces in projective 4-space.