Gromov-Witten theory in dimensions at most 3 (and dimensions greater than 3)
I will start with the moduli space of stable maps, the virtual class, and the virtual dimension formula. The Gromov-Witten theory of local P1 will be calculated (almost) completely using the virtual localization formula and Hodge integral identities. After discussing the DT theory of ideal sheaves for local P1 and the stable pairs theory, I will explain the GW/DT/Pairs correspondence. In the last lecture, I will presentresults about Gromov-Witten theory which are only provable (at the moment) using the correspondences with stable pairs theory.