Gromov-Witten invariants are notoriously hard to compute, and despite much work, we currently lack a good understanding of how Gromov-Witten invariants change under blowups. On the other hand, we have a relatively good understanding of Gromov-Witten invariants of complete intersections in toric varieties and Grassmannians, thanks to theorems by Givental and Ciocan-Fontanine-Kim-Sabbah. I will show that under favorable circumstances we can view blowups as such complete intersections, which allows us to write down explicit generating functions for Gromov-Witten invariants of these blowups. This is joint work with Tom Coates and Qaasim Shafi.
