Felix Thimm (University of British Columbia) – Universal Curve Counting on Calabi–Yau 4-folds

Pardon recently established a type of "cohomology ring of enumeration problems" that all reasonable curve counting theories pair with to produce their invariants. A technical regularization procedure then allows him to prove that, for 3-folds, this ring is generated by local curve elements in the relevant degrees, from which the MNOP correspondence (for primary insertions) between different curve counting theories follows, since it was previously proven in the local curve case. Our work extends this framework to the CY4-fold case, which allows us to prove several curve counting conjectures in the CY4 case. Among the additional technical difficulties in this case is that a more complicated virtual dimension formula leads to more generators than just local curves. In this talk, I will give an overview of this framework and explain the main techniques involved. This is joint work in progress with Ivan Karpov, and partially based on separate work with Jim Bryan.