Counting Curves in Calabi-Yau Threefolds

Explore the intricacies of enumerating curves in algebraic varieties through this 59-minute conference talk delivered by John Pardon from Princeton University and the Simons Center for Geometry and Physics. Delve into the concept of a "universal" enumerative invariant that takes values in a Grothendieck group of 1-cycles, challenging traditional methods that rely on choosing specific compactifications of smooth embedded curves. Discover how the cluster formalism of Ionel and Parker enables nontrivial computations for Calabi-Yau threefolds, potentially simplifying conjectural identities between enumerative invariants. Gain insights into ongoing research that aims to reduce complex conjectures like the MNOP conjecture to simpler cases of "local curves." Presented at AGNES 2023 at Stony Brook University, this talk offers a deep dive into cutting-edge algebraic geometry research.