Counting curves in Calabi-Yau threefolds - John Pardon

AGNES 2023
April 29, 2023
Stony Brook University
Speaker: John Pardon (Princeton University/Simons Center for Geometry and Physics)
Abstract: Enumerating curves in algebraic varieties traditionally involves choosing a compactification of the space of smooth embedded curves in the variety. There are many such compactifications, hence many different enumerative invariants (Gromov--Witten, Donaldson--Thomas, Gopakumar--Vafa, Pandharipande--Thomas, . . .). I will make the case for studying instead a "universal" enumerative invariant which takes values in a certain Grothendieck group of 1-cycles. It is often the case with such "universal" constructions that the resulting group is essentially uncomputable. But in this case, the cluster formalism of Ionel and Parker gives some nontrivial computations for Calabi--Yau threefolds. As a result, we hope to reduce conjectural identities between enumerative invariants (e.g. the MNOP conjecture) to some simple special cases (of "local curves"). This is work in progress.
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