Speaker: Aleksander Doan (Columbia University)

Title: The Gopakumar-Vafa finiteness conjecture

Abstract: The Gopakumar-Vafa conjecture predicts that the Gromov-Witten invariants of a six-dimensional symplectic manifold are related by a universal formula to other invariants called the BPS numbers, which have two interesting properties: (1) they are integers and (2) only finitely many of them are nonzero in every homology class. (The Gromov-Witten invariants have neither of these properties.) The first part of the conjecture was proved in 2018 by Ionel and Parker. I will discuss a proof of the second part, which relies on combining Ionel and Parker's cluster formalism with results from geometric measure theory. The talk is based on joint work with Eleny Ionel and Thomas Walpuski.