Speaker: Aleksander Doan
Title: The Gopakumar-Vafa finiteness conjecture
Abstract: The Gopakumar-Vafa conjecture concerns the Gromov-Witten invariants of symplectic manifolds of dimension six. The first part of the conjecture–the integrality conjecture–asserts that the Gromov-Witten invariants can be expressed in terms of simpler, integer invariants called the BPS numbers. This part was recently proved by Ionel and Parker. The second part of the conjecture–the finiteness conjecture–predicts that only finitely many of the BPS numbers are nonzero. In this talk, based on joint work with E. Ionel and T. Walpuski, I will discuss a proof of the second part of conjecture. The proof combines ideas from the theory of pseudo-holomorphic curves, including Ionel and Parker's cluster formalism, and methods of geometric measure theory, especially Allard's regularity theorem for currents with bounded mean curvature.