Abstract:
How many degree d curves pass through a given number of points? This classical question in enumerative geometry leads to Gromov-Witten invariants, which count holomorphic curves in a space subject to constraints. In the first part of this talk, I'll introduce Gromov-Witten theory through examples and explain the key insight that makes computation possible: even though there are infinitely many invariants to compute, they satisfy remarkable algebraic relations (the WDVV equations) that allow recursive calculation from a few basic values.
In the second part, I'll discuss my recent work with Anna Hollands, May Sella, Qianyi Shu and Jake P. Solomon, computing open Gromov-Witten invariants for the Chiang Lagrangian in ℂℙ³. Instead of counting closed curves (spheres), open invariants count holomorphic disks with boundary on a Lagrangian submanifold. These invariants are much harder to compute and encode important information about the topology and symplectic geometry of the Lagrangian. I'll explain how we combined geometric techniques with the algebraic structure of the open WDVV equations to obtain the first complete computation for a Lagrangian that is not the fixed point set of an anti symplectic involution, and discuss some surprising phenomena that emerge.
Livestream/Recording Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=08f75e85-168a-4073-b48d-b37e00579a69