Geometry of the Gopakumar-Vafa theory.

Abstract: Motivated by classical enumerative geometry and mathematical physics, counting curves in Calabi-Yau 3-folds has been studied intensively for decades, including Gromov-Witten theory and Donaldson-Thomas theory. In recent years, mathematical theory (by Hosono-Saito-Takahashi, Kiem-Li, Maulik-Toda etc) has been developed to realize the idea of Gopakumar and Vafa to recover the curve-counting invariants using the geometry of 1-dimensional sheaves. These developments shed new light on both enumerative geometry and the classical geometry of the relevant moduli spaces. I will discuss 3 particular cases (1) Higgs bundles (2) K3 surfaces, and (3) CP^2, where the Gopakumar-Vafa theory interacts with some other structures and conjectures in a surprising way.

algebraic geometry

Audience: researchers in the topic

Derived seminar

Series comments: https://ed-ac-uk.zoom.us/j/89993982042

Password: a simply-connected two-dimensional variety with trivial canonical bundle (omit the space)