# Intercontinental Moduli and Algebraic Geometry Seminar

November 21, 2022

One of the most challenging problems in geometry and physics is to compute higher genus Gromov-Witten invariants of compact Calabi-Yau 3-folds, such as the famous quintic 3-fold. I will briefly describe how physicists compute Gromov-Witten invariants of the quintic 3-fold up to genus 53, using five mathematical conjectures. Three of them have been already proved, and one of the remaining two conjectures has been solved in some genus. I will explain how to prove the last open one, called the Castelnuovo bound, which predicts the vanishing of Gopakumar-Vafa invariants for a given degree at sufficiently high genus. This talk is based on the joint work with Yongbin Ruan.

For more information see: https://personal.math.ubc.ca/~jbryan/Zoominar-UBC-ETH/