Zhiyu Liu: Castelnuovo bound and Gromov-Witten invariants of the quintic 3-fold

Abstract:One of the most challenging problems in geometry and physics is to compute higher genus Gromov-Witten (GW) invariants of compact Calabi-Yau 3-folds, such as the famous quintic 3-fold. I will briefly describe how physicists compute GW-invariants of the quintic 3-fold up to genus 53, using five mathematical conjectures. Three of them were proved and one of the remaining two conjectures was solved in some genus. I will explain how to prove the last open one, referred to as Castelnuovo bound in the literature. This talk is based on the joint work with Yongbin Ruan.