学术科研-Castelnuovo Bound and Higher Genus Gromov-Witten Invariants of Quintic 3-fold

学术科研

数学大讲堂

Castelnuovo Bound and Higher Genus Gromov-Witten Invariants of Quintic 3-fold

演讲者：阮勇斌（浙江大学）
时间：2023-11-23 16:00-17:00
地点：理学院大楼M1001

Abstract

One of most difficult problems in geometry and physics is to compute higher genus Gromov-Witten (GW) invariants of compact Calabi-Yau 3-folds such as quintic 3-folds. The effort to solve the problem leads to the inventions of several subjects such as mirror symmetry and FJRW theory. Almost twenty years ago, physicist Albrecht Klemm and his group shocked the community to produce explicit predications of higher genus GW invariants up to $g=51$! Their calculation is based on five mathematical conjectures, four BCOV conjectures from B-model and one A-model conjecture called Castelnuovo bound. Several years ago, a spectacular progress has been made to solve four BCOV conjectures. In this talk, I will report the solution of Castelnuovo bound conjecture. This is a joint work with Zhiyu Liu.

About the speaker

Yongbin Ruan is currently a professor at the Institute for Advanced Study (IAS) of Zhejiang University. He was elected to the Chinese Academy of Sciences in 2021 and an invited speaker of the 1998 ICM. Professor Ruan works in the field of symplectic geometry and mathematical physics. He is credited with a few well-known theories, such as the (orbifold) Gromov-Witten theory, relative Gromov-Witten theory, Chen-Ruan cohomology, and Fan-Jarvis-Ruan-Witten theory, and for the resolution of several outstanding conjectures, such as the Arnold conjecture, the generalized Witten conjecture, and the LG/CY correspondence conjecture.