The Gauged Linear Sigma Model and Its Applications

在过去的二十年里，数学和物理之间有了大量的相互作用。物理学中的各种模型对数学产生了很大的影响。其中一个模型是测量线性模型。本项目包括一个全面的计划，研究测量线性西格玛模型的数学理论及其应用。该项目本质上是跨学科的，物理和数学思想都发挥了重要作用。它增加了当前数学与物理相互作用的趋势。该项目还将加强对本科生、研究生以及博士后的培养。在PI在计量线性西格玛模型的代数几何理论方面取得初步成功的基础上，本项目将构建对数计量线性西格玛模型模空间。新理论具有广泛的应用范围，包括一些众所周知的问题，如紧化Calabi-Yau 3-fold的高属Gromov-Witten理论的计算。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

During the past twenty years, there has been a great deal of interaction between mathematics and physics. Various models from physics have had great impact on mathematics. One of these models is the gauged linear sigma model. This project includes a comprehensive program to study the mathematical theory of the gauged linear sigma model and its applications. The project is interdisciplinary in nature, and both physical and mathematical ideas play essential roles. It adds to the current trend of interaction between mathematics and physics. The project will also enhance the training of undergraduate and graduate students, as well as postdoctoral fellows.Building on the PI's initial success on algebraic geometric theory of gauged linear sigma model, this project will construct log gauged linear sigma model moduli space. The new theory has a range of applications including some well-known problems such as the computation of the higher genus Gromov-Witten theory of compact Calabi-Yau 3-folds.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.