The Gauged Linear Sigma Model and Its Applications

在过去的二十年里，数学和物理之间发生了大量的相互作用。物理学的各种模型对数学产生了很大的影响。其中一个模型是计量线性西格玛模型。该项目包括一个全面的项目，研究计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，物理和数学思想都起着至关重要的作用。它增加了目前数学和物理之间相互作用的趋势。该项目还将加强本科生和研究生以及博士后研究员的培养。该项目将在PI基于规范线性西格玛模型的代数几何理论的初步成功的基础上，构建对数规范线性西格玛模型模空间。新的理论有一系列的应用，包括一些众所周知的问题，如紧凑的Calabi-Yau三折的高亏格Gromov-Witten理论的计算。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.