The Gauged Linear Sigma Model and Its Applications

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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.