Degenerations and Moduli Spaces

该奖项支持代数几何的研究，代数几何是数学的一个中心分支，旨在从实践和概念上理解多变量多项式方程系统的解。这个项目的重点是研究代数变种的族，以及这些变种变形和分裂的方式。这些研究在数学的其他领域，如数论和拓扑学，以及物理学中的弦理论中发现了重要的应用。研究生将参与并支持该项目。PI将从事各种以代数变异的退化和模空间的泛函、几何上有意义的紧化为中心的项目。PI将继续他在晶格极化K3曲面模空间的几何意义紧化方面的工作。他还将研究KSBA模空间的交点理论。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。

The award supports research in algebraic geometry, a central branch of mathematics which aims to understand, both practically and conceptually, solutions of systems of polynomial equations in many variables. The particular focus of this project is on the study of families of algebraic varieties and the way these varieties deform and break up. Such studies found important applications in other fields of mathematics, such as number theory and topology, as well as in string theory in physics. Graduate students will be involved in and supported by this project.The PI will work on a variety of projects centered around degenerations of algebraic varieties and functorial, geometrically meaningful compactifications of moduli spaces. The PI will continue his work on the geometrically meaningful compactifications of moduli spaces of lattice polarized K3 surfaces. He will also work on the intersection theory of KSBA moduli spaces.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.