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组的解。这个项目的重点是研究代数变种以及这些变种的变形和分裂方式。这类研究在其他数学领域也有重要的应用，例如数论和拓扑学，以及物理学中的弦理论。研究生将参与并支持这个项目。PI将致力于各种以代数簇的退化和模空间的函数化、几何意义紧化为中心的项目。PI将继续他在格极化K3曲面的模空间的几何意义紧化方面的工作。他还将致力于KSBA模空间的交集理论。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。

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.