Degenerations and Moduli Spaces

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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.