Conference: Arithmetic, Birational Geometry, and Moduli

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This award provides support for the conference "Arithmetic, Birational Geometry, and Moduli Spaces" held at Brown University onJune 12-16, 2023. The conference will connect established experts, early career researchers, and graduate students working in algebraic geometry. Its goals are to encourage collaboration across sub-disciplines within the field and to foster an environment where people at all career stages may interact productively. A poster session will highlight achievements of graduate students and postdocs. Results of the meeting will be disseminated through live-streaming and video archives of lectures. The conference website is https://sites.google.com/view/abgms2023/The technical focus of the meeting will be resolution of singularities and semistable reduction. Resolution refers to the replacement of singular algebraic varieties with smooth models by repeated blowings up. Semistable reduction is the closely related process of finding mildly singular limits of degenerating families of algebraic varieties. These are fundamental tools for constructing birational models and boundary limits in moduli spaces. New tools like algebraic stacks, non-archimedean geometry, logarithmic geometry, and tropical geometry are driving progress on these questions. Novel, stronger forms of resolution and semistable reduction are appearing, even as the proofs of existing results become simpler. These developments offer a deeper understanding of long-standing arithmetic problems.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.