This Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences, under the Mathematical and Physical Sciences (CFDA 47.049) program, is providing $250,000 to Brown University to conduct research on moduli theory and birational geometry within the field of algebraic geometry. The key products and services to be delivered through this 3-year award include:
- Advancing the enumerative geometry of certain moduli spaces of surfaces, a long-standing challenge in this area of mathematics
- Continuing research on the birational geometry of stack-theoretic weighted blowups, which has proven instrumental for understanding the geometry of moduli spaces
- Developing new, simpler algorithms for logarithmic resolution of singularities, and algorithms for resolution in the presence of nested foliations
- Studying singularity invariants in positive characteristic to gain new insights into the challenges of resolution in this context
- Providing research training opportunities for graduate students and broader outreach via lectures and training programs
This award reflects NSF's mission to support fundamental mathematical research with significant potential scientific and technological impacts, such as applications in coding, industrial control, computation, and theoretical physics.
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