Project Grant 2603931
- The National Science Foundation Division of Mathematical Sciences awarded Brown University $270,000 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to support research on minimal surfaces and harmonic maps into singular targets. The project investigates regularity and rigidity questions for harmonic maps and minimal surfaces—geometric objects that minimize energy or area under prescribed constraints. Research focuses on harmonic maps from...
- The National Science Foundation Division of Mathematical Sciences awarded Brown University $300,000 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to advance rigorous computational methods for solving long-standing problems in partial differential equations and mathematical analysis. The project develops and validates computer-assisted proofs and artificial intelligence as trustworthy tools for scientific discovery, combining interval arithmetic,...
- The National Science Foundation Division of Mathematical Sciences awarded Brown University $303,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to support collaborative research on minimal surfaces and hypersurfaces in round spheres. The principal investigators will determine the index and nullity of minimal surface doublings in the round three-sphere and free boundary minimal surface doublings in the unit three-ball, with the goal of characterizing...
- The National Science Foundation Division of Materials Research awarded Brown University $235,878 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop mixed-dimensional materials platforms that enable precise control of structural features for investigating quantum phase emergence. The research addresses how lattice symmetry and structural disorder govern correlation-driven metal-insulator transitions and competing quantum phases in two-dimensional...
- The National Science Foundation Division of Mathematical Sciences awarded Brown University $489,060 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop foundational theory for interacting particle systems on sparse random graphs. The research will establish concentration bounds and long-time behavior analysis for interacting particle systems using tools from stochastic analysis, random graph theory, and percolation, with the aim of producing...
- The National Science Foundation Division of Mathematical Sciences awarded Brown University $199,999 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to support research in combinatorics of Hecke algebras and crystal skeletons. The project uses representation theory and machine learning techniques to study quantum deformations in combinatorics and probability theory. Specific research objectives include developing the combinatorics of the Hecke algebra center,...
- Brown University was awarded a $277,225 project grant from the National Science Foundation Division of Mathematical Sciences on August 1, 2021 to complete work by July 31, 2024. The grant falls under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to strengthen the nation's scientific enterprise through advancing knowledge and understanding of major problems. Specifically, Brown University will conduct research relating to renormalization group flows, embedding theorems,...
- Brown University was awarded a $322,138 project grant from the National Science Foundation Division of Mathematical Sciences. The grant is part of the NSF's Mathematical and Physical Sciences program (CFDA 47.049) and will support research from July 2021 through June 2024 to map class group and fiber bundles. As part of promoting progress in the mathematical sciences, this NSF funding will enable Brown University researchers to increase understanding of major problems in mathematics through...
- The National Science Foundation Directorate for Mathematical and Physical Sciences awarded Brown University $315,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to study the random geometry of empirical risk landscapes in deep neural networks. The award funds collaborative research investigating mathematical principles that explain when neural networks generalize well and when training algorithms find good solutions. The project examines the geometry...
- The National Science Foundation awarded Brown University $102,758 on December 1, 2025, under the Mathematical and Physical Sciences program (CFDA 47.049) to support research in arithmetic dynamical systems on projective varieties, a field that synthesizes number theory and dynamical systems. The project funds investigation into three primary research areas: canonical heights and fields of definition on abelian varieties, including development of quantitative lower bounds on average values of...
The National Science Foundation Directorate for Mathematical and Physical Sciences awarded Brown University $270,000 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to investigate relationships between smooth and discrete symmetries, specifically surface subgroups of lattices in semi-simple Lie groups. The research will classify surface subgroups of lattices aligned with a given SL_2(R) subgroup, beginning with reconciliation of multiple definitions of "closely aligned" and progressing through construction and assembly of pants groups with good matching to produce aligned surface groups. The project will employ artificial intelligence to develop computer programs visualizing crystals and their generalizations in complex symmetry spaces. Final work will apply good pants homology—developed to prove the Ehrenpreis Conjecture—to determine whether good matching can be performed or whether pants proportions can be adjusted to enable matching; Toledo rigidity and related principles may rule out existence of closely aligned surface subgroups in certain cases such as SU(1,1) in SU(2,1). Performance is located in Providence, Rhode Island, with a period of performance through July 31, 2029. The award is classified as a Project Grant, a standard assistance type for NSF fundamental research funding.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $270.0k | 8/5/26 |