Project Grant 2540987
- The National Science Foundation Division of Mathematical Sciences awarded the President and Fellows of Harvard College $210,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct research on the interactions of combinatorics and physics. The award funds research addressing questions at the interface of combinatorics, algebra, and physics. In statistical physics, the project studies the relationship between the asymmetric simple exclusion process...
- The National Science Foundation Division of Mathematical Sciences awarded $200,000 to Harvard College on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to fund research on special varieties in algebraic dynamics. The project investigates mathematical structures governing dynamical systems defined by repeated application of algebraic rules, with focus on identifying when such systems exhibit hidden geometric structure rather than generic chaotic behavior....
- The National Science Foundation Division of Mathematical Sciences awarded $300,000 to President and Fellows of Harvard College on July 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to support research in complex dynamics and moduli spaces. The project, running through June 30, 2029, aims to study moduli spaces—mathematical structures that classify the variety of shapes a recognized type can assume—from perspectives of analysis, algebra, geometry, and dynamics...
- The National Science Foundation Division of Mathematical Sciences awarded $225,000 to President and Fellows of Harvard College on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) for collaborative research on hidden components in complex data using mathematical frameworks such as non-negative matrices and tensors. The project develops innovative methods to uncover hidden patterns in relational datasets including health records, social networks, and ranking...
- The National Science Foundation Division of Mathematical Sciences awarded $255,000 to the President and Fellows of Harvard College on June 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to support research in Galois representations and arithmetic geometry. The research examines structural analysis of mod-p reductions of crystalline representations, algebraic cycles through prismatic cohomology, and de Rham analogues of the Mumford-Tate Conjecture. The project...
- The National Science Foundation Division of Mathematical Sciences awarded $175,000 to President and Fellows of Harvard College on July 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop mathematical and computational tools for integrating high-dimensional datasets with partially shared structures. The project creates new theoretical foundations at the intersection of random matrix theory, manifold learning, and high-dimensional statistics. Key deliverables...
- The National Science Foundation Division of Mathematical Sciences awarded $188,518 to President and Fellows of Harvard College on June 1, 2026, to investigate arithmetic statistics through homological stability under the Mathematical and Physical Sciences program (CFDA 47.049). The recipient will work on main conjectures in arithmetic statistics over function fields, including the Cohen-Lenstra conjectures on class groups of quadratic fields, Malle's conjecture on counting global field...
- The National Science Foundation Division of Materials Research awarded $300,000 to Harvard College on August 1, 2026, to develop and sustain open cyberinfrastructure for training and deploying neural equivariant machine-learned interatomic potentials and materials foundation models under the Mathematical and Physical Sciences program (CFDA 47.049). The project will expand the NEQUIP and ALLEGRO ecosystem to enable researchers to simulate complex materials with near-quantum-mechanical accuracy at...
- The National Science Foundation (NSF) awarded a $395,910 Project Grant to the Massachusetts Institute of Technology (MIT) under the Mathematical and Physical Sciences (MPS) program (CFDA 47.049) to fund research on statistical and computational thresholds in spin glasses and graph inference problems. The 3-year project, which will run from September 1, 2024 to August 31, 2027, aims to develop new methods for analyzing long-range dependencies and characterizing the typical behaviors of large...
- The National Science Foundation Division of Physics awarded a $450,000 Project Grant to President And Fellows Of Harvard College, Office For Sponsored Programs in Cambridge, MA to support the project "SIMULATING SPINS WITH AN ARRAY OF SINGLE MOLECULES" from September 1, 2021 through August 31, 2024. This award will fund research under the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in these scientific fields and strengthen the national...
The National Science Foundation Division of Mathematical Sciences awarded President and Fellows of Harvard College $243,639 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct research on algorithmic spin glass theory and computational phase transitions. The recipient will develop mathematical frameworks explaining when high-dimensional optimization and sampling landscapes can be navigated efficiently by algorithms and when intrinsic barriers prevent broad algorithmic classes from succeeding. The research applies spin glass theory—originating in statistical physics for studying disordered materials—to identify fundamental limits in algorithms for random optimization and sampling, with implications for diffusion-based generative AI, combinatorial optimization, random matrix theory, and quantum algorithms. The project employs the branching overlap gap property as a central tool to identify geometric obstructions to stable algorithms and connect these obstructions with low-degree polynomial methods as evidence for computational hardness. The educational component includes mentoring, new course materials, and a summer school on spin glasses and algorithms for students and early-career researchers. Performance occurs in Cambridge, Massachusetts, with a period of performance through July 31, 2031. This is a Project Grant assistance type.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $243.6k | 8/7/26 |