Project Grant 2554045
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $200,000 on July 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct mathematical research on interactions of Fourier restriction with fractal geometry and number theory. The investigator uses harmonic analysis tools to understand refined behavior of the Fourier transform under special geometric conditions relevant to applications including the...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $271,080 on January 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop AI models that reason constructively about complex mathematical problems and advance formal proof systems. The collaborative research project, spanning January 1, 2026, through December 31, 2028, and performed in Los Angeles, California, aims to synergize artificial...
- The National Science Foundation Division of Mathematical Sciences awarded University of California, Los Angeles $117,567 on July 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to investigate structure, rigidity, and classification of von Neumann algebras using noncommutative boundary techniques. The project runs through June 30, 2029, with performance at UCLA in Los Angeles, California. The investigator applies and develops boundary methods—tools historically used in...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $145,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop rigorous mathematical theory predicting localization and delocalization transitions in complex disordered quantum systems. The research focuses on non-mean-field random matrices and addresses fundamental questions about when electrons, waves, and other excitations remain...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $1.08 million on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop a human-centered, AI-assisted framework for interactive mathematical reasoning and discovery. The project, running through August 31, 2029, establishes effective human-AI collaboration paradigms that adapt to user expertise while preserving interpretability and...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $300,000 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop mathematical foundations and scalable algorithms for high-dimensional sampling and generative modeling. The project develops a unified mathematical and computational framework for sampling and generative modeling applicable to high-dimensional problems in scientific...
- The National Science Foundation awarded a $340,516 project grant to the University of California, Los Angeles Office of Research Administration to support the Expanding Thurston Maps and Fractal Geometry project. The three-year award, made under the Mathematical and Physical Sciences program (CFDA 47.049), will fund research exploring major problems in these fields from July 1, 2021 to June 30, 2024. The Mathematical and Physical Sciences program aims to promote progress in these disciplines and...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $100,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to investigate differentials in the Adams spectral sequence and related problems in algebraic topology. The project addresses deep questions in the classification of high-dimensional spaces, building on the principal investigator's recent resolution of the final unresolved case of the...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Berkeley $100,000 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop and apply the iterated true-stage method and topological game meta-theorem—tools from computable structure theory—to advance results in descriptive set theory. Both tools enable construction of continuous functions using information that lies high in the Borel hierarchy, bridging...
- The National Science Foundation Division of Mathematical Sciences awarded $214,876 to the University of California, Los Angeles on October 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049). The project develops a rigorous theoretical foundation for multi-operator learning, establishing a mathematical framework to understand how neural networks can efficiently learn across collections of complex physical systems. The work addresses gaps between empirical advances in deep...
The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $120,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to advance structural properties of the universe of mathematics through research in forcing, large cardinals, and descriptive set theory. The recipient will investigate three specific subjects: the tree property of cardinal numbers and its connection to large cardinal axioms and consistency proofs; interactions between combinatorial properties of the real number line and the cardinality of the real numbers; and canonical models for large cardinal axioms to establish structural properties of definable sets of real numbers. The project seeks to develop understanding of what is true and what is possible within mathematical axiom systems, particularly by examining how large cardinal axioms affect sets of real numbers. An additional goal is training graduate students in mathematical research methods, including the application of artificial intelligence to future mathematical research. Performance occurs at UCLA's Los Angeles, California campus from August 1, 2026, through July 31, 2029. The assistance type is a project grant.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $120.0k | 7/22/26 |