Project Grant 2605402
- The University of Alabama at Birmingham (UAB) was awarded a $219,951 project grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) to conduct research on asymptotic analysis of almost-periodic operators in quantum mechanics. The three-year award beginning June 1, 2023 will support investigation of the properties of quasi-periodic structures using mathematical models to further understanding of electrical conductivity in modulated crystals and...
- The National Science Foundation Division of Mathematical Sciences awarded the University of Alabama at Birmingham $199,757 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop mathematical tools for analyzing the existence and stability of solitary waves and solitons in systems with multiple interacting components. The project extends variational and spectral techniques from single-equation models to coupled systems of nonlinear partial differential...
- The National Science Foundation Division of Mathematical Sciences awarded the University of Alabama $327,888 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to study quantitative parabolic rectifiability, parabolic partial differential equations, and boundary value problems. The project investigates evolution equations governing heat flow, diffusion, and transport processes in complex regions, with particular focus on how the shape and roughness of domain...
- The National Science Foundation Division of Mathematical Sciences awarded the University of Alabama $179,974 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop new algebraic and geometric tools for studying singular points in symmetric objects across three interconnected research components. The first component will develop algebraic complexes to compute the cohomology of toric vector bundles and prove sharp vanishing theorems, with applications to...
- The National Science Foundation Division of Mathematical Sciences awarded the University of Alabama $229,586 on October 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop neural network-enhanced reduced order modeling methods for solving partial differential equations with high dimensionality, randomness, nonlinear behavior, and multiscale features. The research combines reduced order model stability and efficiency with neural network flexibility to accelerate...
- The National Science Foundation Division of Mathematical Sciences awarded the University of Alabama $170,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop novel homological structures in commutative algebra and their applications. The project will advance homological and homotopical methods in algebraic geometry, including tools from noncommutative geometry, across four interrelated research directions. The first develops a new reconstruction...
- This Project Grant award for $249,454, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, supports research conducted by the University of Alabama in two areas within mathematical analysis: harmonic analysis and partial differential equations. The key objectives are to expand knowledge in harmonic analysis and its applications to the study of partial differential equations, as well as to provide education and mentoring...
- The National Science Foundation (NSF) awarded a $180,935 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to the University of Alabama. The grant, awarded on August 1, 2023, will fund research into cell decompositions of quiver grassmannians, which are related to cluster algebras. This research aims to provide a topological explanation for positivity in cluster algebras, which have connections to various areas of mathematics, physics, and other fields. The project...
- The National Science Foundation Division of Materials Research awarded the University of Alabama $685,101 on July 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to elucidate the effects of grain boundary segregation spectra on spatial variation of grain boundary structural transitions and precipitation in aluminum alloys. The research addresses the assumption in prior grain boundary segregation studies that segregation behavior and elemental composition are...
- This NSF Integrative Activities (CFDA 47.083) project grant, awarded to the University of Alabama at Birmingham (UAB) for $256,892.00, aims to develop a new machine learning-based computational method for simulating quantum effects in large-scale materials systems. The project, which runs from February 1, 2025 to January 31, 2027, will involve a collaboration with researchers at the University of Texas at Austin to apply techniques like density functional theory, Wannier functions, and deep...
The National Science Foundation Division of Mathematical Sciences awarded the University of Alabama at Birmingham $350,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop novel quantum mechanical analysis techniques for studying the spectral properties of disordered and aperiodic solids, with research performance in Birmingham, Alabama through July 31, 2029. The project will advance theoretical understanding of materials with disordered and aperiodic atomic structures—including alloys, glass, quasicrystals, and metallic compounds—by developing new analysis methods applicable to the Schrödinger operator in higher dimensions. The investigators will demonstrate that the density of states of the operator exhibits analyticity in the high-energy region with probability one, analyze the Cantor structure of spectra in aperiodic systems, and apply Rayleigh-Schrödinger perturbation theory to enhance understanding of electrical conductivity in these materials. The analytical toolkit will combine spectral theory, partial differential equations, probability theory, and complex analysis. The work will train graduate and undergraduate students in this research area and is expected to yield relevance beyond materials science to broader challenges in mathematics and physics. This is a Project Grant, the standard assistance type for NSF research funding.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $350.0k | 7/20/26 |