The University of Maryland, College Park received a $300,000 Project Grant award from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The award will fund research into free boundary problems for aggregation phenomena and partial differential equations from August 1, 2023 through July 31, 2026. Specifically, the university will study relationships between local interactions and collective motion in...
This $300,000 federal Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental mathematical and computational research on complex stochastic systems with infinite degrees of freedom. The project aims to develop new theoretical frameworks and analytical techniques for studying the asymptotic behavior of stochastic partial differential equations (SPDEs) with multiple scales and conservation laws. The...
This $100,972 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research on nonlinear partial differential equations and their applications in fields such as crystal growth, combustion, and game theory. The primary investigator (PI) will study the regularity, large-time behavior, and qualitative properties of solutions to these equations, which have connections to areas like the calculus of...
The National Science Foundation awarded The Johns Hopkins University a $320,648 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant will support research into various aspects of the theory of partial differential equations as they relate to the dichotomy between regularity and singularity formation. The Principal Investigator will pursue research in regularity theory and geometric properties for partial differential equations arising in the theory of...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in three canonical classes of nonlinear partial differential equations. The key objectives are to: Advance the understanding of existence, regularity, and large-time behavior of solutions for multi-dimensional Euler alignment equations, nonlinear conservation laws, and the pressure-less system. This involves developing novel...
This Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences (CFDA 47.049 - Mathematical and Physical Sciences) supports research focused on addressing fundamental questions in partial differential equations and optimization theory. The $291,367 award, spanning July 2024 to June 2027, will advance the Principal Investigator's work on characterizing extremal functions for Morrey's inequality, studying solutions to the pressureless Euler system, and...
The University of Maryland, College Park will receive $340,000 from the National Science Foundation under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct research on the regularity and stability analysis of free-boundary problems in fluid dynamics from August 1, 2022 to July 31, 2025. The project focuses on mathematical models commonly used in fluid dynamics applications involving dynamic, evolving boundaries between fluid domains. The university researchers will study...
This National Science Foundation Project Grant of $223,754 awarded on September 1, 2022 supports research into new frontiers in complex variables and holomorphic functions through August 31, 2025. Under the Mathematical and Physical Sciences program (CFDA 47.049), Central Michigan University will investigate construction techniques for holomorphic functions of one or several complex variables using the inhomogeneous Cauchy-Riemann equations and projection operators. The research aims to...
This National Science Foundation (NSF) Project Grant award provides $253,734 to The Johns Hopkins University to support research on the regularity of solutions to elliptic partial differential equations and generalized minimal submanifolds. The award focuses on two main mathematical objectives: studying unique continuation for solutions to elliptic PDEs and investigating the regularity theory for generalized minimal submanifolds. This research under the NSF's Mathematical and Physical Sciences...
This $268,602 federal Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports an interdisciplinary research project led by the Regents of the University of Michigan. The research aims to develop new mathematical tools based on partial differential equations (PDEs) and apply them to address practical challenges in mathematical finance and game theory. Key focus areas include: 1) using infinite-dimensional PDEs to demonstrate...