This Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences federal grant program (CFDA 47.049), provides $229,761 to the University of Maryland, College Park for research exploring unique continuation and regularity of mappings and functions in several complex variables and partial differential equations. The University will investigate unique continuation problems for CR mappings between embedded CR manifolds and...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) provides $210,000.00 to the University of Maryland, College Park to conduct research on microlocal analysis and Monge-Ampère type equations in geometry. The key products and services to be delivered include: Advancing research on the existence of canonical shapes and structures on manifolds or geometric spaces, related to the work of Riemann on curvature...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $300,000.00 to the University of Maryland, College Park to advance research across three classes of nonlinear partial differential equations. The project aims to study emergent phenomena, conservation laws, and the pressure-less early universe model in multiple spatial dimensions. Key focus areas include Euler alignment, nonlinear conservation laws, and the...
This National Science Foundation (NSF) Project Grant Award, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $210,000.00 in funding to the University of Maryland, College Park to support research on the interplay between polylogarithms, cluster algebras, and hyperbolic geometry. The key objectives are to investigate key conjectures, find new examples of hyperbolic manifolds, and compute invariants using cluster coordinates. The project will involve both graduate and...
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...
This National Science Foundation Project Grant award of $424,370 provides funding over five years from June 2022 through May 2027 under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports research at the University of Maryland, College Park to advance fundamental knowledge of dynamical systems through the study of long-term behavior of parabolic systems, which display sub-exponential divergence of orbits in contrast to hyperbolic systems. The...
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 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...
This $204,372 federal Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) supports research on the potential theoretic aspects of complex geometry. The principal investigator will employ methods from potential theory, infinite-dimensional geometry, and geometric analysis to investigate a cluster of interconnected questions and conjectures in complex geometry. The project aims to advance scientific knowledge in this...
This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $232,812 to The Johns Hopkins University from July 1, 2022 to June 30, 2025 to improve understanding of dispersive partial differential equations. Key products include research on the long-time behavior of solutions to critical scaling equations like the Schrödinger maps problem and focusing/mass-critical nonlinear Schrödinger equation. Additional work will analyze energy...