This $124,914 project grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will fund collaborative research between U.S. and U.K. mathematicians to develop innovative methods for studying stability questions in nonlinear partial differential equations across scales. The University of Texas at Austin will partner with other institutions to conduct research, workshops, and student involvement from August...
This Project Grant award of $300,000 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award will support research by the University of Texas at Austin (UT Austin) focused on advancing mathematical models and understanding the dynamics of large systems of interacting particles and waves, and their underlying effective equations. Specifically, the principal investigator and research team will work on...
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 five-year Project Grant from the National Science Foundation's Mathematical and Physical Sciences program, totaling $372,943, will support research investigating mathematical models in geometric calculus of variations and their applications in physics. Funded from June 2023 through May 2028, the award to the University of Texas at Austin will advance basic mathematical research while connecting to natural sciences. Key work includes developing new mathematical tools to study aspects of...
This Project Grant award of $302,028.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) supports fundamental research on nonlinear hyperbolic and dispersive partial differential equations (PDEs). The award aims to deepen the understanding of these PDEs, which are critical for describing natural phenomena across scales, by investigating long-term dynamics, singularity formation, and the stability of special solutions. Key...
This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $292,823 in funding from August 1, 2022 to July 31, 2025 under the Mathematical and Physical Sciences program (CFDA 47.049). The award supports research and training at the University of Chicago on nonlinear partial differential equations with stochastic dependence, homogenization in random media, well-posedness in singular domains, mean-field games, and convergence of growth models. Key areas 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 aimed at advancing the mathematical analysis of nonlinear partial differential equations. The research has three main focus areas: (1) studying fluid dynamics problems with free boundaries, such as water waves, tsunamis, and hurricanes; (2) investigating the dynamics of gases and plasmas under physical kinetic boundary conditions,...
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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) in the amount of $209,999 supports research on the theoretical understanding of partial differential equations arising from physics and how kinetic models can elaborate on the shortcomings of original scientific theories. The research project, conducted by Louisiana State University, consists of four main components: 1) establishing the well-posedness and conditional...
This National Science Foundation (NSF) Project Grant award, under the Mathematical and Physical Sciences (CFDA 47.049) program, will support research on stochastic methods and isoperimetric inequalities at Texas A&M University. The $238,406 award, active from July 2024 to June 2027, will develop techniques to bridge fundamental conjectures in Brunn-Minkowski theory and dual Brunn-Minkowski theory, with a focus on intersection bodies and higher-dimensional generalizations. The research aims...