This three-year Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $659,740 to the University of North Carolina at Chapel Hill to support research centered around stochastic dynamical systems describing interacting particle behavior. The research aims to characterize typical behavior, fluctuation probabilities, and large deviations for such systems as the number of particles...
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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $200,000 to conduct fundamental research on mathematical models that describe complex interactions, growth, and motion in irregular environments with stochastic unpredictability. The goal is to discover general mathematical laws that govern such systems, which have implications for a wide range of real-world phenomena including traffic, communication networks,...
This Project Grant award from the National Science Foundation's (CFDA 47.049 - Mathematical and Physical Sciences) provides $200,000 in funding to the University of Utah to support research on random polymer measures and their applications. The project explores mathematical patterns underlying complex, irregular natural processes such as the spread of infections, crystal formation, and traffic dynamics. By studying the deep mathematical rules governing these random and unpredictable phenomena,...
The National Science Foundation awarded a $330,000 project grant under the Mathematical and Physical Sciences program (CFDA 47.049) to the University of Connecticut for research titled "Asymptotics and Ergodicity of Hypoelliptic Random Processes." The three-year award beginning May 15, 2023 will support research into convergence properties of random systems to equilibrium, with a focus on hypoelliptic diffusions and random walks. The grantee will study limit laws such as small...
This $184,162 Project Grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research on free boundary problems and phase interfaces in heterogeneous media. The project aims to advance the theory of phase interfaces by developing new techniques that connect partial differential equations, geometry, and statistical physics. The key outcomes will be: 1) a theory of large-scale regularity for free boundary and...
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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will provide $150,000 to the University of Wisconsin System to conduct research on asymptotic behavior in partial differential equations from various scientific applications. The key focus areas include: (1) studying long-time propagation and front structure in reaction-diffusion equations in heterogeneous environments; (2) analyzing long-time and white-noise limits of...
This $207,485 federal Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research into the classification and analysis of dynamical systems and group actions at the University of Utah. The project aims to study the concept of "conjugacy" in dynamical systems, exploring generalizations and extensions to better understand the mathematical properties that define equivalence between such systems. This work will...
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,...