This Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) provides $149,164 to the University of Texas at Dallas to study the approximation of analytic functions in one complex variable by polynomials, rational functions, and transcendental entire functions. The project will utilize quasiconformal mappings to better understand the geometric properties of these approximants, such as the location of critical points and values, in order to gain...
This $115,718 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports advanced research into the algebraic and geometric properties of solutions to systems of polynomial equations. The primary goals of the project are to study the algebraic aspects of these solutions using non-archimedean geometry, investigate the complexity of curves within varieties of general type, and develop new non-archimedean...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) Federal Grant Program provides $266,853 to the University of Delaware to conduct research on perturbation theory and generalizations of Aleksandrov-Clark theory. The research aims to analyze the spectrum and long-term behavior of self-adjoint differential operators, which are used to model physical systems. The project will develop perturbation theory methods to study the...
This Project Grant award of $205,606.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on the dynamics and structural properties of complex polynomials of degree three. The project, led by the University of Alabama at Birmingham (UAB), aims to develop a deeper mathematical understanding of the behavior of nonlinear mappings, which have applications across diverse scientific fields. Key objectives include constructing...
This $180,000 Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will fund research and training in approximation theory and elementary submodels at Virginia Commonwealth University from September 1, 2022 to August 31, 2025. The award supports using simpler concepts to approximate and provide insights into more complicated mathematical problems, employing a combination of set-theoretic and...
This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) provides $328,712 to the University of Pittsburgh to conduct research in geometric function theory. The project explores fundamental problems related to mappings and functions with limited differentiability, such as convex functions, Sobolev functions, and Lipschitz/Hölder continuous mappings. The research aims to uncover new mathematical principles that...
This $300,000 Project Grant award from the National Science Foundation (NSF) under the Computer and Information Science and Engineering (CFDA 47.070) program supports collaborative research at North Carolina State University (NC State) to develop new algorithmic approaches for efficiently and rigorously computing real solutions to systems of nonlinear polynomial equations. The project aims to advance both the mathematical theory and computational methods for solving such equations, which are...
This $198,173 Project Grant was awarded on August 1, 2024 by the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) to the University of Rhode Island. The award supports collaborative research to explore the properties, behaviors, and applications of stochastic functional differential equations and functional stochastic approximation algorithms across disciplines including ecology, infectious disease modeling, control engineering, neural networks, 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 $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...