This three-year, $239,774 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research at Stony Brook University on the uniformization and rigidity of fractal metric spaces and the complex plane. Specifically, the principal investigator will develop new techniques to better understand fractal objects with non-smooth, wrinkled or self-similar patterns applying in nature and data storage applications. This includes...
The National Science Foundation awarded a $287,991 Project Grant to The Research Foundation For The State University Of New York, also known as Stony Brook University, to support the research project "COMPLEX DYNAMICS: RENORMALIZATION, GEOMETRY, AND ALGEBRA" from June 1, 2021 through May 31, 2024. This award will fund mathematical research into complex dynamics, renormalization, geometry, and algebra under the NSF's Mathematical and Physical Sciences program (CFDA 47.049). The goal...
This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences (CFDA 47.049) program seeks to advance the understanding of dynamical systems and the evolution from ordered to chaotic behavior. The $249,103 award to the Research Foundation of the City University of New York, effective July 1, 2024 through June 30, 2026, will support research aimed at developing new conceptual ideas, approaches, and theoretical frameworks to transcend the limitations of...
This federal Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, will support research at New York University (NYU) to advance the theory of dynamical systems and investigate its applications in fields such as engineering and the biological sciences. The $375,506 award, effective from July 1, 2024 to June 30, 2029, will fund four primary research projects: Extending finite-dimensional dynamical systems...
This Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences supports research on the theory of dynamical systems and conformal dynamical systems. The award, totaling $262,205 over 3 years starting on August 1, 2024, will fund work to address longstanding conjectures and open new research directions in this field. The project will leverage tools from complex analysis, hyperbolic geometry, and arithmetic geometry to study moduli spaces of one-dimensional...
This $575,244 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research into complex dynamics in higher dimensions at Indiana University from July 1, 2022 to June 30, 2025. The award will fund Ph.D. students' research into topics including holomorphic group actions on complex surfaces from Painlevé 6 differential equations, Migdal-Kadanoff renormalization mappings in statistical physics, and ergodic theory of rational maps...
The National Science Foundation (NSF) awarded a $369,218 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of California, San Diego (UCSD) to develop analytical methods for approximating the state of certain dynamical systems. The project aims to advance the understanding of quantitative aspects of the analysis of dynamical systems, with a focus on rigidity phenomena in the dynamics of group actions on structured spaces. Key research areas include...
The National Science Foundation awarded the University of Chicago a $369,956 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research into dynamical systems and Hodge theory through the study of low-dimensional dynamical systems using tools from algebraic geometry and Hodge theory. Specifically, the Principal Investigator will examine the relationship between Hodge theory and Anosov representations, which were recently connected by the PI...
This three-year Project Grant from the National Science Foundation's Mathematical and Physical Sciences program, totaling $375,740, will support research into dynamical systems and their statistical properties. Specifically, the principal investigator at the University of Chicago will investigate questions around the stability, generic features, and rigid symmetries of smooth dynamical systems. This includes attempting to prove the symplectic version of the C1 Pugh-Shub conjecture regarding when...
The National Science Foundation Division of Mathematical Sciences awarded a $185,579 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to The Research Foundation For The State University Of New York on behalf of Stony Brook University. The five-year award beginning June 1, 2023 will support research advancing understanding of two-dimensional fluid motion through the lens of partial differential equations, geometry, and dynamical systems. Specifically,...