This Project Grant award, valued at $220,000.00, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports research by Brown University to study variational methods in singular geometry, with applications to phenomena like classical mechanics, geodesics, and harmonic maps. The project aims to develop new analytical techniques to investigate the properties of solutions to non-linear elliptic PDEs, and...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $113,376 to Brown University to develop techniques for understanding the geometry of solutions to systems of polynomial equations. The research focuses on three main areas: 1) the natural stratification of the space of vector bundles on a curve, 2) the interpolation problem in other settings like homogeneous spaces, and 3) the rationality problem for varieties...
This Project Grant award, valued at $250,000.00, was provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program to Brown University. The primary focus of this 3-year project is to conduct research in the areas of moduli theory and birational geometry within the field of algebraic geometry, which has important applications in coding, industrial control, computation, and theoretical physics. Key research activities include studying the...
This Project Grant award of $250,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research by Brown University in the geometry of algebraic curves and their moduli spaces. The key activities include: Studying the interpolation of algebraic curves through special configurations of points, particularly as the points specialize or collide. This includes exploring higher-dimensional analogs and systematic understanding of these...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research to develop new mathematical tools and understanding of the long-term dynamics and rigidity of certain infinite-volume mathematical systems. The $300,000 award to Yale University, to be completed by June 30, 2028, focuses on advancing the frontier of pure mathematics, with the goal of enabling applications in areas like data encryption, navigation, and...
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 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research in harmonic analysis and its applications. The PI at Brown University will conduct theoretical and applied research in two main areas: (1) harmonic analysis in non-doubling measure settings, and (2) applying harmonic analysis to problems in complex analysis and operator theory. This includes investigating sparse domination of...
This $157,021 Project Grant, awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, supports quantitative analysis of high-contrast composite materials. The principal investigator (PI) at Brown University will focus on developing new mathematical methods to understand field concentration effects in these materials, which have important applications in bioengineering, medical imaging, and electronics. Key research objectives include...
The National Science Foundation Division of Mathematical Sciences awarded Brown University a $454,629 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to support research on Variational Methods in Singular Geometry from August 15, 2021 through July 31, 2024. Brown University will utilize the funding to advance scientific understanding of major problems confronting the nation through research that promotes progress in the mathematical and physical...
Brown University was awarded a $331,275 Project Grant from the National Science Foundation Division of Mathematical Sciences on September 1, 2021, with a completion date of July 31, 2023. The award is part of the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in these fields and strengthen the nation's scientific enterprise. Under this award, Brown University will research the existence and regularity of solutions to variational problems in...