This National Science Foundation award under the Mathematical and Physical Sciences program (CFDA 47.049) provides $275,396 to the University of Oklahoma from August 1, 2023 through July 31, 2026. The funding supports research into the geometries and topologies of surfaces and graphs. Specifically, the award will advance understanding of how abstract algebraic groups manifest as symmetries of geometric spaces in one and two dimensions. Graduate students will gain research experience applying...
This $285,000 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support research on hyperbolic geometry in two and three dimensions at the University of Utah. The principal investigator and graduate students will study questions around the geometry of hyperbolic 3-manifolds, focusing on the renormalized volume of hyperbolic 3-manifolds and the connection between the Weil-Petersson gradient flow and the volume of the...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a 3-year, $309,585 Project Grant to The Ohio State University to conduct research in the field of hyperbolic dynamical systems, a branch of mathematics with applications in physics, chemistry, and engineering. The research project, titled "A Comprehensive Program in Rigidity," aims to investigate fundamental questions in hyperbolic dynamics, particularly focused on establishing stronger forms of...
This $142,565 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research on the study of manifolds, or geometric objects, with positive or non-negative curvature. The principal investigator (PI) at James Madison University aims to construct new examples of such manifolds and develop new methods for proving rigidity theorems about their properties. The project also includes broader impact activities like outreach,...
The National Science Foundation Division of Mathematical Sciences awarded The University of Iowa a three-year Project Grant totaling $246,264 under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will support research classifying von Neumann algebras through the lens of rigidity, a condition where the entire structure of a mathematical object can be determined from limited prior information. Specifically, the principal investigator will pursue new ideas...
This three-year, $345,394 National Science Foundation Project Grant supports research into the topology of three-dimensional spaces through the study of veering triangulations and their relationship to possible flows through such spaces. Specifically, the principal investigator and collaborators aim to prove that veering triangulations correspond to pseudo-Anosov flows, produce new Cannon-Thurston maps using these triangulations, and establish connectivity properties for triangulations in...
This $189,689 award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research on bifurcation and stability in rotating fluids and galactic structures conducted by the University of Oklahoma (OU). The project aims to advance the mathematical understanding of why galaxies can break circular symmetry and develop elliptical or spiral shapes, as well as model rotating neutron stars and binary star systems using fluid and relativistic...
The National Science Foundation (NSF) awarded a $339,999 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to New York University (NYU) for research on geometric analysis and complex geometry. The award supports the principal investigator's work on studying geometric structures of complex manifolds, including Calabi-Yau manifolds, and investigating the nature of singularities that arise in Ricci flow - a geometric evolution equation. The research aims to enhance...
This $220,000 Project Grant award was provided by the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The primary objective of the award is to support the Principal Investigator's research on "Variational Methods in Singular Geometry", which focuses on studying the mathematical principle of least action and its applications to complex systems like geodesics and harmonic maps. The...
This Project Grant award for $210,000.00 from the National Science Foundation (NSF) Division of Mathematical Sciences supports research on the interplay between polylogarithms, cluster algebras, and hyperbolic geometry. The 3-year award, beginning August 15, 2024 and ending July 31, 2027, aims to investigate key conjectures, find new examples of hyperbolic manifolds, and compute invariants using cluster coordinates. The award will involve both graduate and undergraduate students, and continue...