The National Science Foundation (NSF) awarded a $394,473 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Oklahoma's Office of Research Administration. The grant will fund research by the Principal Investigator on rigidity properties of hyperbolic manifolds, which are multi-dimensional shapes with negative curvature. The projects aim to advance understanding of rigidity and flexibility phenomena in the fundamental groups of real and complex...
The National Science Foundation (NSF) awarded a $204,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to the Regents of the University of Michigan to investigate rigidity phenomena in geometry and dynamics, with a focus on actions of higher rank abelian and semi-simple Lie groups and their lattices. This 3-year research project, with an award period from June 2024 to May 2027, will explore topics such as the classification of higher-rank...
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 (NSF) Division of Mathematical Sciences awarded a $141,490 Project Grant to the University of California, Santa Cruz (UCSC) under the Mathematical and Physical Sciences program (CFDA 47.049). The project seeks to study the geometry and topology of spaces with Ricci curvature bounded below, including both smooth manifolds and singular spaces. Key focus areas include investigating the fundamental groups of complete and non-compact manifolds with non-negative Ricci...
The National Science Foundation awarded a $361,459 Project Grant to the University of California, San Diego under the Mathematical and Physical Sciences program (CFDA 47.049) to expand the scope of rigidity in von Neumann algebras and uncover new applications to group theory, ergodic theory, and C*-algebras from June 1, 2022 to May 31, 2025. Specifically, the award will support research investigating rigidity properties for group von Neumann algebras and related topics, such as Hilbert-Schmidt...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) totaling $249,648 supports research on the relation between geometric and algebraic structures of groups. The award will fund the principal investigator's (PI) investigations into groups with geometric structures, focusing on situations where such groups have subgroups that exhibit undesirable geometric properties. Additionally, the PI will undertake efforts to broaden...
This Project Grant from the National Science Foundation's Division of Mathematical Sciences provides $442,140 to the University of Wisconsin-Madison under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) from September 2022 through September 2025. The funding supports research into the geometry, topology, and dynamics of curves, surfaces, and three-manifolds through investigating the mapping class group of surfaces. Specifically, the principal investigator and...
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...
This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $206,442 to support fundamental research into geometric structures incorporating torsion, with potential applications in mathematics and physics. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), the award to the University of California Irvine from August 15, 2022 through July 31, 2025 will aid in uncovering geometric and analytic aspects of generalized Ricci curvature,...
The National Science Foundation (NSF) awarded a $112,949 Project Grant to The Trustees of the Stevens Institute of Technology to conduct research under the Mathematical and Physical Sciences (CFDA 47.049) program. The project, titled "Uniformization of Surfaces and Mapping Problems in Metric Spaces", aims to develop new mathematical approaches for understanding the geometry of non-smooth spaces, building on the classical Uniformization Theorem. The research will investigate methods for...