Project Grant N000142012498

This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $137,633 to the University of Chicago to investigate the connections between non-Euclidean hyperbolic geometry and Euclidean geometry. The research aims to develop a stronger link between the earthquake and horocycle flows, study the structure of optimal Lipschitz maps between hyperbolic surfaces, and investigate related counting problems on flat and...

The National Science Foundation (NSF) awarded a $285,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Utah to conduct research on hyperbolic geometry in two- and three-dimensional spaces. The project, running from August 1, 2024 to July 31, 2027, will focus on studying the geometry of hyperbolic 3-manifolds, including investigating the renormalized volume of such manifolds and the connection to the Weil-Petersson gradient flow. The...

This three-year National Science Foundation Project Grant of $378,000 will support research into boundaries of groups in geometric group theory and hyperbolic geometry at the University of Illinois at Chicago from September 2022 through August 2025. Specifically, the principal investigator and collaborators will investigate the Cannon Conjecture regarding differences between classical and Gromov hyperbolic geometry in three dimensions in the presence of symmetries. They will continue...

This $178,380 National Science Foundation project grant under the Mathematical and Physical Sciences program enables the Society for Industrial and Applied Mathematics to administer a travel grant program for approximately 100 U.S.-based mathematicians, early career faculty, and graduate students to attend the 2023 International Congress on Industrial and Applied Mathematics in Tokyo, Japan from August 20-25, 2023. SIAM will award travel grants on a competitive basis to support participation...

This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $303,150 to Vanderbilt University's Sponsored Programs Administration Division to conduct research on groups acting on hyperbolic spaces and operator algebras. The key objectives include studying the rigidity properties of acylindrically hyperbolic groups, analyzing groups acting on hyperbolic simplicial complexes, and continuing work on automorphisms of von...

The National Science Foundation awarded Brandeis University a $263,986 project grant under the Mathematical and Physical Sciences program (CFDA 47.049) to support research on Group Actions on Hyperbolic Spaces from July 1, 2021 through June 30, 2024. This funding will allow Brandeis University researchers to advance understanding of major problems in mathematics by investigating the behavior of groups acting on hyperbolic spaces. Specifically, the grant will support mathematical analysis of...

This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program provides $213,094 to The University of Kentucky Research Foundation for research on harmonic analysis and homogenization of elliptic equations in perforated domains from July 1, 2022 to June 30, 2025. The award supports research focusing on establishing optimal quantitative results in homogenization theory for partial differential equations arising in applications involving fluid flows,...

This $256,573 National Science Foundation Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) will support research exploring algebraic aspects of chaotic dynamical systems with hyperbolic behavior at Texas A&M University from July 2022 through June 2025. Specifically, the award will fund investigations into the connections between hyperbolic dynamical systems and group theory, automata theory, and other branches of algebra. The research aims to clarify whether...

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 $299,877 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at Yale University across two major areas. In the first part, the Principal Investigator (PI) aims to prove new formulas for solutions to an equation describing the geometry and curvature of space-time, first studied by Einstein. The second part focuses on studying two-dimensional systems with scale invariance, which the PI will analyze by...