This $473,736 National Science Foundation project grant under the Mathematical and Physical Sciences program (CFDA 47.049) will fund research into the role of symmetry and convexity in isoperimetric-type geometric questions in high dimensions, with potential applications in learning theory and other fields. Principal investigator at Georgia Tech Research Corporation will supervise postdocs, students, and organize seminars to investigate asymptotic geometry questions like the behavior of large...
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...
The National Science Foundation Division of Mathematical Sciences awarded a $389,346 Project Grant to the Georgia TECH Research Corporation for research titled "Topology Between Dimensions Three and Four." The award period is from June 1, 2021 through May 31, 2024. The grant 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 through increasing knowledge and...
This $300,000 Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will support further research into the algebra, geometry, and combinatorics of matroids at Georgia Tech Research Corporation from October 1, 2022 to September 30, 2025. The Principal Investigator and collaborators will prove new results about matroid representations, including representations of 3-connected matroids and quaternary...
This Project Grant award for $330,586, provided by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA No. 47.049), supports research on the geometric and metric properties of two-dimensional surfaces. The principal investigator (PI) at Cornell University will investigate the classification of surfaces under singular flat and hyperbolic metrics, as well as the associated moduli spaces and related mathematical...
This Project Grant award from the National Science Foundation's (CFDA 47.049 - Mathematical and Physical Sciences) provides $150,000 in funding to Georgia Tech Research Corporation to investigate important problems in quantum topology and its connections with classical topology and hyperbolic geometry. The project will focus on three closely related research directions: the AJ conjecture relating colored Jones and HOMFLYPT polynomials to knot fundamental groups, the development of hyperbolic...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research to deepen the understanding of how geometric properties, especially curvature, influence solutions to geometric optimization problems. The $170,996 award to New York University, spanning June 2025 to May 2028, aims to advance the theory of isoperimetric problems and group structures in geometric analysis. Key focus areas include studying isoperimetric...
This $194,972 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program supports research at Emory University focused on addressing open problems in discrete geometry. The central aims are to study the covering and intersection properties of convex geometric objects and explore connections between discrete geometry and other mathematical fields. Key planned activities include mentoring undergraduate students, developing new mathematical...
This National Science Foundation Project Grant award of $472,476 provides funding from July 1, 2022 through June 30, 2025 to support research into variational questions in mathematics and physics. The award is made under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to advance scientific knowledge and understanding of major problems. The principal investigator will pursue research questions related to optimal states and equilibrium conditions in quantum mechanical...
The National Science Foundation Division of Mathematical Sciences awarded a $299,999 Project Grant to the Georgia Tech Research Corporation from July 15, 2021 to June 30, 2024 under the Mathematical and Physical Sciences program (CFDA 47.049). The funding will support research investigating the dynamics and kinetics of physical systems. The Mathematical and Physical Sciences program aims to strengthen the Nation's scientific enterprise by promoting progress in mathematical and physical...
The Georgia Tech Research Corporation was awarded a $315,000 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to conduct research on curves and surfaces in geometry. Over the two-year period from May 2022 to April 2025, the Principal Investigator and collaborators will engage in a range of activities to advance fundamental open questions in the geometry of curves and surfaces, promote these topics to the public through accessible lectures and articles, and introduce students to modern mathematics. Specific projects include investigating isoperimetric problems, isoclinic embeddings, geometric knot theory, polyhedral approximations, and the H-principle as well as studying notions of convexity, optimization, and the interaction of geometric and topological concepts in riemannian submanifolds. Findings from this research have the potential for applications in architecture, shape recognition, and computer graphics.