This $234,951 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into nonlinear partial differential equations and minimal submanifolds in Lagrangian geometry. The project, conducted by the University of North Carolina at Chapel Hill, will generate research opportunities for graduate students and facilitate the mentoring of graduate students and postdocs. The research will focus on two key areas:...
The University of North Carolina at Chapel Hill (UNC-Chapel Hill) was awarded a $366,654 project grant from the National Science Foundation (NSF) under the Mathematical and Physical Sciences (47.049) federal grant program. The grant will fund research in three key areas of applied mathematics: properties of model operators in condensed matter and topological physics; performance of numerical algorithms for studying wave propagation; and studying how the geometry of a domain or graph impacts...
The National Science Foundation awarded a $199,989 Project Grant to the University of North Carolina at Chapel Hill on June 1, 2021 to support research titled "Dualities in Enumerative Geometry and Representation Theory" through May 31, 2024. The grant is funded through NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in these scientific fields and strengthen the national scientific enterprise. Under this award, UNC-Chapel Hill...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill (UNC) a $185,000 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports a three-year research project to develop Hodge theoretic techniques for studying Knizhnik-Zamolodchikov differential equations, which link representation theory, algebraic geometry, and mathematical physics. Key research activities include developing a...
This $185,987 National Science Foundation Division of Mathematical Sciences Project Grant supports continued collaborative research in enumerative algebraic geometry at the University of North Carolina at Chapel Hill from August 1, 2022 through July 31, 2025. Specifically, the investigators and their graduate students will further their work resolving outstanding questions in enumerative algebraic geometry through techniques including intersection theory, equivariant localization, symmetric...
The University of North Carolina at Chapel Hill will use a $280,270 Project Grant from the National Science Foundation to support research titled "Dispersive and Wave Equations in the Presence of Background Geometry" from June 2021 through May 2024. The grant is part of NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to advance scientific knowledge and understanding in these fields. Specifically, the university will investigate dispersive and wave equations...
The National Science Foundation Division of Mathematical Sciences awarded North Carolina State University a $408,832 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will fund research into Lagrangian mechanics and low-dimensional topology from July 2021 through June 2024. As part of the Mathematical and Physical Sciences program's goal of strengthening the nation's scientific enterprise through advances in mathematics and physics, this...
The University of North Carolina at Chapel Hill was awarded a $545,613 Project Grant from the National Science Foundation Division of Materials Research under the Mathematical and Physical Sciences program (CFDA 47.049). The grant will fund research from August 2021 through July 2024 on optical bound states and non-linearity in geometrically-modulated dielectric nanowires. The Mathematical and Physical Sciences program aims to advance scientific knowledge and understanding in these fields...
The National Science Foundation Division of Mathematical Sciences awarded The University of North Carolina at Charlotte a $180,000 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The three-year award will support research using set-theoretic methods in topology and topological dynamics, providing opportunities for graduate student research training. Specifically, the university will explore the topological consequences of principles related to...
This $271,119 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research on complex Lagrangians, integrable systems, and quantization in relation to mirror symmetry. The University of California, Davis will lead a research group investigating mirror symmetry as it relates to symplectic geometry and complex algebraic geometry. The group will establish complex Lagrangian geometry as a tool to study geometric...
The University of North Carolina at Chapel Hill received a $740,299 Project Grant award from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The funding will support research into complex Lagrangian geometry as a tool to study geometric questions and quantization arising at the intersection of geometry and topology. Specifically, the award will allow researchers to construct concrete models demonstrating aspects of mirror symmetry, including symplectic-complex algebraic duality, Langlands duality, the Laplace transform, and relations to three-manifold invariants. The work will employ topological recursion, expected to provide a new mechanism for holomorphic quantization of complex integrable systems and shed light on mirror symmetry. The period of performance is from July 15, 2022 through June 30, 2025.