This $248,882 federal Project Grant, awarded by the National Science Foundation's (NSF) Computer and Information Science and Engineering (CISE) program on June 1, 2024, supports research to address the "curse of dimensionality" in high-dimensional geometric optimization problems. The project, led by the University of Pennsylvania, aims to develop efficient algorithms and foundational principles for solving challenging geometric optimization problems that become intractable as data...
This $369,910 National Science Foundation project grant supports research into the geometry of sets and measures in Euclidean and non-Euclidean spaces at Stony Brook University from June 1, 2022 to May 31, 2025. The awardee will investigate mathematical analogs to organizing and visualizing large data sets, transferring analysis tools from low-dimensional to higher-dimensional settings. Specific activities include exploring quantitative uniform rectifiability theory in novel metric spaces,...
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...
This $419,962 Project Grant awarded by the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) will support the development and analysis of manifold learning algorithms for uncovering low-dimensional intrinsic structures of data sets within Wasserstein space. The research team at the University of North Carolina at Chapel Hill will leverage the eigenvectors of a Laplacian matrix built from a data-dependent graph to provide theoretically provable methods for...
This $275,000 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support collaborative research to develop new statistical approaches for comparing and aligning networks. The research will focus on investigating optimal transport-based distances for Markov embeddings of networks, developing new methods for network alignment and comparison, and establishing theoretical results about these approaches. The...
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 $288,221 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on geometric properties of convex bodies and their applications in fields such as x-ray tomography. The principal investigator (PI) plans to further develop analytical techniques that express geometric properties in terms of integral transforms, enabling the use of harmonic analysis methods to solve geometric problems. Key focus areas include...
The National Science Foundation (NSF) awarded a $343,850 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Cincinnati. This 3-year grant, effective September 1, 2024, will fund research to develop new mathematical tools for analyzing the large-scale geometric behavior of non-smooth metric measure spaces, which have diverse applications across fields like fluid mechanics, neurophysiology, and fractal geometry. The project aims to enhance the...
This $260,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on geometric limits in low dimensional geometry and topology at Boston College. The key objectives of the project are to analyze the global topology of the "space of all hyperbolic manifolds" and study the relationship between the "rank" of closed hyperbolic 3-manifolds and their geometry. In addition to the research...
The National Science Foundation (NSF) awarded a $152,144 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to Princeton University. The grant, titled "Structured Randomness: Random Matrices and Geometry," aims to develop general mathematical tools to explain the interplay between randomness and underlying structure in complex mathematical problems. The research will focus on two areas - random matrix theory and metric geometry - by leveraging...
This $350,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research on understanding the geometric structure of large datasets and the distortions that occur when representing them in simpler spaces. The primary research aims to resolve open questions around determining the minimum distortion required to embed finite metric spaces, such as social networks or protein structures, into Euclidean space. The project will also explore applications of low-distortion embeddings to enable efficient algorithms for scientific tasks. The award, covering the period from July 1, 2025 to June 30, 2028, is made to Princeton University, a leading research institution with extensive capabilities in mathematical sciences and computational modeling. The research findings are expected to yield structural insights and algorithmic innovations with broad applicability across scientific domains.