This $195,929 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research to investigate canonical metrics and stability in complex geometry. The principal investigator at Rutgers, The State University aims to bridge connections between differential geometry and algebraic geometry in the study of projective manifolds and scalar curvature. Key research activities include exploring the Yau-Tian-Donaldson...
This Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), supports research on the geometry of complex manifolds, specifically focusing on Calabi-Yau manifolds and Kähler-Ricci solitons. The $155,345 award, with a period of performance from June 1, 2025, to May 31, 2028, aims to (1) construct examples of non-compact singularity model geometries, (2) describe the moduli of these spaces, and (3) analyze the corresponding...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $222,327 Project Grant to The Trustees of Princeton University, Office of Research and Project Administration to conduct research on the metric geometry and analysis of Einstein manifolds over a 3-year period from August 1, 2023 to July 31, 2026. The research project will focus on investigating the degenerations and quantitative behaviors of Einstein manifolds, building on prior work by the principal investigator...
The National Science Foundation (NSF) awarded a $339,999 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to New York University (NYU) for research on geometric analysis and complex geometry. The award supports the principal investigator's work on studying geometric structures of complex manifolds, including Calabi-Yau manifolds, and investigating the nature of singularities that arise in Ricci flow - a geometric evolution equation. The research aims to enhance...
This $189,661 Project Grant awarded by the National Science Foundation (NSF) Directorate for Mathematical and Physical Sciences (CFDA 47.049) supports research at Pomona College in Claremont, California. The project focuses on developing new methods in noncommutative metric geometry to advance the approximation of infinite-dimensional quantum mechanical algebras by finite-dimensional counterparts. Key outcomes will include enhancing connections between noncommutative topology, noncommutative...
This Project Grant award, valued at $219,328.00, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049). The grant will fund research to utilize powerful geometric concepts, known as classical surface theories, to deepen the understanding of gravity, black holes, and the fabric of spacetime. Key objectives include evaluating the quasi-local mass of binary black holes, defining angular momentum in general...
This $225,000 Project Grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences (MPS) program supports fundamental research in algebraic geometry. The grant aims to develop new tools in moduli theory and use them to advance the classification of algebraic varieties. This includes refining techniques for the deformation theory of stable pairs and analyzing wall-crossing phenomena for higher-dimensional moduli, with the goal of enabling progress in...
This $178,637 Project Grant awarded by the National Science Foundation's Division of Mathematical Sciences on July 15, 2023 supports research on K-stability and moduli spaces of higher dimensional algebraic varieties at Northwestern University. The Principal Investigator will study canonical geometric structures known as Einstein metrics to address the fundamental moduli problem in algebraic geometry. Key research objectives include constructing compact moduli spaces of K-unstable Fano...
This $307,873 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will fund research into geometric, analytic, and algebraic aspects of real submanifolds in complex varieties and their symmetries from June 1, 2022 to May 31, 2025. The University of California, San Diego will study properties of various metrics and kernels related to Kähler-Einstein metrics on higher-dimensional spaces, with goals of characterizing domains and...
This $280,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research in birational geometry at New York University from April 2022 through March 2025. Specifically, the principal investigator will use methods from Galois cohomology of function fields, properties of algebraic cycles over non-algebraically closed fields, K-theory, and degeneration techniques to advance understanding of rationality and stable...