Project Grant 2506596
- This three-year $350,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program will support research at the University of Maryland, College Park on moduli spaces of Higgs bundles, gauge theory, and related topics in complex geometry. The principal investigator will further studies on moduli spaces of Higgs bundles on Riemann surfaces, including work on parabolic lambda-connections, construction of a universal moduli space, and the asymptotic and...
- 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 federal Project Grant award in the amount of $177,469.00 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences Grant Program (CFDA #47.049). The award will support research into the geometry of moduli spaces from low-dimensional topology and applications, with a focus on three main directions: studying higher algebraic structures in instanton Floer homology, analyzing the properties of generalized Seiberg-Witten equations, and exploring the...
- This National Science Foundation (NSF) Project Grant Award, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $210,000.00 in funding to the University of Maryland, College Park to support research on the interplay between polylogarithms, cluster algebras, and hyperbolic geometry. The key objectives are to investigate key conjectures, find new examples of hyperbolic manifolds, and compute invariants using cluster coordinates. The project will involve both graduate and...
- This federal Project Grant award of $130,500 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research on moduli spaces in algebraic geometry. The research aims to: (1) construct and investigate specific moduli spaces of fibered varieties, (2) explore the birational geometry of algebraic stacks, and (3) study the local and global geometry of moduli spaces of varieties of general type and polarized Calabi-Yau varieties. The award...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $210,000 in funding to the University of Maryland, College Park (UMD) from July 1, 2025 to June 30, 2028. The research project focuses on microlocal analysis and Monge-Ampere type equations in geometry. Key areas of focus include investigating the existence of canonical shapes and structures on manifolds or geometric spaces, exploring connections between complex...
- This $201,798 Project Grant was awarded by the National Science Foundation (NSF) through its Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award will support the Principal Investigator's research on applying new techniques in algebraic geometry to study the geometry of solution sets to systems of polynomial equations. The research will focus on three main directions: cohomology of moduli spaces of stable and smooth curves, and conjectures related to hypersurface...
- This federal Project Grant award of $117,892 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on the geometry of mapping class groups and surface bundles, which are fundamental concepts in mathematics. The research project, conducted by the Regents of the University of California at Riverside, aims to develop combinatorial techniques for studying the geometry of these mathematical objects. Additionally, the educational...
- This federal Project Grant award of $240,914 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on algebraic geometry and its applications. The project, led by Georgia Tech Research Corporation, focuses on developing new techniques and moduli theories for studying higher-dimensional algebraic varieties, particularly leveraging the concept of K-stability to construct moduli spaces for Fano varieties and Calabi-Yau manifolds. The...
- This $279,965.00 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will support research at the University of Michigan to investigate open questions in the areas of complex analysis and geometry using innovative non-Archimedean methods. The key focus areas include studying the Yau--Tian--Donaldson conjecture on an algebro-geometric criterion for the existence of constant scalar curvature metrics, examining the existence of...
This federal Project Grant award, valued at $150,000.00 and provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports research at the University of Maryland, College Park on the geometric, analytic, and algebraic properties of moduli spaces in complex geometry. The key products and services to be delivered under this grant include: (1) developing a gauge theoretic construction of a joint moduli space of Higgs bundles over varying Riemann surfaces; (2) further understanding the asymptotic structure and topological properties of the Hitchin moduli space, which has important implications for supersymmetric gauge theories; and (3) extending previous work on Chern-Simons line bundles to moduli spaces. This research aims to deepen the understanding of the mathematical structures underlying gauge theories and their applications in fields such as robotics. The grant period runs from August 15, 2025 to July 31, 2027.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $150.0k | 8/15/25 |