This Project Grant award of $100,000.00 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports research in algebraic combinatorics, which investigates combinatorial structures arising in algebra and geometry. Specifically, the project aims to develop new combinatorial techniques in classical incidence geometry and further the theory and applications of cluster algebras. The research will involve...
This $172,000 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research by Michigan State University on the birational classification of algebraic varieties. The key goals are to investigate the moduli theory and boundedness of Fano varieties over the integers, explore connections between birational geometry and commutative algebra/arithmetic geometry, and apply new techniques from derived algebraic geometry to study...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research on algebraic cycles, automorphic forms, and L-functions. The $230,000 award to The Trustees of Columbia University in the City of New York, spanning July 1, 2024 to June 30, 2027, aims to deepen the understanding of these mathematical objects and their connections, particularly in high dimensions. The research will include work on the...
This National Science Foundation (NSF) Division of Mathematical Sciences Project Grant award to Michigan State University totaling $160,279 supports research in the field of algebraic geometry. The project will explore the constraints placed on smooth nonlinear shapes from modular forms, and then examine which features persist when the shapes acquire singularities. This will require the use of more general tools called quasi-modular and mock modular forms. The project offers opportunities for...
The National Science Foundation (NSF) awarded a $204,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to the Regents of the University of Michigan to investigate rigidity phenomena in geometry and dynamics, with a focus on actions of higher rank abelian and semi-simple Lie groups and their lattices. This 3-year research project, with an award period from June 2024 to May 2027, will explore topics such as the classification of higher-rank...
This Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), supports a research project on the interaction of algebra and geometry, with a focus on the resolution of singularities. The $209,771 award, effective August 15, 2024 through July 31, 2027, will fund research conducted by the University of Missouri System, exploring topics such as properties and applications of filtrations in local rings, inseparable local...
This $405,998 Project Grant was awarded by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049) to Regents of the University of Michigan, Office of Research and Sponsored Projects, doing business as the University of Michigan. The grant supports the principal investigator's research into the deformation spaces of geometric structures on n-dimensional manifolds. This includes studying the Hitchin component of...
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...
This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) will support fundamental research by Brigham Young University in the field of algebraic geometry. The key goals of the $125,000 award, with a performance period from July 15, 2025 to June 30, 2027, are to: Understand the motivic Euler characteristic, a crucial algebraic geometry invariant, for Hilbert schemes of K3 surfaces, including characterizing its...
This federal Project Grant award for $190,000 was provided by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) grant program. The award supports a postdoctoral research fellowship for Yelena Mandelshtam at the University of Michigan - Ann Arbor, under the mentorship of sponsoring scientist Thomas Lam. The funded research project is titled "Algebraic Curves, Grassmannians, and Integrable Systems", and it...