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 National Science Foundation Project Grant award of $302,854 provides funding from July 1, 2022 through June 30, 2025 to support research in algebraic geometry at Michigan State University. The PI will investigate relationships between hyperkähler manifolds, Fano varieties, Calabi-Yau varieties, and varieties of general type through moduli theory. Specifically, the PI aims to 1) formalize geometric constructions relating Fano varieties to hyperkähler manifolds of K3 type, 2) study which...
The National Science Foundation (NSF) awarded a $100,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to the Regents of the University of Michigan. The grant, awarded on August 15, 2024, will fund research into algebraic combinatorics and incidence geometry, with a focus on developing new combinatorial techniques and investigating connections between cluster algebras, singularity theory, and low-dimensional topology. The project aims to extend...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $300,000 Project Grant to the Regents of the University of Michigan under the Mathematical and Physical Sciences program (CFDA 47.049) to pursue two lines of investigation related to cluster algebras and cluster varieties. The first line of investigation involves constructing cluster structures on braid varieties, Richardson varieties, and related geometric spaces that have applications in representation theory and...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a 3-year, $250,000 Project Grant to the University of Wisconsin - Madison under the Mathematical and Physical Sciences program (CFDA 47.049) to investigate moduli spaces of surfaces with additional geometric structure. The grant will fund research to solve long-standing conjectures about the geometry and topology of these moduli spaces, which are mathematical spaces that parameterize the shapes an object can take....
This National Science Foundation Project Grant award in the amount of $241,311 provides funding from June 1, 2022 through May 31, 2025 to support research into arithmetic questions in the theory of linear algebraic groups at Michigan State University. The principal investigator will investigate the arithmetic, geometric, and structural aspects of algebraic groups over higher-dimensional fields, with a focus on various finiteness properties. Specific objectives include establishing finiteness...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $170,443 Project Grant to the University of Massachusetts Boston (UMass Boston) under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research in "Critical Symplectic Geometry, Lagrangian Cobordisms, and Stable Homotopy Theory." The project aims to incorporate ideas from homotopy theory and category theory into symplectic geometry to prove structural results about...
Michigan State University was awarded a $314,000 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) for work on "Noncommutative Algebras and Their Interactions with Algebraic and Arithmetic Geometry" over a three-year period from July 1, 2021 to June 30, 2024. The grant aims to advance understanding of major problems in mathematics through research exploring noncommutative algebras and their relationships to algebraic and...
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...
The National Science Foundation (NSF) awarded a $250,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to The Trustees of Princeton University Office of Research and Project Administration Division, doing business as Princeton University. This grant, awarded on June 1, 2024, will fund research centered on algebraic geometry and singularities in arithmetic settings, with the goal of developing new techniques to describe higher differential forms in positive...