This $353,236 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research at Northwestern University focused on questions at the interface of dynamical systems and the rigidity of group actions. The project aims to employ tools from dynamical systems to study group actions, with the goal of classifying certain actions, the underlying spaces they act on, and invariant geometric structures. The research will also...
This $299,999 Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), will support fundamental research on the rigidity and bounded cohomology of groups acting on nonpositively curved spaces. The principal investigator (PI) will focus on understanding the dynamical, topological, and geometric properties of infinite transformation groups that act in a distance-preserving manner on spaces like Euclidean and hyperbolic...
This $105,981 project grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research at the intersection of number theory, representation theory, and geometry. The research aims to explore geometric techniques in representation theory, with a focus on connections between representations of reductive algebraic groups over local fields and geometric constructions like...
The National Science Foundation (NSF) awarded a Project Grant of $349,929.00 on June 1, 2024 to Northwestern University under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The grant supports a 3-year research program focused on advancing the structural understanding of measurable and topological dynamical systems. The research aims to gain deeper insights into the interactions among different dynamical properties, using a combinatorial and symbolic approach. The...
The National Science Foundation Division of Mathematical Sciences awarded a $141,400 Project Grant to the University of Illinois under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will support research into Galois structures and arithmetic statistics in number theory from August 15, 2022 to July 31, 2025. Specifically, the principal investigator and collaborators will modify non-abelian Cohen-Lenstra heuristics when the base field contains roots of unity;...
The National Science Foundation Division of Mathematical Sciences awarded $270,000 under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to Northwestern University from July 1, 2021 to June 30, 2024. The Project Grant funding will support research into Linear Partial Differential Equations on Singular Spaces. The Mathematical and Physical Sciences program aims to strengthen the nation's scientific enterprise through advancing knowledge and understanding of major...
This $183,474 federal Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) will support the principal investigator's research program on group theory and its applications. The award will fund research into problems related to the characterization and efficient representation of finite simple groups, with a focus on using character-theoretic and algebraic geometry methods. Additionally, the grant will provide support for...
This $100,011 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on stochastic growth models and mathematical structures called line ensembles, which have applications in fields ranging from magnetization to protein synthesis. The research aims to expand knowledge of line ensembles and related techniques, leading to solutions for previously intractable problems. The award includes organizing conferences...
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 $115,718 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports advanced research into the algebraic and geometric properties of solutions to systems of polynomial equations. The primary goals of the project are to study the algebraic aspects of these solutions using non-archimedean geometry, investigate the complexity of curves within varieties of general type, and develop new non-archimedean...
This $299,998 federal Project Grant award was made by the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The award will support fundamental research by the principal investigator at Northwestern University to develop and apply probabilistic methods for studying the typical behavior and symmetries of deterministic mathematical objects with sophisticated structure, such as random subgroups of semisimple Lie groups. The research aims to address several important conjectures in areas like geometric and combinatorial group theory, algebraic number theory, and representation theory, with potential impacts on fields like differential geometry, topology, and theoretical physics. The award will also fund training and educational activities, including the organization of a year-long emphasis program, a spring school, and an international conference, as well as the supervision of undergraduate research students. No sub-awards are planned under this grant, which runs from July 1, 2025 to June 30, 2028.