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...
The National Science Foundation Division of Mathematical Sciences awarded Purdue University a three-year $183,426 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will support research into singularities of algebraic varieties and more general objects over arbitrary characteristic fields and Noetherian rings. Specifically, the Principal Investigator will further develop the theory of singularities, build necessary tools and techniques, and...
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...
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...
The National Science Foundation (NSF) awarded a $405,500 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to Duke University to support a research program in A1-homotopy theory and its applications to enumerative geometry and number theory. The award will fund research to develop enriched counting methods that can detect differences in the number of solutions to equations requiring real or imaginary numbers, with potential applications in number theory and...
The National Science Foundation (NSF) awarded a 3-year, $155,000 Project Grant under the Integrative Activities (CFDA 47.083) program to the Board of Regents of the University of Nebraska, doing business as the University of Nebraska, for research in commutative algebra and algebraic geometry. The project focuses on three areas: symbolic powers of ideals and higher-order polynomial interpolation, homological properties of symmetric ideals, and the algebraic Lefschetz property. The research...
This $260,000 Project Grant awarded by the National Science Foundation's (NSF) Division of Mathematical Sciences aims to advance the understanding of algebraic points on mathematical varieties. The primary research focus is on characterizing the arithmetic and local properties of algebraic points on curves, with complementary projects exploring higher dimensional varieties such as surfaces. The award also supports mentoring and training of early career mathematicians, particularly from...
This $185,987 National Science Foundation Division of Mathematical Sciences Project Grant supports continued collaborative research in enumerative algebraic geometry at the University of North Carolina at Chapel Hill from August 1, 2022 through July 31, 2025. Specifically, the investigators and their graduate students will further their work resolving outstanding questions in enumerative algebraic geometry through techniques including intersection theory, equivariant localization, symmetric...
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...
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) Division of Mathematical Sciences awarded a $110,000 Project Grant to the University of Kansas Center for Research Inc. to study the singularities of algebraic varieties and develop methods to precisely quantify the complexity of polynomial systems through the use of invariants. This 3-year grant, which runs from September 1, 2023 to August 31, 2026, will train graduate students in technical mathematical research, implementation of results using open-source software, and effective communication of findings. The project will also mentor underrepresented undergraduate students to prepare them for STEM careers in industry and academia. Key deliverables include developing discrete and continuous invariants to characterize singular systems, implementing these in open-source computer algebra systems, and disseminating the results to a wide audience. This award falls under the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to strengthen the nation's scientific enterprise by advancing knowledge in these domains.