This Project Grant award of $120,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) aims to further develop the understanding of set-theoretic methods and their role in the field of topology, particularly in relation to concepts like compactness and convergence. The research project has three key components: Classifying the simplest nonmetrizable compact topological spaces under the additional axiomatic assumption of the Proper Forcing...
The National Science Foundation Division of Mathematical Sciences awarded The University of North Carolina at Charlotte a $180,000 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The three-year award will support research using set-theoretic methods in topology and topological dynamics, providing opportunities for graduate student research training. Specifically, the university will explore the topological consequences of principles related to...
The National Science Foundation Division of Mathematical Sciences awarded a $317,099 Project Grant to Rutgers, The State University under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The three-year award will support research into infinitary combinatorics and set theory, focusing on analyzing combinatorial principles such as the tree property, stationary reflection, and square principles in relation to cardinal arithmetic, especially singular cardinal arithmetic....
This $290,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (MPS) program supports research in computable model theory and invariant descriptive computability theory. The award, spanning July 2024 to June 2027, will fund work that explores connections between computability theory and the fields of model theory and set theory within mathematical logic. Key objectives include investigating cases where mathematically equivalent objects have...
This $118,647 Project Grant award from the National Science Foundation's Division of Mathematical Sciences (CFDA 47.049, Mathematical and Physical Sciences) supports fundamental research in descriptive set theory and its connections to other mathematical fields, including computability, operator algebras, topological dynamics, and ergodic theory. The award will fund research on questions related to amenability and hyperfiniteness, as well as investigations into classical geometrical paradoxes...
This federal Project Grant award for $300,000.00, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program, supports research to significantly expand the investigator's work on applications of model theory to the study of geometric structures. The key objectives are to: 1) tackle major transcendence problems such as the Ax-Lindemann-Weierstrass and Ax-Schanuel conjectures for uniformizing functions of geometric structures in higher...
This Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences federal grant program (CFDA 47.049), provides $440,000 to support research in model theory from August 1, 2022 to July 31, 2025. The Principal Investigator at the University of Maryland, College Park will investigate mechanisms by which a theory can control combinatorial configurations in its models. Specific areas of focus include monadic expansions of...
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 Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) will support research in descriptive set theory and computability at the University of California, Berkeley. The $170,000 award, spanning August 2024 to July 2027, will fund work in several areas: Studying questions on amenability and hyperfiniteness using tools from Gromov's theory of asymptotic dimension, with applications to topological dynamics and operator algebras. Research on...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $119,999 to the University of Illinois to conduct research centered around three main projects involving model theory. The first project aims to continue progress in resolving long-standing open problems for algebraic differential and difference equations using model theory. The second project seeks to develop connections between model theory and machine...