This National Science Foundation (NSF) Project Grant award, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $117,782.00 to Rutgers, The State University to conduct research on combinatorics of filters, large cardinal and Prikry-type forcing. The project aims to study principles related to singular cardinal arithmetic and the interaction between extensions of the standard Zermelo-Fraenkel set theory axioms and unsettled mathematical statements. The research will...
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...
This National Science Foundation Project Grant award of $360,000 provides funding from August 15, 2022 through July 31, 2025 to further develop set-theoretic methods and their applications to problems in mathematics. Specifically, the awardee Cornell University will conduct research into understanding the structure of the algebra of piecewise linear functions on the unit interval using transfinite ordinals, compactness, and large cardinals. This includes attempting to prove conjectures regarding...
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...
The National Science Foundation Division of Mathematical Sciences awarded a $226,529 Project Grant to Rutgers, The State University of New Jersey, Camden under the Mathematical and Physical Sciences program (CFDA 47.049). The grant will support research on spectral theory and geometric analysis in several complex variables from July 15, 2021 to June 30, 2024. The Mathematical and Physical Sciences program aims to advance scientific knowledge and understanding in these fields through support of...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $120,000 to Cornell University to further develop the understanding of set-theoretic methods and their role in topology, particularly in relation to compactness and convergence. The research aims to classify the simplest nonmetrizable compact topological spaces, the cofinal types of uniform ultrafilters on the first uncountable cardinal, and support graduate...
The National Science Foundation Division of Mathematical Sciences awarded a $195,001 Project Grant to the University of Notre Dame under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The three-year award will support research into model-theoretic tree properties and their applications in algebra and combinatorics. Specifically, the Principal Investigator will continue developing the theory of model-theoretic tree properties and pursue applications of these...
This Project Grant award for $100,000.00 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049). The funding supports research into inner models, combinatorics, and determinacy related to the Large Cardinal Axioms (LCAs) in set theory. The primary objectives are to advance the state of knowledge regarding canonical models for LCAs and their relationship with other foundational frameworks in set theory. This includes exploring...
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 Project Grant award from the National Science Foundation's (CFDA 47.049 - Mathematical and Physical Sciences) program provides $180,000 in funding to Rutgers, The State University to focus on two central combinatorial research topics. The first topic explores balancing problems for partially ordered sets, which are motivated by fundamental algorithmic questions. The second topic examines thresholds in discrete random systems, a central area of probabilistic combinatorics and statistical...