Project Grant 2247424
- This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program provides $325,855 to the University of Houston from June 2022 through May 2025. The funding supports research and training opportunities for graduate students in the theory of operator algebras generated by unitary group representations and their connections to discrete group structure. Specifically, the principal investigator will investigate new operator algebraic rigidity phenomena for...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $303,150 to Vanderbilt University's Sponsored Programs Administration Division to conduct research on groups acting on hyperbolic spaces and operator algebras. The key objectives include studying the rigidity properties of acylindrically hyperbolic groups, analyzing groups acting on hyperbolic simplicial complexes, and continuing work on automorphisms of von...
- This $249,410 National Science Foundation project grant supports research at Texas A&M University exploring the relationship between hyperbolic geometry and quantum invariants. Specifically, the grantee will study the asymptotics of quantum invariants and their connection to the hyperbolic volume of 3-dimensional manifolds and mapping tori of self-homeomorphisms of surfaces. The grantee will pursue three related research themes: developing an explicit formula for adjoint twisted Reidemeister...
- This National Science Foundation (NSF) Project Grant award, funded under the Mathematical and Physical Sciences grant program (CFDA 47.049), supports a collaborative research project exploring the connections between algebra and dynamics through the study of mathematical structures known as operator algebras. The $130,611 project, which runs from September 1, 2025 to August 31, 2028, aims to advance fundamental knowledge in pure mathematics by investigating how symmetry and complexity interact...
- This $256,573 National Science Foundation Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) will support research exploring algebraic aspects of chaotic dynamical systems with hyperbolic behavior at Texas A&M University from July 2022 through June 2025. Specifically, the award will fund investigations into the connections between hyperbolic dynamical systems and group theory, automata theory, and other branches of algebra. The research aims to clarify whether...
- The National Science Foundation awarded a $368,340 Project Grant to Texas A&M University under the Mathematical and Physical Sciences program (CFDA 47.049) for work on "Quantitative Operator K-Theory and Applications." The Principal Investigator and students will develop quantitative operator K-theory to investigate problems at the intersection of noncommutative geometry, classical geometry, topology, and mathematical physics. They will focus on applying quantitative operator...
- This Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences supports research on the theory of dynamical systems and conformal dynamical systems. The award, totaling $262,205 over 3 years starting on August 1, 2024, will fund work to address longstanding conjectures and open new research directions in this field. The project will leverage tools from complex analysis, hyperbolic geometry, and arithmetic geometry to study moduli spaces of one-dimensional...
- This Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research related to chromatic homotopy theory, algebraic K-theory, and L-functions. The $182,359 award to Trustees of Indiana University, doing business as Indiana University, aims to further explore the connections between number theory and homotopy theory. The research will investigate generalizations of the Quillen-Lichtenbaum conjecture, the multiplicative...
- 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 $297,450 National Science Foundation project grant supports research into hyperbolic dynamical systems with singularities and coexistence of hyperbolic and non-hyperbolic behavior at the University of Houston from August 1, 2022 to July 31, 2025. The project aims to develop a better understanding of systems displaying hyperbolic behavior in the presence of singularities or coexisting hyperbolic and non-hyperbolic dynamics. Specific activities include studying the properties of such...
C*-ALGEBRAS ASSOCIATED TO MINIMAL AND HYPERBOLIC DYNAMICAL SYSTEMS -MATHEMATICIANS USE INVARIANTS TO STUDY AND CLASSIFY HIGHLY ABSTRACT OBJECTS. THE KEY PROPERTIES OF A USEFUL INVARIANT ARE THAT IT IS COMPUTABLE AND THAT IT DISTINGUISHES MANY DIFFERENT OBJECTS. FOR DYNAMICAL SYSTEMS, AN IMPORTANT CLASS OF MATHEMATICAL OBJECTS, THE CONSTRUCTION OF INVARIANTS IS VERY DIFFICULT. THIS PROJECT STUDIES INVARIANTS OF DYNAMICAL SYSTEMS USING ABSTRACT OPERATOR ALGEBRAS (IN PARTICULAR C*-ALGEBRAS). THE SPECIFIC INVARIANT IS THE K-THEORY OF THE RELEVANT OPERATOR ALGEBRA, WHICH IN TURN IS AN INVARIANT OF THE RELEVANT DYNAMICAL SYSTEM. THE PROJECT WILL INVOLVE SIGNIFICANT CONTRIBUTIONS FROM EARLY-CAREER RESEARCHERS, GRADUATE STUDENTS, AND UNDERGRADUATE STUDENTS, WHO WILL BENEFIT FROM TRAINING THROUGH RESEARCH INVOLVEMENT. THE PRINCIPAL INVESTIGATOR WILL STUDY THE RANGE OF THE ELLIOTT INVARIANT, WHICH CONSISTS OF K-THEORY AND TRACIAL INFORMATION, FOR C*-ALGEBRAS CONSTRUCTED FROM MINIMAL AND HYPERBOLIC DYNAMICAL SYSTEMS. THIS RESEARCH REPRESENTS A CONTINUATION OF THE INVESTIGATOR?S PREVIOUS WORK. HOWEVER, IN ADDITION TO THE STUDY OF K-THEORY AS AN ABSTRACT GRADED GROUP, THE INVESTIGATOR WILL ALSO STUDY THE ORDER STRUCTURE ON K-THEORY AND THE TRACES OF THE RELEVANT C*-ALGEBRAS. FURTHERMORE, THIS RESEARCH GOES BEYOND THE STUDY OF UNIFORMLY HYPERBOLIC DYNAMICAL SYSTEMS (E.G., SMALE SPACES) TO STUDY GENERAL EXPANSIVE SYSTEMS. SPECIFIC PROJECTS INCLUDE THE STUDY OF MINIMAL HOMEOMORPHISMS ON ODD DIMENSIONAL SPHERES, THE ORDER STRUCTURE ON K-THEORY FOR MINIMAL CROSSED PRODUCTS, THE FINER STRUCTURE OF SMALE SPACE C*-ALGEBRAS, AND THE HK-CONJECTURE FOR C*-ALGEBRAS ASSOCIATED TO DYNAMICAL SYSTEMS. THIS AWARD REFLECTS NSF'S STATUTORY MISSION AND HAS BEEN DEEMED WORTHY OF SUPPORT THROUGH EVALUATION USING THE FOUNDATION'S INTELLECTUAL MERIT AND BROADER IMPACTS REVIEW CRITERIA.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $108.6k | 8/14/25 | ||
| Not listed | $213.8k | 7/17/23 |