Federal Project Grant Award Summary

The University of Maryland, College Park received a $300,000 Project Grant from the National Science Foundation's Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), awarded June 15, 2026, with a completion date of May 31, 2029. The award supports fundamental research into the ergodic and statistical properties of smooth dynamical systems on manifolds, with emphasis on understanding how deterministic systems can exhibit random-like behavior comparable to sequences of independent coin tosses. The research addresses three primary directions: (1) chaotic properties of systems with non-zero Lyapunov exponents, (2) slow chaos and quantitative properties in entropy-zero systems including mixing rates and spectral characteristics, and (3) interactions between ergodic properties and geometric/number-theoretic phenomena.

The project delivers research outputs and workforce development through investigation of fundamental dynamical phenomena with potential applications across mathematics, physics, and economics. Deliverables include advances in understanding chaos and statistical behavior of smooth systems, with particular focus on cases where some (but not all) Lyapunov exponents are zero—areas significantly less understood than fully hyperbolic systems. The award incorporates research training opportunities for graduate and undergraduate students and postdoctoral researchers, contributing to the development of the nation's scientific workforce while advancing knowledge in ergodic theory and its interdisciplinary applications.