Conference: New Frontiers in Parabolic Dynamics and Renormalization

University Of Maryland, College Park, College Park MD

Investigators

Abstract

This award will support U.S.-based mathematicians – with a priority on early-career researchers – to participate in the dynamical systems conference “New Frontiers in Parabolic Dynamics and Renormalization,” to be held at the University of Bologna, Italy, July 24-28, 2024. The mathematical field of dynamical systems concerns the evolution of systems over time, including real-world systems such as the weather, traffic patterns, and planetary systems. Some of the most important examples exhibit chaotic behavior. Parabolic dynamics encompasses one class of dynamical systems with chaotic behavior, and renormalization is a powerful tool for uncovering its properties. This conference seeks to bring leading international researchers together to discuss systems that extend beyond parabolic systems and understand techniques that would expand the scope of renormalization and discover new techniques for studying such systems. Examples of parabolic dynamical systems include horocycle flows on hyperbolic surfaces and, more generally, unipotent flows in homogeneous dynamics, smooth area-preserving flows on surfaces, and nilflows on nilmanifolds. If we allow for the presence of singularities, it also encompasses the study of interval exchange transformations (IETs) and translation flows. More recently, another example that has attracted a lot of attention is the horocycle flow in the moduli space of translation surfaces. Many important examples of parabolic flows also arise from models in mathematical physics, such as the Ehrenfest model of Lorentz gases, systems of Eaton lenses, and the Novikov model, leading to flows on Fermi energy level surfaces in solid-state physics. A key technique used to study parabolic systems is renormalization, an idea that originated from physics, entered dynamical systems decades ago, and has become an increasingly powerful tool for understanding the long-term behavior of many classes of parabolic dynamical systems. This conference seeks to bring together leading researchers from around the world to share their recent advances with the community, which would include US-based graduate students and postdocs. More information about the conference can be found at https://events.unibo.it/parabolicdynamics. 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.