Conference: Dynamical Systems and Fractal Geometry

University Of North Texas, Denton TX

Investigators

Abstract

This award provides support for participants to attend the conference “Dynamical Systems and Fractal Geometry” to be held at the University of North Texas from May 14-17, 2024. The primary goal of the conference is to foster interaction and collaboration between researchers in several fields of mathematics: fractal geometry, complex dynamics, thermodynamic formalism, random dynamical systems, and open dynamical systems. These fields are interrelated through both the methods used and in the fundamental questions of their study. The conference will bring together mathematicians from these fields ranging from senior experts to graduate students; experts will give standard 45–50-minute plenary lectures, and students will have the opportunity to give 5-10 minute “lightning talks”. The conference will also include a career panel. More information on the conference, including a list of speakers, can be found on the conference website: https://pcallaart3.wixsite.com/conference. The fields represented in this conference have broad motivations and applications in several classical areas of mathematics and physics beyond dynamical systems and geometry, including number theory, probability theory, and statistical mechanics. Thermodynamic formalism is a framework for unifying many aspects of these fields, and its investigation triggers research and collaboration on the problem of the existence and uniqueness of equilibrium states of the various systems studied in these fields. Limit sets of conformal dynamical systems, and in particular Julia sets arising in complex dynamics, are typically of a fractal nature and understanding their fine fractal properties such as Hausdorff, packing, Assouad and Fourier dimensions provides a true challenge for fractal geometers. The conference aims to advance research in these directions. 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.