Conference: Dynamical Systems and Fractal Geometry

该奖项为参加将于2024年5月14日至17日在北德克萨斯大学举行的“动力系统和分形几何”会议的参与者提供支持。会议的主要目标是促进多个数学领域研究人员之间的互动与合作：分形几何、复杂动力学、热力学形式主义、随机动力系统和开放动力系统。这些领域通过所使用的方法和研究的基本问题相互关联。会议将汇集来自这些领域的数学家，从资深专家到研究生;专家将进行标准的45-50分钟的全体演讲，学生将有机会进行5-10分钟的“闪电演讲”。会议还将包括一个职业小组。有关会议的更多信息，包括发言人名单，可在会议网站上找到：https://pcallaart3.wixsite.com/conference。本次会议所代表的领域在动力系统和几何学之外的数学和物理学的几个经典领域中具有广泛的动机和应用，包括数论，概率论和统计力学。热力学形式主义是统一这些领域的许多方面的框架，它的研究引发了对这些领域中研究的各种系统的平衡态的存在性和唯一性问题的研究和合作。共形动力系统的极限集，特别是复杂动力学中产生的Julia集，通常具有分形性质，并且理解它们的精细分形性质，如Hausdorff，packing，Assouad和Fourier维数，为分形几何学家提供了真正的挑战。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.