Conference: Renormalization and Visualization for packings, billiards and surfaces

该奖项为美国暑期学校“包装、台球和表面的规范化和可视化”的参与者提供了部分支持，该暑期学校将于2023年7月10日至14日在法国卢米尼的国际数学<s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1>)中心举行。这个暑期学校的目标是培养多样化的一代研究人员，他们可以将这一结果进一步推广，并将其扩展到新的领域。特别是，通过将多个领域的研究人员聚集在一起，组织者希望在数学、计算和可视化的交叉领域看到新的有趣的影响。暑期学校将以三个小课程为中心，分别以几何、数论和动力学的重整化为主题。重整化涉及对动态、几何或数论现象进行重新缩放，以观察多个尺度上的行为，重整化思想导致了引人注目的视觉和计算现象，并揭示了看似不同的数学领域之间的新联系。这个研究学院正在探索的思想圈子包括由物理学激发的问题，例如，二维和三维台球的经典牛顿力学，以及圆形包装的几何和数论。数学、计算和可视化之间的相互作用有望产生有趣的开源软件和引人注目的视觉效果，可以在数学界共享，用于研究和教育目的。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，认为值得支持。

This award provides partial support for U.S. based participants of the summer school "Renormalization and Visualization for packing, billiards and surfaces", to take place from 10 - 14 July 2023 at the Centre International de Rencontres Mathématiques, in Luminy, France. The goal of this summer school is to develop a diverse generation of researchers who can take this circle of results further, and to extend them to new domains. In particular, by bringing together researchers in multiple fields, the organizers expect to see new and interesting impacts at the intersection of mathematics, computation, and visualization. The summer school will be centered on three minicourses, on the theme of renormalization in geometry, number theory, and dynamics respectively. Renormalization involves rescaling dynamical, geometric, or number theoretic phenomenon to observe behaviors at multiple scales, and renormalization ideas have led to striking visual and computational phenomena and uncovered new connections between seemingly disparate areas of mathematics. The circle of ideas being explored in this research school includes problems motivated by physics, for example, the classical Newtonian mechanics of billiards in two and three dimensions, as well as the geometry and number theory of circle packings. The interactions between mathematics, computation, and visualization are expected to produce interesting pieces of open-source software and striking visuals which can be shared amongst the mathematics community for both research and educational purposes. The conference website is https://conferences.cirm-math.fr/2794.htmlThis 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.