Conference: Renormalization and Visualization for packings, billiards and surfaces

该奖项为暑期班的美国学员提供部分支持，该暑期班将于2023年7月10日至14日在法国鲁米尼的国际伦孔特斯数学中心举行，主题为“包装、台球和表面的重整化和可视化”。这个暑期班的目标是培养多样化的一代研究人员，他们可以进一步推动这一成果的循环，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点上看到新的和有趣的影响。暑期班将围绕三门小课程展开，分别是几何、数论和动力学中的重整化。重整化涉及对动力学、几何或数论现象进行重新标度，以在多个尺度上观察行为，重整化思想导致了惊人的视觉和计算现象，并揭示了看似不同的数学领域之间的新联系。这一研究学派正在探索的思想圈包括由物理驱动的问题，例如，经典的牛顿二维和三维台球力学，以及圆填充的几何和数论。数学、计算和可视化之间的互动有望产生有趣的开源软件和醒目的视觉效果，可以在数学界共享，用于研究和教育目的。会议网站是https://conferences.cirm-math.fr/2794.htmlThis奖，反映了国家科学基金会的法定使命，并通过使用基金会的智力优势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 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.