Conference: Analysis on fractals and networks with applications, at Luminy

该奖项资助美国的研究人员参加在法国卢明国际数学<s:1> <s:1> <s:1>材料交换和材料交换中心举行的“分形和网络分析及其应用”国际会议（2024年3月18日至22日）。会议的目的是将不同群体的成熟和早期职业研究人员聚集在一起，讨论分形和网络分析的最新进展和应用。会议的主要主题包括纯数学和应用数学、科学和工程中的不规则性；网络分析；以及涉及到分形和不规则形状的应用。一个明确的重点将放在面向工程和科学应用的理论和数值方法。预期的影响包括增加国际联合研究项目的活动、学术访问、资助申请以及涉及应用数学和纯数学专家的研讨会活动。研究人员对纯数学和应用数学中分形模型的新研究问题的参与产生了额外的影响，导致后续活动，如学生交流和在理论和应用研究机构的实习。这次会议是计划中的一系列会议中的第一次，将促进一个充满活力的国际研究社区，明确关注分形模型在应用数学，工程和科学中的应用。分形模型在科学和工业应用中的应用是一个有前途的研究领域，具有显著的近期智力进步潜力。虽然有相当多的理论知识，但将这些知识转化为应用学科的工作仍然不发达。为了实现这种转移，需要进行两种主要的活动。首先是为观测到的现象设计新的理论模型，对于这些现象，传统的（平滑的）模型要么不能应用，要么不能描述相关特征。其次是开发工具来获取这些理论模型的应用。在许多情况下，分形模型既不能用于数值方法，也不能用于构造原型。相反，我们必须依靠可处理的、非分形的近似来捕捉真正分形模型的基本特征，并得到理论近似结果（例如，谱收敛、图或度量图近似）和合适的数值方法（新的特定域分解和网格、预处理技术、鲁棒和快速收敛方案）的支持。本次会议的目标是促进纯研究和应用研究社区之间的联系，以推进上述知识转移。https://conferences.cirm-math.fr/2950.htmlThis奖反映了美国国家科学基金会的法定使命，并通过使用基金会的智力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 funds the participation of U.S.-based researchers in the international conference "Analysis on fractals and networks, and applications" (18 – 22 March, 2024) at the Centre International de Rencontres Mathématiques in Luminy, France. The objective of the conference is to bring together a diverse group of established and early-career researchers to discuss recent advances in, and applications of, analysis on fractals and networks. Major themes of the conference include irregularity in pure and applied mathematics, science, and engineering; analysis of networks; and applications involving fractals and irregular shapes. A clear emphasis will be put on theoretical and numerical methods oriented towards applications in engineering and the sciences. Anticipated impacts include increased activity in joint international research projects, academic visits, funding applications, and workshop activities involving experts from applied and pure mathematics. Additional impact is generated through the involvement of beginning researchers in novel research questions on fractal models in pure and applied mathematics, leading to follow-up activities such as student exchanges and internships at theoretical and applied research institutions. This event, the first in a planned series of conferences dedicated to the topic, will foster a vibrant international research community with a clear focus on the use of fractal models in applied mathematics, engineering, and the sciences.The use of fractal models in scientific and industrial applications is a promising area of research, with significant near-term potential for intellectual advances. Although a considerable body of theoretical knowledge is available, the transfer of that knowledge into applied disciplines remains underdeveloped. Two major types of activities are needed in order to effect such a transfer. First is the design of new theoretical models for observed phenomena, for which traditional (smooth) models either cannot be applied or fail to describe relevant features. Second is the development of tools to harvest these theoretical models for applications. In many cases, the fractal model is neither accessible to numerical methods nor useful to construct prototypes. Instead, one must rely on tractable, non-fractal approximations that capture essential features of the truly fractal model, buttressed by theoretical approximation results (e.g., spectral convergence, approximations by graphs or metric graphs) and suitable numerical methods (new specific domain decompositions and meshes, preconditioning techniques, robust and fast-converging schemes). The goal of this conference is to foster ties between pure and applied research communities in order to advance the aforementioned knowledge transfer.https://conferences.cirm-math.fr/2950.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.