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

该奖项资助美国研究人员参加2024年3月18-22日在法国鲁米尼国际数学中心举行的“关于分形学和网络及其应用的分析”国际会议。这次会议的目的是将一群不同的成熟的和职业生涯早期的研究人员聚集在一起，讨论最近在分形和网络分析方面的进展和应用。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；以及涉及分形学和不规则形状的应用。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上。预期的影响包括在联合国际研究项目、学术访问、资助申请以及有应用数学和纯数学专家参加的讲习班活动中的活动增加。通过让初级研究人员参与有关理论数学和应用数学中的分形模型的新的研究问题，产生更多的影响，从而产生后续活动，如在理论和应用研究机构进行学生交流和实习。这次活动是计划中的一系列专门讨论这一主题的会议的第一次，将培养一个充满活力的国际研究社区，明确关注应用数学、工程和科学中分形模型的使用。在科学和工业应用中使用分形模型是一个很有前途的研究领域，具有巨大的近期智力进步潜力。虽然有相当多的理论知识可用，但将这些知识转化为应用学科的工作仍然不发达。要实现这种转移，需要两种主要类型的活动。首先是为观察到的现象设计新的理论模型，对于这些现象，传统的(平滑)模型要么不能应用，要么无法描述相关特征。其次是工具的开发，以收获这些理论模型的应用。在许多情况下，分数维模型既不适用于数值方法，也不适用于构造原型。取而代之的是，人们必须依靠可处理的、非分形的近似来捕捉真正的分形模型的基本特征，并由理论近似结果(例如，谱收敛、图形或度量图形的近似)和适当的数值方法(新的特定区域分解和网格、预条件技术、健壮和快速收敛的方案)支撑。这次会议的目标是促进理论研究和应用研究社区之间的联系，以推进上述知识transfer.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 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.