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

会议：分形和网络分析及其应用，在 Luminy 举行

• 批准号: 2334026
• 负责人: Alexander Teplyaev
• 金额: $ 5万
• 依托单位: University of Connecticut
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2334026&HistoricalAwards=false
• 关键词: Conference; Analysis; fractals; networks; applications

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.

该奖项为总部位于美国的研究人员参加国际会议“分形和网络分析以及应用程序”（2024年3月18日至22日）在法国卢米尼市的国际国际de RencontresMathématiques中资助。会议的目的是汇集一个既定的和早期研究人员的潜水者群体，讨论分形和网络的分析的最新进展和应用。会议的主要主题包括纯粹和应用数学，科学和工程学的违规行为；网络分析；以及涉及分形和形状不规则的应用。明确的紧急情况将以针对工程和科学应用的理论和数值方法提出。预期的影响包括在国际联合研究项目，学术访问，资金应用程序以及涉及应用和纯数学专家的研讨会活动中增加活动。通过参与初学者研究人员在纯数学和应用数学中的分形模型中的新研究问题，从而产生了其他影响，从而导致了在理论和应用研究机构中的学生交流和国际船舶等后续活动。这项活动是专门针对该主题的一系列计划会议中的第一次，将培养一个充满活力的国际研究界，清楚地关注分形模型在应用数学，工程和科学中的使用。在科学和工业应用中使用分形模型是研究的有望领域，具有近期的近代知识卓越潜力。尽管可以使用理论知识的考虑体系，但是将这些知识转移到应用学科中仍然不发达。为了实现这种转移，需要两种主要的活动。首先是针对观察到的现象的新理论模型的设计，对于传统（平滑）模型无法应用或无法描述相关特征。其次是开发用于收集这些应用理论模型的工具。在许多情况下，分形模型既无法使用数值方法，也不可用于构造原型。取而代之的是，必须依靠可捕捉的，非骨折的近似值来捕获真正分形模型的基本特征，这些特征是由理论近似结果（例如，光谱收敛，图形或度量图的近似值）和合适的数值方法（新的特定领域分解和网状分解和网格，预先调节技术，坚固和快速convering Schems）的束缚。这次会议的目的是建立纯粹和应用研究社区之间的关系，以提高优先提到的知识转移。