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

University Of Connecticut, Storrs CT

Investigators

Abstract

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.html This 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.