Nonlocal School on Fractional Equations

该奖项支持参加2022年6月9日至11日在爱荷华州立大学校园举行的非本地分数方程学校（NSFE）。科学和工程中的分数（非局部）模型可以解释远距离相互作用，并且在适用于非光滑场景方面具有显著的灵活性。受这些事实和几个应用的启发，这个研究领域最近在理论和计算方面都吸引了大量的关注。例子包括成像、地球物理、等离子体、深度神经网络、最小表面和相变等领域的新型分数导数模型。这些新兴的应用产生了发展现代理论、新的数值方法和随后的非局部分数模型控制的需要。NSFE 2022会议旨在解决这些主题中的大多数。学校的主要目标是向学生和早期职业研究人员介绍非局部方程的当前趋势，以及提供一个充满活力的网络环境。将有2个（3小时）小型辅导式讲座和6个来自该领域主要研究人员的邀请演讲。本次会议将推进非局部建模、最优控制、数值分析、实现和软件开发方面的知识。这些主题涉及概率论、优化和变分分析、凸分析以及应用和计算数学的许多方面。该学院旨在刺激这些重要数学领域的新发展，以及它们在金融、物理、生物、数据科学和工程领域的应用。会议还旨在为研究生、博士后和其他早期职业科学家提供一个独特的机会，与分数非局部模型的主要研究人员进行互动。组织者正在做出特别努力，从STEM的少数群体和少数群体服务机构招募参与者。讲座视频和讲稿将上传到会议网站：https://pabloraulstinga.github.io/NSFE2022.htmlThis该奖项反映了美国国家科学基金会的法定使命，并通过基金会的智力价值和更广泛的影响审查标准进行评估，认为值得支持。

This award supports participation in the Nonlocal School on Fractional Equations (NSFE) 2022, held on campus of Iowa State University on June 9 – 11, 2022. Fractional (nonlocal) models in science and engineering can account for long range interactions and are notably flexible in being applicable to non-smooth scenarios. Motivated by these facts and several applications, this research area has attracted a significant amount of recent attention on both theoretical and computational fronts. Examples include novel fractional-derivative-based models in imaging, geophysics, plasmas, deep neural networks, minimal surfaces, and phase transitions. These emerging applications have created a need for development of a modern theory, new numerical methods, and subsequent control of the nonlocal fractional models. The NSFE 2022 meeting aims to address most of these topics. A primary goal of the school is to introduce students and early-career researchers to current trends in nonlocal equations, as well as to provide a vibrant networking environment. There will be two (three hour long) mini-tutorial style lectures and six invited talks from leading researchers in the field. This meeting will advance knowledge in nonlocal modeling, optimal control, numerical analysis, implementation, and software development. These topics involve numerous aspects of probability theory, optimization and variational analysis, convex analysis, and applied and computational mathematics. The school aims to stimulate new developments in these important areas of mathematics and their application to finance, physics, biology, data science, and engineering. The meeting also aims to provide a unique opportunity for graduate students, postdocs, and other early career scientists to interact with leading researchers in fractional nonlocal models. The organizers are making a special effort to recruit participants from minority groups in STEM and from minority serving institutions. Videos of the lectures as well as lecture notes will be uploaded on the conference website: https://pabloraulstinga.github.io/NSFE2022.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.