Conference: CBMS Conference: Inverse Problems and Nonlinearity

会议：CBMS 会议：反问题和非线性

• 批准号: 2329399
• 负责人: Shitao Liu
• 金额: $ 3.96万
• 依托单位: Clemson University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2329399&HistoricalAwards=false
• 关键词: Conference; CBMS; Inverse; Problems; Nonlinearity

This award supports the National Science Foundation (NSF) and the Conference Board of the Mathematical Sciences (CBMS) conference "Inverse Problems and Nonlinearity", which is to be held June 3--7, 2024 at Clemson University in Clemson, South Carolina. The conference will feature ten hour-long main lectures delivered by the Principal Lecturer Professor Gunther Uhlmann, who is a leading expert in the field of inverse problems for partial differential equations (PDEs). In addition to the main lectures, two supplementary lectures will be given by Dr. Ru-Yu Lai and Dr. Yiran Wang, who are both early career active researchers working in the subject areas covered in the main lectures. These lectures along with other activities will give plenty opportunities for the conference participants, especially those young researchers and students from underrepresented groups, to learn and discuss the fundamental ideas and the most recent development of inverse problems for nonlinear PDEs. The regional emphasis of this conference will also strengthen the research collaborations among researchers working in inverse problems and related fields in the southeast, as well as establish new research programs. Inverse problems, which are interdisciplinary in nature, occur in the mathematical modeling of real-world applications where direct observations of certain properties are not possible. While there have been many important work on inverse problems over the past few decades, most of them have focused on linear PDEs or PDE systems. Contrary to the common belief that the presence of nonlinearity is an obstacle, a recent major breakthrough has shown that nonlinearity can actually be used as a tool to solve inverse problems. The series of lectures given in this conference will show in detail how nonlinearity may help for a variety of inverse problems arising in nonlinear wave propagation, nonlinear analogs of Calderon's inverse problems, nonlinear transport equations, and inverse scattering for nonlinear PDEs. In particular, the role of higher order linearization as a key technique to deal with the nonlinearity, will be emphasized. Several open problems will be formulated by the principal Lecturer and actively discussed by the lecturers and participants.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.

该奖项支持国家科学基金会（NSF）和数学科学会议委员会（CBMS）会议“反问题和非线性”，该会议将于2024年6月3日至7日在南卡罗来纳州克莱姆森的克莱姆森大学举行。该会议将由首席讲师冈瑟·乌尔曼（Gunther Uhlmann）教授冈瑟（Gunther Uhlmann）教授进行十个小时的主要讲座，后者是偏微分方程（PDES）的反向问题领域的主要专家。除了主要讲座外，Ru-Yu Lai博士和Yiran Wang博士还将进行两次补充讲座，他们都是在主要讲座中涵盖的学科领域工作的早期职业活跃研究人员。这些讲座以及其他活动将为会议参与者，尤其是来自代表性不足的团体的年轻研究人员和学生提供足够的机会，以学习和讨论非线性PDE的基本思想以及最新的反向问题的发展。这次会议的区域强调还将加强从事反问题和东南相关领域的研究人员之间的研究合作，并建立新的研究计划。本质上是跨学科的反问题发生在现实世界应用的数学建模中，在这些应用程序无法直接观察某些属性。尽管在过去几十年中，尽管有许多关于反问题的重要工作，但其中大多数都集中在线性PDE或PDE系统上。与普遍认为，非线性的存在是一个障碍，最近的一个重大突破表明，非线性实际上可以用作解决反问题的工具。在本次会议中进行的一系列讲座将详细介绍非线性如何有助于在非线性波传播中产生的各种反问题，Calderon的反问题的非线性类似物，非线性传输方程以及非线性PDE的逆散射。特别是，将强调高阶线性化作为处理非线性的关键技术的作用。首席讲师将提出几个开放问题，并由讲师和参与者积极讨论。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，认为值得通过评估来获得支持。