Conference: CBMS Conference: Inverse Problems and Nonlinearity

该奖项支持美国国家科学基金会（NSF）和数学科学会议委员会（CBMS）会议“逆问题和非线性”，这是将于2024年6月3日至7日在克莱姆森大学在南卡罗来纳州克莱姆森举行。会议将有10个小时的主要讲座，由首席讲师Gunther Uhlmann教授主讲，他是偏微分方程（PDE）反问题领域的领先专家。除了主要讲座外，两个补充讲座将由Ru-Yu Lai博士和Yiran Wang博士提供，他们都是在主要讲座所涵盖的主题领域工作的早期职业积极研究人员。这些讲座沿着其他活动将为与会者，特别是那些年轻的研究人员和学生代表性不足的群体，提供大量的机会，学习和讨论的基本思想和最新发展的非线性偏微分方程反问题。本次会议的区域重点还将加强东南部反问题及相关领域研究人员之间的研究合作，并建立新的研究项目。反问题，这是跨学科的性质，发生在现实世界的应用程序的数学建模，其中某些属性的直接观察是不可能的。虽然在过去的几十年里有许多重要的反问题的工作，他们中的大多数都集中在线性偏微分方程或偏微分方程系统。与普遍认为非线性的存在是一个障碍相反，最近的一项重大突破表明，非线性实际上可以用作解决逆问题的工具。在这次会议上给出的一系列讲座将详细展示如何非线性可能有助于各种反问题所产生的非线性波传播，卡尔德龙的反问题，非线性输运方程的非线性模拟，以及非线性偏微分方程的逆散射。特别是，高阶线性化的作用作为一个关键技术来处理非线性，将被强调。几个开放的问题将由首席讲师制定，并由讲师和参与者积极讨论。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.