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(CBMS)会议的会议委员会，该会议将于2024年6月3-7日在南卡罗来纳州克莱姆森大学举行。会议将由首席讲师甘瑟·乌尔曼教授主讲十个小时，他是偏微分方程逆问题领域的领先专家。除了主讲外，还将有两场补充讲座由赖如玉博士和王亦然博士主讲，他们都是在主讲所涵盖的学科领域工作的早期职业活跃研究人员。这些讲座和其他活动将给与会者提供大量的机会，特别是那些年轻的研究人员和来自代表不足的群体的学生，学习和讨论非线性偏微分方程组反问题的基本思想和最新发展。这次会议的地区性重点还将加强东南地区反问题和相关领域研究人员之间的研究合作，以及建立新的研究计划。逆问题本质上是跨学科的，它发生在真实世界应用的数学建模中，其中不可能直接观察某些性质。在过去的几十年里，关于反问题已经有了许多重要的工作，但大多数都集中在线性偏微分方程组或偏微分方程组上。与普遍认为非线性的存在是一种障碍相反，最近的一项重大突破表明，非线性实际上可以被用作解决逆问题的工具。这次会议的系列讲座将详细展示非线性如何帮助解决在非线性波传播中出现的各种反问题、Calderon反问题的非线性类比、非线性输运方程以及非线性偏微分方程组的反散射。特别强调了高阶线性化作为处理非线性的关键技术的作用。几个未解决的问题将由首席讲师制定，并由讲师和参与者积极讨论。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.