Conference: CBMS Conference: Inverse Problems and Nonlinearity

Clemson University, Clemson SC

Investigators

Abstract

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.