Inverse Problems and Nonlinearity Lecture Slides

Gunther Uhlmann, University of Washington, Lecturer

June 3 – 7, 2024 at Clemson University

Shitao Liu and Jeong-Rock Yoon organizers, liul@clemson.edu or jryoon@clemson.edu

website: https://sites.google.com/view/cbmsclemson2024

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 has been much important work on inverse problems over the last few decades, most of these efforts 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 at this conference will show in detail how nonlinearity can help in 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. The lectures along with other activities will afford opportunities for the conference participants, especially graduate students and young researchers, to discuss fundamental ideas and open problems. The regional emphasis of this conference also will strengthen the collaborations among researchers working in inverse problems
and related fields in the southeast, as well as establish new research programs.