Less is More: Geometric Inverse Problems with Partial Data

Abstract

There is a geophysical question of determining the inner structure of the Earth from the measurements of travel times of seismic waves at the surface. The mathematical formulation of the question consists of recovering a function or more generally a Riemannian metric from the distance or lens data, which is known as the boundary or lens rigidity problem. The linearization of the problem is concerned with the inversion of the X-ray transform of scalar functions or tensor fields, and has important applications in medical imaging techniques. In this talk, the speaker will present recent progress on inverting X-ray transforms with a possible weight through a local-to-global approach initiated by Uhlmann and Vasy. He will also discuss their applications to the rigidity problems, as well as to other non-linear inverse problems. Part of the talk is based on joint work with Gabriel Paternain, Mikko Salo and Gunther Uhlmann.

About the speaker

Prof. Zhou Hanming received his PhD in Mathematics in 2015 from the University of Washington, under the supervision of Prof Gunther Uhlmann. He then became a Postdoctoral Research Associate at the University of Cambridge during 2015-2017. He joined the University of California, Santa Barbara in 2017 and is currently an Assistant Professor in the Department of Mathematics.

Prof. Zhou's research focuses on the mathematical analysis of inverse problems and their connections with concrete applications, often motivated by problems arising in medical imaging, geophysics, mathematical physics, etc. His work is at the interface of several disciplines including partial differential equations (PDEs), differential geometry, microlocal analysis and mathematical physics.

About the program

For more information, please refer to the program website at http://iasprogram.ust.hk/inverseproblems.