Free Boundary Methods in Inverse Scattering

Abstract

The speaker and his research group study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? If this happens, the obstacle would be invisible for this choice of incident wave. This phenomenon is closely related to inverse problems with a single measurement.

There are several results on corner scattering showing that obstacles with corners typically scatter every incident wave. It was recently observed that the theory of free boundary problems can be used to shed light on this issue. They use free boundary methods and quadrature domains to give examples of invisible penetrable obstacles. Moreover, under a nonvanishing condition for the incident wave, they show that there is a dichotomy for boundary points of any invisible obstacle: either the boundary is regular, or the complement of the obstacle has to be very thin near the point.

This talk is based on joint works with Pu-Zhao KOW (Jyväskylä), Simon LARSON (Chalmers), and Henrik SHAHGHOLIAN (KTH).

About the Speaker

Prof. Mikko SALO received his MS in Mathematics from the University of Oulu in 2001 and his PhD in Applied Mathematics from the University of Helsinki in 2004. He continued his research as a Postdoctoral Researcher at the University of Helsinki in 2005-2008 and as an Academy Research Fellow at the University of Helsinki and the University of Jyväskylä in 2008-2013. Since 2013, he has become a Professor in the Department of Mathematics at the University of Jyväskylä.

Prof. Salo’s work is in mathematical analysis, geometry and applications. His research group focuses on fundamental theoretical aspects of inverse problems such as the Calderón problem in electrical imaging and travel time tomography in seismic imaging. He is the Managing Editor of Inverse Problems and Imaging and the Editor of Mathematica Scandinavica and Annales Fennici Mathematici.

Prof. Salo is the recipient of the 2012 MediaV Young Researcher Award at the International Conference on Inverse Problems, the 2013 Calderón Prize of the Inverse Problems International Association and the 2014 Väisälä Prize of the Finnish Academy of Science and Letters. In 2019, he was elected a Member of the Finnish Academy of Science and Letters.

For Attendees' Attention

This talk will be held online via Zoom. To attend, please join the Zoom meeting at https://hkust.zoom.us/j/96287303973 (Meeting ID: 962 8730 3973 / Passcode: iasip2022).

About the Program

For more information, please refer to the program website at https://iasprogram.hkust.edu.hk/inverseproblems/.