M. V. Klibanov (University of North Carolina at Charlotte, USA) will present his report in the room 4-46 at 3.30 p. m.
M. V. Klibanov, Professor
Department of Mathematics and Statistics
University of North Carolina at Charlotte, USA
Title: 3-d phaseless inverse scattering and other coefficient inverse problems
We consider inverse scattering problems in the frequency domain in the case when only the modulus of the scattering complex valued wavefield is measured. The unknown is either the coefficient in the generalized Helmholtz equation or the potential in the Schrodinger equation. Until 2014 no results were available for these problems. Uniqueness theorems will be presented (obtained in 2014). In addition, first rigorous reconstruction procedures (jointly with V.G. Romanov) will be presented. Numerical testing of those reconstruction procedures will be discussed.
Results related to the Schrodinger equation completely solve a well known long standing problem posed by French mathematicians K. Shadan and P. Sabatier in 1977.
The second part of the talk will be dedicated to globally convergent numerical methods for coefficient inverse scattering problems. Results for experimental data will be presented. Surprisingly, there is a close linkage between these methods and the phaseless inverse scattering problems.
Finally, if time will allow, then it will be shown how to become profitable on trading stock options if solving an ill-posed problem for the Black-Scholes equation. Results for real market data for 368 stock options will be presented.