PIMS - UCalgary Geometric Analysis Seminar Series: Ali Feizmohammadi

Abstract: We introduce a method of solving inverse boundary value problems for wave equations on Lorentzian manifolds, and show that zeroth order coefficients can be recovered under certain curvature bounds. The set of Lorentzian metrics satisfying the curvature bounds has a non-empty interior in the sense of smooth, compactly supported perturbations of the metric, whereas all previous results on this problem impose conditions on the metric that force it to be real analytic with respect to a suitably defined time variable. The analogous problem on Riemannian manifolds is called the Calder ́on problem, and in this case the known results require the metric to be independent of one of the variables. Our approach is based on a new unique continuation result in the exterior of the double null cone emanating from a point. The approach shares features with the classical Boundary Control method, and can be viewed as a generalization of this method to cases where no real analyticity is assumed. The talk is based on joint work with Spyros Alexakis and Lauri Oksanen.

Speaker Biography: I received my Ph.D in June 2018 under the supervision of Prof. Spyros Alexakis and Prof. Adrian Nachman. From 2018 to 2021 I was a Research Associate at University College London working with Prof. Lauri Oksanen. Since 2021, I am a Simons postdoctoral fellow at the Fields institute for research in mathematical sciences. My research interests lie in partial differential equations and geometric analysis, especially the rapidly expanding field of inverse problems. I have also worked on finite element methods associated to data assimilation and control problems subject to wave equations.