Tu, March 18, 2025, 9:00-10:00 am PDT:
Manuel Cañizares (Johann Radon Institute for Computational and Applied Mathematics, Austria).
Title: Indentifying electric potentials via the local near-field scattering pattern at fixed energy.
Abstract: We study the inverse scattering problem with electric potentials. We prove that local measurements of electromagnetic waves at fixed energies can uniquely determine a rough compactly supported potential in dimension n ≥ 3.
By rough, we mean that the potential can be decomposed into a part that
lives in L^{n/2}, a part that is supported in a compact hypersurface, and a part
that corresponds to the sth derivative of an L^∞ function, with s < 1.
We will review how Harmonic Analysis plays into solving the forward problem, but we will center the talk in the solution of the inverse problem. Caro and Garcia proved in 2020 that measuring waves at a fixed energy on a sphere surrounding the potential would give its unique determination. To extend these results to smaller set of measurements, in this case to a small hypersurface in the vicinity of the potential, we prove a Runge approximation result via unique continuation and interior regularity arguments.
Also, solving of a Neumann problem for the Helmholtz equation is key in
the proof of this Runge approximation. We will show how domain perturbation
techniques allow us to find a solution to this boundary value problem.
Tu, April 1, 2025, 9:00-10:00 am PDT:
Amir Vig (University of Michigan, USA).
Title: TBA.
Abstract: TBA.
Tu, April 15, 2025, 9:00-10:00 am PDT:
Simon St-Amant (University of Cambridge, England).
Title: TBA.
Abstract: TBA.
Tu, April 29, 2025, 9:00-10:00 am PDT:
TBA.
Title: TBA.
Abstract: TBA.
Tu, May 13, 2025, 9:00-10:00 am PDT:
TBA.
Title: TBA.
Abstract: TBA.