28 June – María Ángeles García-Ferrero: On the Inverse Conductivity Problem
The classical Calderón problem is the inverse problem of determining the electrical conductivity of the interior of a medium from voltage and current measurements on its surface. With applications in medi-cal imaging and geophysics, its study has led many developments in the area of inverse problems since the eighties.
In this talk we will introduce some important questions about the Calderón problem and the main in-gredients to answer them (for three or higher dimensions). We will also consider the inverse problem of determining the potential in a Schrödinger equation from boundary measurements of solutions, which, under certain regularity conditions, is equivalent to the Calderón problem. Finally, we will see nonlocal versions of this inverse problem, which exhibit remarkable differences with respect to the local one.
María Ángeles García-Ferrero is a CSIC researcher at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid. Previously, she held positions at the University of Barcelona, the Basque Center for Applied Mathematics in Bilbao, the Heidelberg University and the Max-Planck Institute for Mathematics in the Sciences in Leipzig. Her research interests include partial differential equations, inverse problems and mathematical physics.