On the (Fractional) Calderón Problem

The classical Calderón problem is a prototypical elliptic inverse problem. One seeks to recover in a non-invasive way an unknown conductivity of a conducting medium from voltage-to-current measurements at the surface of the medium. In this talk I survey the major (uniqueness) results and the associated techniques for this problem. These will then be contrasted with the results and techniques for the fractional Calderón problem, a non-local analogue of the classical Calderón problem. Here surprising new effects arise due to nonlocality. Results of surprising strength are available and close connections to control theory and unique continuation emerge. The results on the fractional Calderón problem are joint work with Maria-Angeles Garcia-Ferrero, Tuhin Ghosh, Mikko Salo and Gunther Uhlmann. Contact Jianfeng Lu for zoom link: jianfeng@math.duke.edu.