The inverse Calderón problem with Lipschitz conductivities

In this talk I will present a recent uniqueness result for an inverse boundary value problem consisting of recovering the conductivity of a medium from boundary measurements. This inverse problem was proposed by Calderón in 1980 and is the mathematical model for a medical imaging technique called Electrical Impedance Tomography which has promising applications in monitoring lung functions and as an alternative/complementary technique to mammography and Magnetic Resonance Imaging for breast cancer detection. Since in real applications, the medium to be imaged may present quite rough electrical properties, it seems of capital relevance to know what are the minimal regularity assumptions on the conductivity to ensure the unique determination of the conductivity from the boundary measurements. This question is challenging and has been brought to the attention of many analysts. The result I will present provides uniqueness for Lipschitz conductivities and was proved in collaboration with Keith Rogers.