The goal is to find coefficients of a differential equation or an obstacle in a reference domain from the data about its solution outside this domain. Both theoretical and numerical methods of a wide range of levels (from very elementary to most sophisticated) are used to study these problems and to design numerical algorithms for their solution.  Problems involving elliptic and parabolic equations are exponentially ill conditioned and only few parameters of an unknown object can be reliably recovered, while use of waves or higher wave numbers and hyperbolic equations can result in a very high resolution, like in the X-ray tomography. Applications include biomedicine, geophysics, financial markets, homeland security, and material science.


Alexander Bukhgeim - Integral geometry, Volterra integral equations,stability of difference schemes,tomography, Carleman estimates
Tom DeLillo - Numerical conformal mapping, fluid mechanics, computational methods for inverse problems
Ziqi Sun -  Anisotropic Calderon’s Problem, Quasilinear inverse boundary value problems