The workshop will focus on the recent advances in geometric inverse problems. This includes linear problems of integral geometry type like the geodesic ray transform on functions, tensor fields, classical and generalized Radon transforms and the light ray transform in Lorentzian geometry. Those transforms are of independent interest but also appear often in non-linear inverse problems which are one of the topics of the workshop. Such problems are boundary rigidity, lens rigidity and scattering rigidity, where one wants to recover a Riemannian metric, a matrix field or a connection in a compact or a singular manifold from the boundary distance function, the lens relation or the scattering data (non-abelian X-ray). Related problems include recovery of the geometry from boundary or scattering observations of solutions of hyperbolic or elliptic linear or non-linear PDEs, for example the Einstein, or the Yang-Mills-Higgs equations. Recent advances in inverse spectral problems will be presented as well.

The interest of those problems is motivated also by applications in medical imaging, seismology and cosmology.