The Euro Summer School NEW ANALYTIC AND GEOMETRIC METHODS IN INVERSE PROBLEMS belongs to the field of mathematics and applied mathematics. It was selected to have the status EMS Summer School by the European Mathematical Society (EMS). Inverse problems constitute a wide and dynamic field of research in mathematical sciences, physics and engineering. The application areas are ample, including medical imaging, non-destructive material testing and geophysical exploration. In typical inverse problems, the goal is to retrieve information from an inaccessible region by performing measurements outside the region. Mathematically, the problem is to estimate the distributed parameters of a differential or integral equation when a set of its solutions is known at the boundary of the region.
The requirements of the applications have led the mathematical research to consider new types of problems that cannot be solved by using the traditional inversion methods. Such problems arise e.g. from the modelling of human tissue in medical applications or composite materials in non-destructive evaluation. It has become evident that many of these new inverse problems are geometric in nature and require methods that do not belong to the traditional expertise of the researchers in this field. The Euro Summer School focuses to these new techniques. The lectures cover the mathematical background as well as demonstrate how these new methods and techniques can be applied to solve inverse problems of scientific and socio-economic significance. The Summer School is the first in the series of actions to consolidate the inverse problems research and training in the EU area.