Inverse problems constitute an interdisciplinary field of science concentrating on the mathematical theory and practical interpretation of indirect measurements. Their applications include medical imaging, atmospheric remote sensing, industrial process monitoring, and astronomical imaging. The common feature is extreme sensitivity to measurement noise. Computerized tomography, MRI, and exploration of the interior of earth by using earthquake data are typical inverse problems where mathematics has played an important role. By using the methods of inverse problems it is possible to bring modern mathematics to a vast number of applied fields. Genuine scientific innovations that are found in mathematical research, say in geometry, stochastics, or analysis, can be brought to real life applications through modelling. The solutions are often found by combining recent theoretical and computational advances. The study of inverse problems is one of the most active and fastest growing areas of modern applied mathematics, and the most interdisciplinary field of mathematics or even science in general.The exciting but high risk problems in the research plan of the PI include mathematics of invisibility cloaking, invisible patterns, practical algorithms for imaging, and random quantum systems. Progress in these problems could have a considerable impact in applications such as construction of metamaterials for invisible optic fibre cables, scopes for MRI devices, and early screening for breast cancer. The progress here necessitates international collaboration. This will be realized in upcoming programs on inverse problems. The PI is involved in organizing semester programs in inverse problems at MSRI in 2010, Isaac Newton Institute in 2011, and Mittag-Leffler -institute in 2012.