Objective Inverse problems research concentrates on the mathematical theory and practical interpretation of indirect measurements. Applications are found in virtually every research field involving scientific, medical, or industrial imaging and mathematical modelling. Familiar examples include X-ray Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Inverse problems methods make it possible to employ important advances in modern mathematics in a vast number of application areas. Also, applications inspire new questions that are both mathematically deep and have a close connection to other sciences. This has made inverse problems research one of the most important and topical fields of modern applied mathematics.The research team proposes to study fundamental mathematical questions in the theory of inverse problems. Particular emphasis will be placed on questions involving the interplay of mathematical analysis, partial differential equations, and Riemannian geometry. A major topic in the research programme is the famous inverse conductivity problem due to Calderón forming the basis of Electrical Impedance Tomography (EIT), an imaging modality proposed for early breast cancer detection and nondestructive testing of industrial parts. The geometric version of the Calderón problem is among the outstanding unsolved questions in the field. The research team will attack this and other aspects of the problem field, partly based on substantial recent progress due to the PI and collaborators. The team will also work on integral geometry questions arising in Travel Time Tomography in seismic imaging and in differential geometry, building on the solution of the tensor tomography conjecture in two dimensions obtained by the PI and collaborators in 2011. The research will focus on fundamental theoretical issues, but the motivation comes from practical applications and thus there is potential for breakthroughs that may lead to important advances in medical and seismic imaging. Fields of science medical and health sciencesclinical medicineoncologybreast cancernatural sciencesmathematicspure mathematicsgeometryengineering and technologymedical engineeringdiagnostic imagingmagnetic resonance imagingnatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicsapplied mathematicsmathematical model Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2012-StG_20111012 See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Coordinator JYVASKYLAN YLIOPISTO Address Seminaarinkatu 15 40100 Jyvaskyla Finland See on map Region Manner-Suomi Länsi-Suomi Keski-Suomi Activity type Higher or Secondary Education Establishments Administrative Contact Tero Kilpeläinen (Prof.) Principal investigator Mikko Salo (Mr.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all JYVASKYLAN YLIOPISTO Finland EU contribution € 1 041 240,00 Address Seminaarinkatu 15 40100 Jyvaskyla See on map Region Manner-Suomi Länsi-Suomi Keski-Suomi Activity type Higher or Secondary Education Establishments Administrative Contact Tero Kilpeläinen (Prof.) Principal investigator Mikko Salo (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Other funding No data
