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Inverse Problems in Partial Differential Equations and Geometry

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.

Field of science

  • /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations/partial differential equations
  • /engineering and technology/medical engineering/diagnostic imaging/magnetic resonance imaging
  • /medical and health sciences/clinical medicine/cancer/breast cancer
  • /natural sciences/mathematics/pure mathematics/geometry

Call for proposal

ERC-2012-StG_20111012
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

JYVASKYLAN YLIOPISTO
Address
Seminaarinkatu 15
40100 Jyvaskyla
Finland
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 041 240
Principal investigator
Mikko Salo (Mr.)
Administrative Contact
Tero Kilpeläinen (Prof.)

Beneficiaries (1)

JYVASKYLAN YLIOPISTO
Finland
EU contribution
€ 1 041 240
Address
Seminaarinkatu 15
40100 Jyvaskyla
Activity type
Higher or Secondary Education Establishments
Principal investigator
Mikko Salo (Mr.)
Administrative Contact
Tero Kilpeläinen (Prof.)