Objective
This proposal is concerned with the mathematical theory of inverse problems. This is a vibrant research field at the intersection of pure and applied mathematics, drawing techniques from PDE, geometry, and harmonic analysis as well as generating new research questions inspired by applications. Prominent questions include the Calderón problem related to electrical imaging, the Gel'fand problem related to seismic imaging, and geometric inverse problems such as inversion of the geodesic X-ray transform.
Recently, exciting new connections between these different topics have begun to emerge in the work of the PI and others, such as
- the explicit appearance of the geodesic X-ray transform in the Calderón problem
- an unexpected connection between the Calderón and Gel’fand problems involving control theory
- pseudo-linearization as a potential unifying principle for reducing nonlinear problems to linear ones
- the introduction of microlocal normal forms in inverse problems for PDE
These examples strongly suggest that there is a larger picture behind various different inverse problems, which remains to be fully revealed.
This project will explore the possibility of a unified theory for several inverse boundary problems. Particular objectives include:
1. The use of normal forms and pseudo-linearization as a unified point of view, including reductions to questions in integral geometry and control theory
2. The solution of integral geometry problems, including the analysis of convex foliations, invertibility of ray transforms, and a systematic Carleman estimate approach to uniqueness results
3. A theory of inverse problems for nonlocal models based on control theory arguments
Such a unified theory could have remarkable consequences even in other fields of mathematics, including controllability methods in transport theory, a solution of the boundary rigidity problem in geometry, or a general pseudo-linearization approach for solving nonlinear operator equations.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
ERC-COG - Consolidator Grant
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2017-COG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
40100 Jyvaskyla
Finland
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.