Objective
This proposal is concerned with the mathematical theory of inverse problems. This is a vibrant research field in mathematics, drawing techniques from partial differential equations (PDE), differential geometry, harmonic analysis, integral geometry and microlocal analysis, as well as generating new research questions inspired by applications.
A particular focus of this proposal is the Calderón problem together with its many variants. This foundational inverse problem for PDE serves as the mathematical model for electrical and optical imaging methods. Important current trends in research include an emphasis on geometric and Lorentzian cases, a shift of interest from linear to nonlinear and nonlocal PDE where nonlinearity or nonlocality is used as a beneficial tool for solving inverse problems, and the study of single measurement problems via scattering singularities. The PI has made fundamental contributions in each of these directions.
This project will address important current challenges, and particular objectives include:
1. Solution of the anisotropic Calderón problem in certain Lorentzian and Riemannian settings
2. Precise study of resolution in nonlinear inverse problems, also for algorithms based on neural networks
3. Inverse problems for nonlinear and nonlocal elliptic PDE, with novel approaches not based on linearization
4. Free boundary methods in inverse scattering and a detailed understanding of scattering singularities
Progress in any of these topics would be a significant development in the theory of inverse problems and would contribute to new connections between the inverse problems, nonlinear PDE and free boundary communities.
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
- natural sciences mathematics applied mathematics mathematical model
- natural sciences computer and information sciences artificial intelligence computational intelligence
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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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HORIZON.1.1 - 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.
HORIZON-ERC - HORIZON ERC Grants
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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-2025-ADG
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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.