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IPTheoryUnified SIGNED

Inverse boundary problems: toward a unified theory

Total Cost €

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EC-Contrib. €

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Partnership

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Project "IPTheoryUnified" data sheet

The following table provides information about the project.

Coordinator
JYVASKYLAN YLIOPISTO 

Organization address
address: SEMINAARINKATU 15
city: JYVASKYLA
postcode: 40100
website: http://www.jyu.fi

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Finland [FI]
 Project website https://www.jyu.fi/science/en/maths/research/inverse-problems
 Total cost 920˙880 €
 EC max contribution 920˙880 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2017-COG
 Funding Scheme ERC-COG
 Starting year 2018
 Duration (year-month-day) from 2018-05-01   to  2023-04-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    JYVASKYLAN YLIOPISTO FI (JYVASKYLA) coordinator 920˙880.00

Map

 Project 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.

 Deliverables

List of deliverables.
Data Management Plan Open Research Data Pilot 2019-02-26 15:18:47

Take a look to the deliverables list in detail:  detailed list of IPTheoryUnified deliverables.

 Publications

year authors and title journal last update
List of publications.
2019 Rakesh, Mikko Salo
Fixed angle inverse scattering for almost symmetric or controlled perturbations
published pages: , ISSN: , DOI:
2019-12-17
2019 Cristóbal J. Meroño, Leyter Potenciano-Machado, Mikko Salo
Resolvent estimates for the magnetic Schrödinger operator in dimensions $$ge 2$$≥2
published pages: , ISSN: 1139-1138, DOI: 10.1007/s13163-019-00316-z
Revista Matemática Complutense 2019-12-17
2019 Mikko Salo
Applications of microlocal analysis to inverse problems
published pages: , ISSN: , DOI:
2019-12-17
2019 R Rakesh, Mikko Salo
The fixed angle scattering problem and wave equation inverse problems with two measurements
published pages: , ISSN: 0266-5611, DOI: 10.1088/1361-6420/ab23a2
Inverse Problems 2019-12-17
2018 Pablo Angulo-Ardoy, Daniel Faraco, Luis Guijarro, Mikko Salo
Limiting Carleman weights and conformally transversally anisotropic manifolds
published pages: , ISSN: , DOI:
2019-12-17
2018 Matti Lassas, Tony Liimatainen, Mikko Salo
The Poisson embedding approach to the Calderón problem
published pages: , ISSN: , DOI:
2019-12-17
2019 Matti Lassas, Tony Liimatainen, Yi-Hsuan Lin, Mikko Salo
Inverse problems for elliptic equations with power type nonlinearities
published pages: , ISSN: , DOI:
2019-12-17
2018 Tuhin Ghosh, Angkana Rüland, Mikko Salo, Gunther Uhlmann
Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
published pages: , ISSN: , DOI:
2019-12-17
2018 Gabriel P. Paternain, Mikko Salo
Carleman estimates for geodesic X-ray transforms
published pages: , ISSN: , DOI:
2019-12-17
2019 Covi, Giovanni
\"An inverse problem for the fractional Schr\"\"odinger equation in a magnetic field\"\"\"
published pages: , ISSN: , DOI:
1 2019-12-17
2018 Covi, Giovanni
Inverse problems for a fractional conductivity equation
published pages: , ISSN: , DOI:
2 2019-12-17
2019 Colin Guillarmou, Mikko Salo, Leo Tzou
The Linearized Calderón Problem on Complex Manifolds
published pages: 1043-1056, ISSN: 1439-8516, DOI: 10.1007/s10114-019-8129-7
Acta Mathematica Sinica, English Series 35/6 2019-12-17
2019 Bastian Harrach, Valter Pohjola, Mikko Salo
Dimension Bounds in Monotonicity Methods for the Helmholtz Equation
published pages: 2995-3019, ISSN: 0036-1410, DOI: 10.1137/19m1240708
SIAM Journal on Mathematical Analysis 51/4 2019-12-17
2019 Matti Lassas, Tony Liimatainen, Yi-Hsuan Lin, Mikko Salo
Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations
published pages: , ISSN: , DOI:
2019-12-17
2019 Angkana Rüland, Mikko Salo
The fractional Calderón problem: low regularity and stability
published pages: , ISSN: , DOI:
2019-12-17

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