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Inverse Problems and Flows

Total Cost €


EC-Contrib. €






Project "IPFLOW" data sheet

The following table provides information about the project.


Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794

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 France [FR]
 Total cost 1˙133˙236 €
 EC max contribution 1˙133˙236 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-COG
 Funding Scheme ERC-COG
 Starting year 2017
 Duration (year-month-day) from 2017-01-01   to  2021-12-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

In this project, we propose to study mixing and rigidity properties of a large class of flows in geometry and dynamical systems using novel microlocal and spectral methods. Such methods, recently developed for flows with hyperbolicity, are based on the construction of new functional spaces, adapted to the considered flow, on which the generating vector field is Fredholm with discrete spectrum, known as the resonance spectrum. We want to apply these tools to the following categories of long-standing problems:

1) Geometric inverse problems: boundary and lens rigidity problems, analysis of the X-ray transforms for geodesic flows and its applications to Calderon and Gelfand inverse problems. 2) Rigidity for Anosov flows: determination of the minimal regularity of the stable/unstable foliations providing rigidity, rigidity questions for regular conjugacies of flows. 3) Rate of mixing for flows of hyperbolic type: decay of correlations of Axiom A flows, Anosov flows, and their compact Lie groups extensions, frame flows of negatively curved manifolds. 4) Resonances for locally symmetric spaces: relation between resonances of the flow and the spectrum of Laplacians on bundles.

To address these problems, we will develop a thorough analysis for the regularity and the long time properties of solutions to transport equations. We are convinced that the proposed approach will provide solutions to these problems, which have been out of reach for a long time.


year authors and title journal last update
List of publications.
2019 Thibault Lefeuvre
Boundary rigidity of negatively-curved asymptotically hyperbolic surfaces
published pages: , ISSN: 0010-2571, DOI:
Commentarii Mathematici Helvetici 2019-08-30
2019 Colin Guillarmou, Rémi Rhodes, Vincent Vargas
Polyakov’s formulation of 2 d $2d$ bosonic string theory
published pages: , ISSN: 0073-8301, DOI: 10.1007/s10240-019-00109-6
Publications mathématiques de l\'IHÉS 2019-08-30
2018 N.V. Dang, C.Guillarmou, G. Rivière, S. Shen
Fried conjecture in small dimensions
published pages: , ISSN: , DOI:
2019 Thibault Lefeuvre
Local Marked Boundary Rigidity Under Hyperbolic Trapping Assumptions
published pages: , ISSN: 1050-6926, DOI: 10.1007/s12220-019-00149-8
The Journal of Geometric Analysis 2019-08-30
2018 C. Guillarmou, A. Hassell, K. Krupchyk
Eigenvalue bounds for non-self-adjoint Schrödinger operators with non-trapping metrics
published pages: , ISSN: , DOI:
2019 Thibault Lefeuvre
On the s-injectivity of the x-ray transform on manifolds with hyperbolic trapped set
published pages: 1275-1295, ISSN: 0951-7715, DOI: 10.1088/1361-6544/aaf81b
Nonlinearity 32/4 2019-08-30
2019 Guillarmou, Lefeuvre
The marked length spectrum of Anosov manifolds
published pages: 321, ISSN: 0003-486X, DOI: 10.4007/annals.2019.190.1.6
Annals of Mathematics 190/1 2019-08-05
2018 Colin Guillarmou, Frédéric Faure
Horocyclic invariance of Ruelle resonant states for contact Anosov flows in dimension $3$
published pages: 1405-1427, ISSN: 1073-2780, DOI: 10.4310/mrl.2018.v25.n5.a3
Mathematical Research Letters 25/5 2019-06-12
2018 Semyon Dyatlov, Colin Guillarmou
Afterword: Dynamical zeta functions for Axiom A flows
published pages: 337-342, ISSN: 0273-0979, DOI: 10.1090/bull/1628
Bulletin of the American Mathematical Society 55/3 2019-06-12
2019 Robin Graham, Colin Guillarmou, Plamen Stefanov, Gunther Uhlmann
X-ray transform and boundary rigidity for asymptotically hyperbolic manifolds
published pages: , ISSN: 0373-0956, DOI:
Annales de l\'Institut Fourier 2019-06-06
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 2019-06-06
2019 Colin Guillarmou, Marco Mazzucchelli, Leo Tzou
Boundary and lens rigidity for non-convex manifolds
published pages: , ISSN: 0002-9327, DOI:
American Journal of Mathematics 2019-06-06
2018 C. Guillarmou, J. Hilgert, T. Weich
High frequency limits for invariant Ruelle densities
published pages: , ISSN: , DOI:
2019 Küster, Benjamin; Weich, Tobias
Pollicott-Ruelle resonant states and Betti numbers
published pages: , ISSN: , DOI:
1 2019-08-30

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