ERC Consolidator grant project IPFLOW no 725967

Principal Investigator : Colin Guillarmou

Benjamin Kuster (2018-2020), Mihajlo Cekic (2019-2021), Victor Arnaiz (2019-2021),

Other members of the group:  Thibault Lefeuvre (PhD 2017-2020), Yann Chaubet (PhD 2018-2020)


The subject of the ERC project is Inverse Problems and the analytic study of flows (Anosov flows, Axiom A flows, geodesic flows etc).
We aim to study :
* X-ray transform and boundary rigidity problems: can we recover a function/tensor from its integrals along geodesics ? Can  we recover a metric from the length of its geodesics ?
* Ruelle resonance spectrum for hyperbolic flows and long time dynamics.
* Microlocal methods for problems on flows, like rigidity questions.


* June 26-30, 2017: Summer school: Microlocal Analysis and Applications in Cardiff
* July 3-7, 2017: Summer school: Analytical aspects of hyperbolic flows
* February 7-8-9, 2018: mini workshop/working group seminars in Orsay
* June 4-8, 2018: workshop Analytic Study of Flows, Peyresq
* December 10-12, 2018:
mini workshop/working group seminars in Orsay

Papers/publications of the group during the ERC project IPFLOW:


1) F. Faure, C. Guillarmou, Horocyclic invariance of Ruelle resonant states for contact Anosov flows in dimension 3.
Math Research Letters, 25 (2018), no 5, 1405--1427. [arXiv:1705.07965]
2) R. Graham, C. Guillarmou, P. Stefanov, G. Uhlmann, X-ray transform and boundary rigidity for asymptotically hyperbolic manifolds.
Ann. Inst. Fourier, special volume in memory of Marcel Berger, to appear. [arXiv:1709.05053]
3) C. Guillarmou, A. Hassell, K. Krupchyk, Eigenvalue bounds for non-self-adjoint Schrödinger operators with non-trapping metrics,
Analysis and PDE, to appear. [arXiv:1709.09759]
4) C. Guillarmou, M. Mazzucchelli, L. Tzou, Boundary and lens rigidity for non-convex manifolds.
Amer. Journ. Math., to appear. [arXiv:1711.10059]


5) S. Dyatlov, C. Guillarmou, Dynamical zeta functions for Axiom A flows
Bull. AMS, 55 (2018), 337--342 . [arXiv: 1801.00348]
6) C. Guillarmou, J. Hilgert, T. Weich, High frequency limits for invariant Ruelle densities
Preprint submitted. [arXiv:1803.06717].
7) T. Lefeuvre, Local marked boundary rigidity under hyperbolic trapping assumptions,
J Geom Anal (2019) doi:10.1007/s12220-019-00149-8. [arXiv:1804.02143]
8) C. Guillarmou, M. Salo, L. Tzou, The linearized Caleron problem on complex manifolds
Acta Mathematica Sinica, English Series, 35(6), 1043-1056 (special volume for 65th birthday of Carlos Kenig). [arXiv:1805.00752]
9) T. Lefeuvre, Boundary rigidity of negatively-curved asymptotically hyperbolic surfaces,
Commentarii Math Helvetici, to appear. [arXiv: 1805.05155]
10) C. Guillarmou, T. Lefeuvre, The marked length spectrum of Anosov manifolds
Annals of Math 190 (2019), no 1. [arXiv:1806.04218]
11) N.V. Dang, C. Guillarmou, G. Riviere, S. Shen, Fried conjecture in small dimensions
Invent. math. (2019) doi:10.1007/s00222-019-00935-9. [arXiv:1807.01189]
12) T. Lefeuvre, On the s-injectivity of the X-ray transform for manifolds with hyperbolic trapped set,
Nonlinearity, 32 (2019) no4, 1275--1295.


13) B. Kuster, T. Weich, Pollicott-Ruelle resonant states and Betti numbers
Preprint submitted. [arXiv:1903.01010]
14) Y. Guedes Bonthonneau, T. Lefeuvre, Local rigidity of manifolds with hyperbolic cusps I. Linear theory and microlocal tools
Preprint submitted. [arXiv:1907.01809]
15) C. Guillarmou, M. Mazzucchelli, L. Tzou, Asymptotically Euclidean metrics without conjugate points are flat,
Preprint. [arXiv:1909.01488]
16) C. Guillarmou, G. Knieper, T. Lefeuvre, Geodesic stretch, pressure metric and marked length spectrum rigidity,
Preprint submitted. [arXiv:1909.08666]
17) Y. Guedes Bonthonneau, T. Lefeuvre, Local rigidity of manifolds with hyperbolic cusps II. Nonlinear theory,
Preprint submitted. [arXiv:1910.02154]
18) C. Guillarmou, M. Lassas, L. Tzou, X-Ray Transform in Asymptotically Conic Spaces,
Preprint submitted. [arXiv:1910.09631]
19) Y. Chaubet, N.V. Dang, Dynamical torsion for contact Anosov flows,
Preprint [arXiv:1911.09931]
20) M. Cekic, G. Paternain, Resonant spaces for volume preserving Anosov flows,
Preprint submitted [arXiv:1911.03881]