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
* September 6-10, 2021: Hyperbolic dynamical systems and resonances

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, 69 (2019), no. 7, 2857-2919. Past, Present and Future an homage to Marcel Berger. [arXiv:1709.05053]
3) C. Guillarmou, A. Hassell, K. Krupchyk, Eigenvalue bounds for non-self-adjoint Schr´┐Żdinger operators with non-trapping metrics,
Analysis and PDE 13 (2020), no 6, 1633-1670. . [arXiv:1709.09759]
4) C. Guillarmou, M. Mazzucchelli, L. Tzou, Boundary and lens rigidity for non-convex manifolds.
Amer. Journ. Math. 143 (2021), no 2, 533-575 [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
Annales Henri Lebesgue, Volume 4 (2021) , pp. 81-119. [arXiv:1803.06717].
7) T. Lefeuvre, Local marked boundary rigidity under hyperbolic trapping assumptions,
J Geom Anal 30 (2019), 448-465. [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 95 (2020) no 1, 129-166. [arXiv: 1805.05155]
10) C. Guillarmou, T. Lefeuvre, The marked length spectrum of Anosov manifolds
Annals of Math 190 (2019), no 1, 321-344. [arXiv:1806.04218]
11) N.V. Dang, C. Guillarmou, G. Riviere, S. Shen, Fried conjecture in small dimensions
Inventiones Math. 220 (2020), 525-579. [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
Communications in Mathematical Physics 378 (2), 917-941. [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,
Ergodic Theory and Dynamical Systems. Special volume in memory of Anatole Katok. DOI: 10.1017/etds.2021.75 [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,
International Mathematics Research Notices, (2020), rnaa286. [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,
Pure and Applied Analysis 2 (2020) no 4, 795-840. [arXiv:1911.03881]
21) B. Kuster, P. Ramacher, Asymptotic expansion of generalized Witten integrals for circle actions on symplectic manifolds,
Preprint submitted. [arXiv:1910.04752]


22) C. Guillarmou, B. Kuster, Spectral theory of the frame flow on hyperbolic 3-manifolds (with an appendix by Charles Hadfield),
Annales Henri Poincare 2021, DOI: 10.1007/s00023-021-01068-7. [arXiv:2005.08387]
23) C. Guillarmou, A. Kupiainen, R. Rhodes, V. Vargas, Conformal bootstrap in Liouville Theory ,
Preprint. [arXiv:2005.11530]
24) Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, T. Weich, Ruelle-Taylor resonances of Anosov actions ,
Preprint. [arXiv:2007.14275]
25) M. Cekic, C. Guillarmou, First band of Ruelle resonances for contact Anosov flows in dimension 3,
Commun. in Math Phys. 386 (2021) no. 2, 1289-1318. [arXiv:2011.05959]
26) M. Cekic, T. Lefeuvre, Generic dynamical properties of connections on vector bundles
IMRN rnab069 (2021). [arXiv:2008.09191]
27) M. Cekic, S. Dyatlov, B. Kuster, G. Paternain, The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
Preprint. [arXiv:2009.08558]
28) V. Arnaiz, F. Macia, Localization and delocalization of eigenmodes of Harmonic Oscillators
Preprint. [arXiv:2010.13436]
29) V. Arnaiz, Construction of quasimodes for non-selfadjoint operators via propagation of Hagedorn wave-packets
Preprint. [arXiv:2010.14967]
30) Y. Guedes Bonthonneau, T. Lefeuvre, Radial source estimates in Holder-Zygmund spaces for hyperbolic dynamics
Preprint. [arXiv:2011.06403]


31 Y. Chaubet, Closed geodesics with prescribed intersection numbers,
Preprint [arXiv:2103.16301]
32) Y. Guedes Bonthonneau, C. Guillarmou, T. Weich, SRB measures for Anosov actions,
Preprint [arXiv:2103.12127]
33) C. Guillarmou, T. de Poyferre (with an Appendix by Y. Guedes Bonthonneau), A paradifferential approach for hyperbolic dynamical systems and applications,
Preprint [arXiv:2103.15397]
34) M. Cekic, T. Lefeuvre, The Holonomy Inverse Problem
Preprint [arXiv:2105.06376]
35) Y. Chaubet, Poincare series for surfaces with boundary
Preprint [arXiv:2106.07604]
36) V. Arnaiz, C. Guillarmou, Stability estimates in inverse problems for the Schrodinger and wave equations with trapping
Preprint [arXiv:2106.11167]
37) M. Cekic, T. Lefeuvre, Generic injectivity of the X-ray transform
Preprint [arXiv:2107.05119]
38) Y. Chaubet, Closed billiard trajectories with prescribed bounces
Preprint [arXiv:2108.11340]