Postdoc: 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)

Description:

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.

Activities:

* 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:

2017

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]

2018

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.

2019

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]