ERC Consolidator grant project IPFLOW

Principal Investigator : Colin Guillarmou

Benjamin Kuster (2018-2020)

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 in the theme of the ERC project IPFLOW:


* 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]
* 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]
* C. Guillarmou, M. Mazzucchelli, L. Tzou, Boundary and lens rigidity for non-convex manifolds.
Amer. Journ. Math., to appear. [arXiv:1711.10059]


* S. Dyatlov, C. Guillarmou, Dynamical zeta functions for Axiom A flows
Bull. AMS, 55 (2018), 337--342 . [arXiv: 1801.00348]
C. Guillarmou, J. Hilgert, T. Weich, High frequency limits for invariant Ruelle densities
Preprint. [arXiv:1803.06717].
C. Guillarmou, M. Salo, L. Tzou, The linearized Caleron problem on complex manifolds
Acta Math. Sinica, special volume for 65th birthday of Carlos Kenig, to appear. [arXiv:1805.00752]
C. Guillarmou, T. Lefeuvre, The marked length spectrum of Anosov manifolds
Preprint submitted. [arXiv:1806.04218]
* N.V. Dang, C. Guillarmou, G. Riviere, S. Shen, Fried conjecture in small dimensions
Preprint submitted. [arXiv:1807.01189]