Postdoc: Benjamin Kuster (2018-2020)

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 in the theme of the ERC project IPFLOW:

2017

* 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]

2018

* 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]