Resonances: Geometric Scattering and Dynamics
March 13 -17, 2017

Mathematically, resonances appear either as discrete eigenvalues of the quantization of a Hamiltonian or as eigenvalues of the transfer operator of a classical flow. They are important data relating classical and quantum dynamics. They provide useful information on the geometric properties of the flow and occur naturally in trace formulas relating geometric invariants and spectral invariants (like Selberg’s trace formula).

This workshop, which is a follow-up of a workshop organized at CIRM in March 2015, intends to bring together researchers working on the different aspects of the geometric and dynamical theories of resonances (spectral and geometric analysis, geometric scattering theory, microlocal analysis, representation theory, analytic number theory, mathematical physics).
The purpose is to provide participants with the opportunity to present their latest results, share their points of view and ideas, and hence make progress towards solving the many interesting (and difficult) open problems about  resonances. Particular attention will be paid to the geometric situations of higher dimension or higher rank.

Scientific & Organizing Committee

Colin Guillarmou (ENS Paris)
Joachim Hilgert (University of Paderborn)
Angela Pasquale (Université de Lorraine)
Tomasz Przebinda (University of Oklahoma)


  • Alex Adam (Institut Mathématique de Jussieu, Paris) 

Resonances for Anosov diffeomorphisms

Linear response for discontinuous observables

  • Ben Bellis (University of California, Los Angeles)

Resolvent estimates for non-self-adjoint semiclassical Schrödinger operators

Ruelle resonances for cusps

Asymptotics of Resonances for Hyperbolic Surfaces  

Resonances of Morse gradient flows and the Witten complex

  • Alix Deleport (Université de Strasbourg)

Toeplitz operators for spin systems   (pdf)

Pollicott-Ruelle resonances via kinetic Brownian motion

Fractal upper bound for the density of Ruelle spectrum of Anosov flows   (pdf)

Quantum resonances on asymptotically hyperbolic manifolds

Spectral determinant for Hurwitz and Mandelstam diagrams

The stability of Kerr-de Sitter black holes

The scattering matrix and its spectrum in the semiclassical limit   (pdf)

Resonances for Open Quantum Map   (pdf)

Ruelle resonances on homogeneous vector bundles

Spectra on p-forms of lens spaces from norm one length-spectra of congruence lattices

Dynamical zeta functions of locally symmetric spaces of finite volume

Resonances in the large p limit

Boundary values, resonances, and scattering poles (rank-one case)

Isomorphisms between eigenspaces of slow and fast transfer operators  

Dynamical zeta functions and validated numerical computation

Correlation spectrum of Morse-Smale flows   (pdf)

Generalised Analytic Functions and Applications to Scattering Theory  

Microlocal analysis for Kerr-de Sitter black holes

Classical and quantum resonances on hyperbolic surfaces

Asymptotic of resonances created by a multi-barrier potential

Normal forms of pseudodifferential operators on Lagrangian submanifolds of radial points