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.

Speakers

• Alex Adam (Institut Mathématique de Jussieu, Paris) 

Resonances for Anosov diffeomorphisms

• Viviane Baladi (IMJ-PRG, CNRS and UPMC, Paris)

Linear response for discontinuous observables

• Ben Bellis (University of California, Los Angeles)

Resolvent estimates for non-self-adjoint semiclassical Schrödinger operators

• Yannick Bonthonneau (Université Rennes 1)

​Ruelle resonances for cusps

• David Borthwick (Emory University, Atlanta)

Asymptotics of Resonances for Hyperbolic Surfaces  

• Nguyen Viet Dang (Université Lille 1)

Resonances of Morse gradient flows and the Witten complex

• Alix Deleport (Université de Strasbourg)

Toeplitz operators for spin systems   (pdf)

• Alexis Drouot (University of California, Berkeley)

Pollicott-Ruelle resonances via kinetic Brownian motion

• Frédéric Faure  (Institut Joseph Fourier, Grenoble)

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

• Charles Hadfield (Ecole Normale Supérieure, Paris)

Quantum resonances on asymptotically hyperbolic manifolds

• Luc Hilliaret (Université d’Orléans) 

Spectral determinant for Hurwitz and Mandelstam diagrams

• Peter Hintz (University of California, Berkeley)

The stability of Kerr-de Sitter black holes

• Maxime Ingremeau (Université Paris-Sud)

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

• Long Jin (Purdue University)

Resonances for Open Quantum Map   (pdf)
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• Benjamin Küster (Universität Marburg)

Ruelle resonances on homogeneous vector bundles

• Roberto Miatello (University of Cordoba)

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

• Werner Müller (Bonn University)

Dynamical zeta functions of locally symmetric spaces of finite volume

• Frédéric Naud (Université d’Avignon)

Resonances in the large p limit

• Aprameyan Parthasarathy (Universität Paderborn)

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

• Anke Pohl (University of Jena)

Isomorphisms between eigenspaces of slow and fast transfer operators  

• Mark Pollicott (Warwick University)

Dynamical zeta functions and validated numerical computation

• Gabriel Rivière (Université de Lille)

Correlation spectrum of Morse-Smale flows   (pdf)

• Alexander Strohmaier (University of Leeds)

Generalised Analytic Functions and Applications to Scattering Theory  

• Andras Vasy (Stanford University)

Microlocal analysis for Kerr-de Sitter black holes

• Tobias Weich (Universität Paderborn)

Classical and quantum resonances on hyperbolic surfaces

• Maher Zerzeri (Université Paris 13)

​Asymptotic of resonances created by a multi-barrier potential

• Jupiter (Beite) Zhu (Stanford University)

Normal forms of pseudodifferential operators on Lagrangian submanifolds of radial points