Abstracts
Viviane Baladi
Title:
The spectrum of Sinai billiard flows (Joint with M. Demers and C. Liverani)
Absract: Sinai billiard maps in dimension two have been known to be exponentially mixing (L.-S. Young) for almost two decades, and recent work of Demers and Zhang have shed new light on the spectrum of their transfer operators. The situation for the continuous time Sinai billiard is more delicate. I will present recent results and ongoing work on their spectrum.
Absract: Sinai billiard maps in dimension two have been known to be exponentially mixing (L.-S. Young) for almost two decades, and recent work of Demers and Zhang have shed new light on the spectrum of their transfer operators. The situation for the continuous time Sinai billiard is more delicate. I will present recent results and ongoing work on their spectrum.
Colin Guillarmou
Title:
The Ruelle spectrum of geodesic flow of compact hyperbolic
manifold
Absract: We describe the Ruelle spectrum of the geodesic flow of compact hyperbolic manifolds (joint work with Dyatlov and Faure).
Absract: We describe the Ruelle spectrum of the geodesic flow of compact hyperbolic manifolds (joint work with Dyatlov and Faure).
Luc Hillairet
Title:
On embedded eigenvalues in hyperbolic triangles with one cusp
Absract: we study the existence of embedded eigenvalues in the continuous spectrum of the Neumann Laplace operator in a hyperbolic triangle with one cusp. We prove that generically in the space of such triangles there are no embedded eigenvalues. Joint with Chris Judge.
Absract: we study the existence of embedded eigenvalues in the continuous spectrum of the Neumann Laplace operator in a hyperbolic triangle with one cusp. We prove that generically in the space of such triangles there are no embedded eigenvalues. Joint with Chris Judge.
Frédéric Naud
Title:
Résonances et sous-groupes de congruence
Absract: On exposera divers résultats et conjectures sur la théorie des résonances des surfaces de "congruence" qui sont obtenues en prenant des sous-groupes d'indice infini de SL2(Z). On motivera cet exposé par des problèmatiques de théorie des nombres (travaux de Bourgain, Gamburd, Sarnak).
Absract: On exposera divers résultats et conjectures sur la théorie des résonances des surfaces de "congruence" qui sont obtenues en prenant des sous-groupes d'indice infini de SL2(Z). On motivera cet exposé par des problèmatiques de théorie des nombres (travaux de Bourgain, Gamburd, Sarnak).
Stéphane Nonnenmacher
Title:
Resonances for a normally hyperbolic trapping (joint with M.Zworski)
Absract: We investigate the distribution of resonances for semiclassical quantum scattering systems for which the trapped set of the classical dynamics is a normally hyperbolic symplectic submanifold. We prove the presence of a resonance gap (or resonance free strip) related with the minimal rate of transverse hyperbolicity. This generalizes an old result of Gérard-Sjöstrand to the smooth setting. Such a gap has consequences on the dispersion of waves in various situations. Besides, following the strategy of Faure-Sjöstrand, this result can also be applied to recover the exponential mixing rate of contact Anosov flows proved a few years ago by Tsujii.
Absract: We investigate the distribution of resonances for semiclassical quantum scattering systems for which the trapped set of the classical dynamics is a normally hyperbolic symplectic submanifold. We prove the presence of a resonance gap (or resonance free strip) related with the minimal rate of transverse hyperbolicity. This generalizes an old result of Gérard-Sjöstrand to the smooth setting. Such a gap has consequences on the dispersion of waves in various situations. Besides, following the strategy of Faure-Sjöstrand, this result can also be applied to recover the exponential mixing rate of contact Anosov flows proved a few years ago by Tsujii.
Mark Pollicott
Title:
Zeta functions for Anosov and Axiom A flows
Absract: We consider the two most basic questions for Ruelle zeta functions, defined in terms of the closed orbits for Anosov, and more generally, for Axiom A flows: (i) To how large a domain can the zeta function be meromorphically extended? (ii) What can be said about the location of the zeros?
Absract: We consider the two most basic questions for Ruelle zeta functions, defined in terms of the closed orbits for Anosov, and more generally, for Axiom A flows: (i) To how large a domain can the zeta function be meromorphically extended? (ii) What can be said about the location of the zeros?
Gabriel Rivière
Title:
Perturbation of the Schrödinger equation on
negatively curved su! rfaces.
Absract: I will consider small pertubations of the geodesic flow on compact negatively curved surfaces. I will discuss some statistical properties satisfied by these families of perturbed flows and I will give applications of these results to the long time dynamics (below the Ehrenfest time) of the Schrödinger equation on such surfaces.
Absract: I will consider small pertubations of the geodesic flow on compact negatively curved surfaces. I will discuss some statistical properties satisfied by these families of perturbed flows and I will give applications of these results to the long time dynamics (below the Ehrenfest time) of the Schrödinger equation on such surfaces.
Johannes Sjöstrand (sous réserve)
Title:
Distributions de valeurs propres pour des grands
blocs de Jordan avec des perturbations aléatoires
Absract: On applique une méthode maintenant bien établie pour des opérateurs différentiels avec perturbations aléatoires (dévéloppée par M. Hager, W. Bordeaux-Montrieux, Sjöstrand) au cas des perturbations de grands blocs de Jordan. Par rapport à un travail de E.B. Davies et Hager, on trouve aussi la distribution angulaire des valeurs propres.
Absract: On applique une méthode maintenant bien établie pour des opérateurs différentiels avec perturbations aléatoires (dévéloppée par M. Hager, W. Bordeaux-Montrieux, Sjöstrand) au cas des perturbations de grands blocs de Jordan. Par rapport à un travail de E.B. Davies et Hager, on trouve aussi la distribution angulaire des valeurs propres.
Luchezar Stoyanov
Title:
Ruelle transfer operators with two complex parameters
for contact Anosov flows
Absract: The talk concerns Ruelle transfer operators related to a given Markov partition for contact Anosov flows satisfying certain regularity conditions. In the classical case these operators depend on just one complex parameter and it is important to have information about their spectra when the (absolute value of this) parameter is large. However there are problems in hyperbolic dynamics that lead naturally to the study of Ruelle transfer operators depending on two complex parameters. We will discuss how to get strong spectral estimates of such operators under certain natural assumptions when the absolute values of both complex parameters are large.
Absract: The talk concerns Ruelle transfer operators related to a given Markov partition for contact Anosov flows satisfying certain regularity conditions. In the classical case these operators depend on just one complex parameter and it is important to have information about their spectra when the (absolute value of this) parameter is large. However there are problems in hyperbolic dynamics that lead naturally to the study of Ruelle transfer operators depending on two complex parameters. We will discuss how to get strong spectral estimates of such operators under certain natural assumptions when the absolute values of both complex parameters are large.
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