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29 juin 2017: 1 événement

  • Séminaires GSD

    Jeudi 29 juin 10:30-11:30 - Daniel Juteau - Laboratoire de Mathématiques Nicolas Oresme

    Séminaires GSD, Daniel Juteau

    Lieu : Salle 318

    En savoir plus : Séminaires GSD

29 juin 2017: 1 événement

  • Colloquium

    Jeudi 29 juin 16:30-17:30 - Dmitry Korotkin - Université Concordia, Montréal

    Symplectic geometry of the moduli space of projective structures on Riemann surfaces

    Résumé : We study symplectic properties of monodromy map for the seccond
    order linear differential equation on a Riemann surface. We show that the
    natural Poisson bracket on the space of coefficients implies the Goldman
    bracket on the space of SL(2,C) monodromy representaions. The talk in
    based on joint work with B.Bertola and C.Norton.

    En savoir plus : Colloquium

29 juin 2017: 1 événement

  • Séances du groupe travail ICB/IMB

    Jeudi 29 juin 14:00-16:00 - Michael Hitrik - Department of Mathematics, UCLA

    Mini-cours Michael Hitrik : Spectral Properties of Semiclassical Non-Selfadjoint Operators

    Résumé : Non-selfadjoint operators appear naturally in many settings, from kinetic theory and quantum mechanics to linearizations of equations of mathematical physics. An essential feature of their spectral analysis, making the latter notoriously difficult, is that for such operators, the spectrum does not control the resolvent, which may become very large even far from the spectrum. This creates a challenge, but also an opportunity, accounting for some of the complex and fascinating traits in the spectral behavior of non-selfadjoint operators.
    Powerful tools of analytic microlocal analysis become available in the case of non-selfadjoint differential operators with analytic coefficients, and in this case it turns out that the spectrum is often determined by the behavior of the holomorphic continuation of the symbol along suitable complex deformations of the real phase space. The purpose of this mini-course is to provide an overview of some of the recent developments in the non-selfadjoint spectral theory, with an emphasis on the analytic setting in dimension two, and to attempt to illustrate some of its inner workings. The tentative plan of the lectures is as follows :
    Lecture 1. Semiclassical non-selfadjoint pseudodifferential operators, their spectra and semiclassical pseudospectra. Absence of eigenvalues and resolvent bounds close to the boundary of the pseudospectrum under a non-trapping condition. Harmonic approximation for non-selfadjoint operators and spectral asymptotics for the low-lying eigenvalues. Hörmander-Davies quasimodes and spectral instability for non-normal semiclassical operators.
    Lecture 2. Non-selfadjoint pseudodifferential operators with holomorphic symbols. FBI-Bargmann transformations and pseudodifferential operators on the FBI transform side. Phase space exponential weights and complex deformations of the real cotangent space. Method of averaging for analytic non-selfadjoint operators. Bohr-Sommerfeld quantization conditions for non-selfadjoint analytic operators in dimension one.
    Lectures 3—4. Non-selfadjoint perturbations of analytic selfadjoint operators with completely integrable classical flows in dimension two. Microlocal normal forms near Diophantine Lagrangian tori and spectral asymptotics. Extensions to KAM classical flows. Weyl laws for the distribution of the imaginary parts of the eigenvalues. Spectral contributions of rational invariant tori and spectral centipedes. (The material in these lectures is based on joint work with Johannes Sjöstrand.)

    Lieu : Salle A318

    En savoir plus : Séances du groupe travail ICB/IMB