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# Documents : Multi angle  Conférences Vidéo | enregistrements trouvés : 200

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## Multi angle  Cohomological obstructions to local-global principles - lecture 4 Demarche, Cyril (Auteur de la Conférence) | CIRM (Editeur )

Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these cohomological tools.

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## Multi angle  Interactions of analytic number theory and geometry - lecture 2 Schindler, Damaris (Auteur de la Conférence) | CIRM (Editeur )

A general introduction to the state of the art in counting of rational and integral points on varieties, using various analytic methods with the Brauer-Manin obstruction.

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## Multi angle  Interactions of analytic number theory and geometry - lecture 3 Schindler, Damaris (Auteur de la Conférence) | CIRM (Editeur )

A general introduction to the state of the art in counting of rational and integral points on varieties, using various analytic methods with the Brauer-Manin obstruction.

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## Multi angle  Interactions of analytic number theory and geometry - lecture 4 Schindler, Damaris (Auteur de la Conférence) | CIRM (Editeur )

A general introduction to the state of the art in counting of rational and integral points on varieties, using various analytic methods with the Brauer-Manin obstruction.

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## Multi angle  Geodesic beams in eigenfunction analysis (part 2 of 2) Galkowski, Jeffrey (Auteur de la Conférence) | CIRM (Editeur )

This talk is a continuation of ‘Understanding the growth of Laplace eigenfunctions’. We explain the method of geodesic beams in detail and review the development of these techniques in the setting of defect measures. We then describe the tools and give example applications in concrete geometric settings.

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## Multi angle  Linear stability of slowly rotating Kerr spacetimes Hintz, Peter (Auteur de la Conférence) | CIRM (Editeur )

I will describe joint work with Dietrich Häfner and Andràs Vasy in which we study the asymptotic behavior of linearized gravitational perturbations of Schwarzschild or slowly rotating Kerr black hole spacetimes. We show that solutions of the linearized Einstein equation decay at an inverse polynomial rate to a stationary solution (given by an infinitesimal variation of the mass and angular momentum of the black hole), plus a pure gauge term. Our proof uses a detailed description of the resolvent of an associated wave equation on symmetric 2-tensors near zero energy.
I will describe joint work with Dietrich Häfner and Andràs Vasy in which we study the asymptotic behavior of linearized gravitational perturbations of Schwarzschild or slowly rotating Kerr black hole spacetimes. We show that solutions of the linearized Einstein equation decay at an inverse polynomial rate to a stationary solution (given by an infinitesimal variation of the mass and angular momentum of the black hole), plus a pure gauge term. Our ...

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## Multi angle  ALC manifolds with exceptional holonomy Foscolo, Lorenzo (Auteur de la Conférence) | CIRM (Editeur )

We will describe the construction of complete non-compact Ricci-flat manifolds of dimension 7 and 8 with holonomy $G_{2}$ and Spin(7) respectively. The examples we consider all have non-maximal volume growth and an asymptotic geometry, so-called ALC geometry, that generalises to higher dimension the asymptotic geometry of 4-dimensional ALF hyperkähler metrics. The interest in these metrics is motivated by the study of codimension 1 collapse of compact manifolds with exceptional holonomy. The constructions we will describe are based on the study of adiabatic limits of ALC metrics on principal Seifert circle fibrations over asymptotically conical orbifolds, cohomogeneity one techniques and the desingularisation of ALC spaces with isolated conical singularities. The talk is partially based on joint work with Mark Haskins and Johannes Nordstrm.
We will describe the construction of complete non-compact Ricci-flat manifolds of dimension 7 and 8 with holonomy $G_{2}$ and Spin(7) respectively. The examples we consider all have non-maximal volume growth and an asymptotic geometry, so-called ALC geometry, that generalises to higher dimension the asymptotic geometry of 4-dimensional ALF hyperkähler metrics. The interest in these metrics is motivated by the study of codimension 1 collapse of ...

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## Multi angle  Emergence of the quantum wave equation in classical deterministic hyperbolic dynamics Faure, Frédéric (Auteur de la Conférence) | CIRM (Editeur )

In the 80’s, D. Ruelle, D. Bowen and others have introduced probabilistic and spectral methods in order to study deterministic chaos (”Ruelle resonances”). For a geodesic flow on a strictly negative curvature Riemannian manifold, following this approach and use of microlocal analysis, one obtains that long time fluctuations of classical probabilities are described by an effective quantum wave equation. This may be surprising because there is no added quantization procedure. We will discuss consequences for the zeros of dynamical zeta functions. This shows that the problematic of classical chaos and quantum chaos are closely related. Joint work with Masato Tsujii.
In the 80’s, D. Ruelle, D. Bowen and others have introduced probabilistic and spectral methods in order to study deterministic chaos (”Ruelle resonances”). For a geodesic flow on a strictly negative curvature Riemannian manifold, following this approach and use of microlocal analysis, one obtains that long time fluctuations of classical probabilities are described by an effective quantum wave equation. This may be surprising because there is no ...

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## Multi angle  Delocalization of eigenfunctions and quantum chaos - lecture 1 Anantharaman, Nalini (Auteur de la Conférence) | CIRM (Editeur )

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## Multi angle  Delocalization of eigenfunctions and quantum chaos - lecture 2 Anantharaman, Nalini (Auteur de la Conférence) | CIRM (Editeur )

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## Multi angle  Large deviations for the largest eigenvalue of random matrices Guionnet, Alice (Auteur de la Conférence) | CIRM (Editeur )

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## Multi angle  Delocalization of eigenfunctions and quantum chaos - lecture 3 Anantharaman, Nalini (Auteur de la Conférence) | CIRM (Editeur )

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## Multi angle  Eigenvector convergence for minors of unitarily invariant infinite random matrices Najnudel, Joseph (Auteur de la Conférence) | CIRM (Editeur )

We give a new expression for the law of the eigenvalues of the discrete Anderson model on the finite interval [0, N], in terms of two random processes starting at both ends of the interval. Using this formula, we deduce that the tail of the eigenvectors behaves approximately like exponential of a Brownian motion with a drift. A similar result has recently been shown by B. Rifkind and B. Virag in the critical case, that is, when the random potential is multiplied by a factor 1/ √N.
We give a new expression for the law of the eigenvalues of the discrete Anderson model on the finite interval [0, N], in terms of two random processes starting at both ends of the interval. Using this formula, we deduce that the tail of the eigenvectors behaves approximately like exponential of a Brownian motion with a drift. A similar result has recently been shown by B. Rifkind and B. Virag in the critical case, that is, when the random ...

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## Multi angle  Transfer operators for Sinai billiards - lecture 3 Baladi, Viviane (Auteur de la Conférence) | CIRM (Editeur )

We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.

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## Multi angle  Transfer operators for Sinai billiards - lecture 2 Baladi, Viviane (Auteur de la Conférence) | CIRM (Editeur )

We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.

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## Multi angle  Transfer operators for Sinai billiards - lecture 1 Baladi, Viviane (Auteur de la Conférence) | CIRM (Editeur )

We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.

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## Multi angle  Transfer operators for Anosov flows - lecture 1 Tsuijii, Masato (Auteur de la Conférence) | CIRM (Editeur )

We present a functional-analytic approach to the study of transfer operators for Anosov flows. To study transfer operators, a basic idea in semi-classical analysis suggests to look at the action of the flow on the cotangent bundle. Though this idea is simple and intuitive (as we will explain in the lectures), we need some framework to make it work. In the lectures, we present such a framework based on a wave-packet transform.

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## Multi angle  Transfer operators for Anosov flows - lecture 2 Tsuijii, Masato (Auteur de la Conférence) | CIRM (Editeur )

We present a functional-analytic approach to the study of transfer operators for Anosov flows. To study transfer operators, a basic idea in semi-classical analysis suggests to look at the action of the flow on the cotangent bundle. Though this idea is simple and intuitive (as we will explain in the lectures), we need some framework to make it work. In the lectures, we present such a framework based on a wave-packet transform.

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## Multi angle  Transfer operators for Anosov flows - lecture 3 Tsuijii, Masato (Auteur de la Conférence) | CIRM (Editeur )

We present a functional-analytic approach to the study of transfer operators for Anosov flows. To study transfer operators, a basic idea in semi-classical analysis suggests to look at the action of the flow on the cotangent bundle. Though this idea is simple and intuitive (as we will explain in the lectures), we need some framework to make it work. In the lectures, we present such a framework based on a wave-packet transform.

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## Multi angle  Additive combinatorics methods in fractal geometry - lecture 1 Shmerkin, Pablo (Auteur de la Conférence) | CIRM (Editeur )

In the last few years ideas from additive combinatorics were applied to problems in fractal geometry and led to progress on some classical problems, particularly on the smoothness of Bernoulli convolutions and other self-similar measures. We will introduce some of these tools from additive combinatorics and present some of the main applications, including the smoothness of Bernoulli convolutions outside of a small set of exceptions, and for explicit values of the parameter.
In the last few years ideas from additive combinatorics were applied to problems in fractal geometry and led to progress on some classical problems, particularly on the smoothness of Bernoulli convolutions and other self-similar measures. We will introduce some of these tools from additive combinatorics and present some of the main applications, including the smoothness of Bernoulli convolutions outside of a small set of exceptions, and for ...

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