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# Documents  53D25 | enregistrements trouvés : 6

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## Post-edited  A microlocal toolbox for hyperbolic dynamics Dyatlov, Semyon (Auteur de la Conférence) | CIRM (Editeur )

I will discuss recent applications of microlocal analysis to the study of hyperbolic flows, including geodesic flows on negatively curved manifolds. The key idea is to view the equation $(X + \lambda)u = f$ , where $X$ is the generator of the flow, as a scattering problem. The role of spatial infinity is taken by the infinity in the frequency space. We will concentrate on the case of noncompact manifolds, featuring a delicate interplay between shift to higher frequencies and escaping in the physical space. I will show meromorphic continuation of the resolvent of $X$; the poles, known as Pollicott-Ruelle resonances, describe exponential decay of correlations. As an application, I will prove that the Ruelle zeta function continues meromorphically for flows on non-compact manifolds (the compact case, known as Smale's conjecture, was recently settled by Giulietti-Liverani- Pollicott and a simple microlocal proof was given by Zworski and the speaker). Joint work with Colin Guillarmou. I will discuss recent applications of microlocal analysis to the study of hyperbolic flows, including geodesic flows on negatively curved manifolds. The key idea is to view the equation $(X + \lambda)u = f$ , where $X$ is the generator of the flow, as a scattering problem. The role of spatial infinity is taken by the infinity in the frequency space. We will concentrate on the case of noncompact manifolds, featuring a delicate interplay between ...

## Post-edited  Persistence modules and Hamiltonian diffeomorphisms - Part 1 Polterovich, Leonid (Auteur de la Conférence) | CIRM (Editeur )

Theory of persistence modules is a rapidly developing field lying on the borderline between algebra, geometry and topology. It provides a very useful viewpoint at Morse theory, and at the same time is one of the cornerstones of topological data analysis. In the course I'll review foundations of this theory and focus on its applications to symplectic topology. In parts, the course is based on a recent work with Egor Shelukhin arXiv:1412.8277

## Multi angle  Spectrum of geodesic flow on negatively curved manifold Tsujii, Masato (Auteur de la Conférence) | CIRM (Editeur )

We consider the one-parameter families of transfer operators for geodesic flows on negatively curved manifolds. We show that the spectra of the generators have some "band structure" parallel to the imaginary axis. As a special case of "semi-classical" transfer operator, we see that the eigenvalues concentrate around the imaginary axis with some gap on the both sides.

## Multi angle  Persistence modules and Hamiltonian diffeomorphisms - Part 2 Polterovich, Leonid (Auteur de la Conférence) | CIRM (Editeur )

Theory of persistence modules is a rapidly developing field lying on the borderline between algebra, geometry and topology. It provides a very useful viewpoint at Morse theory, and at the same time is one of the cornerstones of topological data analysis. In the course I'll review foundations of this theory and focus on its applications to symplectic topology. In parts, the course is based on a recent work with Egor Shelukhin arXiv:1412.8277

## Multi angle  Persistence modules and Hamiltonian diffeomorphisms - Part 3 Polterovich, Leonid (Auteur de la Conférence) | CIRM (Editeur )

Theory of persistence modules is a rapidly developing field lying on the borderline between algebra, geometry and topology. It provides a very useful viewpoint at Morse theory, and at the same time is one of the cornerstones of topological data analysis. In the course I'll review foundations of this theory and focus on its applications to symplectic topology. In parts, the course is based on a recent work with Egor Shelukhin arXiv:1412.8277

## Multi angle  Persistence modules and Hamiltonian diffeomorphisms - Part 4 Polterovich, Leonid (Auteur de la Conférence) | CIRM (Editeur )

Theory of persistence modules is a rapidly developing field lying on the borderline between algebra, geometry and topology. It provides a very useful viewpoint at Morse theory, and at the same time is one of the cornerstones of topological data analysis. In the course I'll review foundations of this theory and focus on its applications to symplectic topology. In parts, the course is based on a recent work with Egor Shelukhin arXiv:1412.8277

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