English
Persistence modules and Hamiltonian diffeomorphisms - Part 1
Post-edited
Auteurs : Polterovich, Leonid (Auteur de la Conférence)
CIRM (Editeur )
37Cxx - Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]
37Jxx - Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx]
53D25 - Geodesic flows
53D40 - Floer homology and cohomology, symplectic aspects
53D42 - Symplectic field theory; contact homology
CIRM (Editeur )
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| persistence module Morse theory Floer theory Rips complex normal form theorem - barcode interleaving Question |
Résumé :
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
Codes MSC : 37Cxx - Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]
37Jxx - Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx]
53D25 - Geodesic flows
53D40 - Floer homology and cohomology, symplectic aspects
53D42 - Symplectic field theory; contact homology
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 21/10/2015 Date de captation : 21/09/15 Sous collection : Research School arXiv category : Dynamical Systems ; Symplectic Geometry Domaine : Geometry ; Dynamical Systems & ODE Format : QuickTime (.mov) Durée : 00:50:55 Audience : Researchers Download : https://videos.cirm-math.fr/2015-09-21_Polterovich_part1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair - Doctoral school: Elliptic Methods and Moduli Spaces / Chaire Jean-Morlet - Ecole doctorale : Méthodes elliptiques et espaces de modulesOrganisateurs de la rencontre : Cornea, Octav ; Frauenfelder, Urs ; Lalonde, François ; Viterbo, Claude ; Teleman, Andrei Dates : 21/09/15 - 25/09/15 Année de la rencontre : 2015 URL Congrès : https://www.chairejeanmorlet.com/1257.html
Données de citation
DOI : 10.24350/CIRM.V.18839803Citer cette vidéo: Polterovich, Leonid (2015). Persistence modules and Hamiltonian diffeomorphisms - Part 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18839803 URI : http://dx.doi.org/10.24350/CIRM.V.18839803 |
Voir aussi
- [Multi angle] Persistence modules and Hamiltonian diffeomorphisms - Part 4 / Auteur de la Conférence Polterovich, Leonid.
- [Multi angle] Persistence modules and Hamiltonian diffeomorphisms - Part 3 / Auteur de la Conférence Polterovich, Leonid.
- [Multi angle] Persistence modules and Hamiltonian diffeomorphisms - Part 2 / Auteur de la Conférence Polterovich, Leonid.
Bibliographie
- Polterovich, L., & Shelukhin, E. (2015). Autonomous Hamiltonian flows, Hofer's geometry and persistence modules.
