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Persistence modules and Hamiltonian diffeomorphisms - Part 1
Post-edited
Authors : Polterovich, Leonid (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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| persistence module Morse theory Floer theory Rips complex normal form theorem - barcode interleaving Question |
Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 21/10/2015 Conference Date : 21/09/15 Subseries : Research School arXiv category : Dynamical Systems ; Symplectic Geometry Mathematical Area(s) : Geometry ; Dynamical Systems & ODE Format : QuickTime (.mov) Video Time : 00:50:55 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-09-21_Polterovich_part1.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair - Doctoral school: Elliptic Methods and Moduli Spaces / Chaire Jean-Morlet - Ecole doctorale : Méthodes elliptiques et espaces de modulesEvent Organizers : Cornea, Octav ; Frauenfelder, Urs ; Lalonde, François ; Viterbo, Claude ; Teleman, Andrei Dates : 21/09/15 - 25/09/15 Event Year : 2015 Event URL : https://www.chairejeanmorlet.com/1257.html
Citation Data
DOI : 10.24350/CIRM.V.18839803Cite this video as: 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 |
See Also
- [Multi angle] Persistence modules and Hamiltonian diffeomorphisms - Part 4 / Author of the conference Polterovich, Leonid.
- [Multi angle] Persistence modules and Hamiltonian diffeomorphisms - Part 3 / Author of the conference Polterovich, Leonid.
- [Multi angle] Persistence modules and Hamiltonian diffeomorphisms - Part 2 / Author of the conference Polterovich, Leonid.
Bibliography
- Polterovich, L., & Shelukhin, E. (2015). Autonomous Hamiltonian flows, Hofer's geometry and persistence modules.
