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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

37Cxx ; 37Jxx ; 53D25 ; 53D40 ; 53D42

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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

37Cxx ; 37Jxx ; 53D25 ; 53D40 ; 53D42

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I will discuss work in progress aimed towards defining contact homology using "virtual" holomorphic curve counting techniques.

37J10 ; 53D35 ; 53D40 ; 53D42 ; 53D45 ; 57R17

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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

37Cxx ; 37Jxx ; 53D25 ; 53D40 ; 53D42

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

37Cxx ; 37Jxx ; 53D25 ; 53D40 ; 53D42

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Documents 53D42 5 résultats

Persistence modules and Hamiltonian diffeomorphisms - Part 1 - Polterovich, Leonid (Auteur de la Conférence) | CIRM H Nouveau

Persistence modules and Hamiltonian diffeomorphisms - Part 3 - Polterovich, Leonid (Auteur de la Conférence) | CIRM H Nouveau

Virtual fundamental cycles and contact homology - Pardon, John (Auteur de la Conférence) | CIRM H Nouveau

Persistence modules and Hamiltonian diffeomorphisms - Part 2 - Polterovich, Leonid (Auteur de la Conférence) | CIRM H Nouveau

Persistence modules and Hamiltonian diffeomorphisms - Part 4 - Polterovich, Leonid (Auteur de la Conférence) | CIRM H Nouveau