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Audiovisual Mathematics Library

Audiovisual Mathematics Library

Documents 53D40 11 results

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Persistence modules and Hamiltonian diffeomorphisms - Part 1 - Polterovich, Leonid (Author of the conference) | CIRM H

Post-edited

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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Persistence modules and Hamiltonian diffeomorphisms - Part 3 - Polterovich, Leonid (Author of the conference) | CIRM H

Multi angle

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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The spectral norm, rigidity and all that - Gurel, Basak (Author of the conference) | CIRM H

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The spectral norm is an important invariant of a Hamiltonian diffeomorphism and its properties have recently found numerous nontrivial applications to dynamics. We will explore the behavior of the spectral norm under iterations of a Hamiltonian diffeomorphism and some related phenomena. This feature is closely related to the existence of invariant sets (the Le Calvez–Yoccoz type theorems), Hamiltonian pseudo-rotations, rigidity and the strong closing lemma. The talk is based on joint work with Erman Çineli and Viktor Ginzburg.[-]
The spectral norm is an important invariant of a Hamiltonian diffeomorphism and its properties have recently found numerous nontrivial applications to dynamics. We will explore the behavior of the spectral norm under iterations of a Hamiltonian diffeomorphism and some related phenomena. This feature is closely related to the existence of invariant sets (the Le Calvez–Yoccoz type theorems), Hamiltonian pseudo-rotations, rigidity and the strong ...[+]

53D40 ; 37J11 ; 37J46

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Symplectic mapping class groups: structural properties from smooth to $C^{0}$ - Keating, Ailsa (Author of the conference) | CIRM H

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The aims of this talk are two-fold: a) to give a biased overview of some structural properties of (smooth) symplectic mapping class groups, together with some key proof ingredients, and b) to present some open questions, both about those groups and about their $C^{0}$ counterparts, whose study was recently initiated by Alexandre Jannaud.

53D05 ; 53D40 ; 57R17

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Virtual fundamental cycles and contact homology - Pardon, John (Author of the conference) | CIRM H

Post-edited

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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Nearby Lagrangians are simply homotopic - Abouzaid, Mohammed (Author of the conference) | CIRM H

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I will describe joint work with Thomas Kragh proving that closed exact Lagrangians in cotangent bundles are simply homotopy equivalent to the base. The main two ideas are (i) a Floer theoretic model for the Whitehead torsion of the projection from the Lagrangian to the base, and (ii) a large scale deformation of the Lagrangian which allows a computation of this torsion.

53D40 ; 55P35 ; 55P42

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Persistence modules and Hamiltonian diffeomorphisms - Part 2 - Polterovich, Leonid (Author of the conference) | CIRM H

Multi angle

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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Persistence modules and Hamiltonian diffeomorphisms - Part 4 - Polterovich, Leonid (Author of the conference) | CIRM H

Multi angle

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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On the algebraic structure of groups of area-preserving homeomorphisms - Seyfaddini, Sobhan (Author of the conference) | CIRM H

Virtualconference

In the late 70s, Fathi showed that the group of compactly supported volume-preserving homeomorphisms of the ball is simple in dimensions greater than 2. We present our recent article which proves that the remaining group, that is area-preserving homeomorphisms of the disc, is not simple. This settles what is known as the simplicity conjecture in the affirmative. This is joint work with Dan Cristofaro-Gardiner and Vincent Humiliere.

53DXX ; 53D40 ; 37E30

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Symplectic Landau-Ginzburg models and their Fukaya categories - Auroux, Denis (Author of the conference) | CIRM H

Virtualconference

This partly expository talk focuses on the notion of ”symplectic Landau-Ginzburg models”, i.e. symplectic manifolds equipped with maps to the complex plane, ”stops”, or both, as they naturally arise in the context of mirror symmetry. We describe several viewpoints on these spaces and their Fukaya categories, their monodromy, and the functors relating them to other flavors of Fukaya categories. (This touches on work of Abouzaid, Seidel, Ganatra, Hanlon, Sylvan, Jeffs, and others).[-]
This partly expository talk focuses on the notion of ”symplectic Landau-Ginzburg models”, i.e. symplectic manifolds equipped with maps to the complex plane, ”stops”, or both, as they naturally arise in the context of mirror symmetry. We describe several viewpoints on these spaces and their Fukaya categories, their monodromy, and the functors relating them to other flavors of Fukaya categories. (This touches on work of Abouzaid, Seidel, Ganatra, ...[+]

53D37 ; 14J33 ; 53D40

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