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Documents  Polterovich, Leonid | enregistrements trouvés : 13

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Research talks;Geometry;Topology

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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Outreach;Mathematics Education and Popularization of Mathematics

Dusa McDuff is the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College. At Barnard, she currently teaches "Calculus I", "Perspectives in Mathematics" and courses in geometry and topology.
Professor McDuff gained her early teaching experience at the University of York (U.K.), the University of Warwick (U.K.) and MIT. In 1978, she joined the faculty of the Department of Mathematics at SUNY Stony Brook, where she was awarded the title of Distinguished Professor in 1998.
Professor McDuff has honorary doctorates from the University of Edinburgh, the University of York, the University of Strasbourg and the University of St Andrews. She is a fellow of the Royal Society, a member of the National Academy of Sciences, a member of the American Philosophical Society, and an honorary fellow of Girton College, Cambridge.
She has received the Satter Prize from the American Mathematical Society and the Outstanding Woman Scientist Award from AWIS (Association for Women in Science).
Professor McDuff's service to the mathematical community has been extensive. She is particularly interested in issues connected with the position of women in mathematics, and currently serves on the MSRI Board of Trustees. Together with Dietmar Salamon, she has written several foundational books on symplectic topology as well as many research articles.
Dusa McDuff is the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College. At Barnard, she currently teaches "Calculus I", "Perspectives in Mathematics" and courses in geometry and topology.
Professor McDuff gained her early teaching experience at the University of York (U.K.), the University of Warwick (U.K.) and MIT. In 1978, she joined the faculty of the Department of Mathematics at SUNY Stony Brook, where she was awarded the ...

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Research schools;Exposés de recherche;Dynamical Systems and Ordinary Differential Equations;Geometry

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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Research talks;Geometry;Topology

Given a smooth cobordism with an almost complex structure, one can ask whether it is realized as a Liouville cobordism, that is, an exact symplectic manifold whose primitive induces a contact structure on the boundary. We show that this is always the case, as long as the positive and negative boundaries are both nonempty. The contact structure on the negative boundary will always be overtwisted in this construction, but for dimensions larger than 4 we show that the positive boundary can be chosen to have any given contact structure. In dimension 4 we show that this cannot always be the case, due to obstructions from gauge theory. Given a smooth cobordism with an almost complex structure, one can ask whether it is realized as a Liouville cobordism, that is, an exact symplectic manifold whose primitive induces a contact structure on the boundary. We show that this is always the case, as long as the positive and negative boundaries are both nonempty. The contact structure on the negative boundary will always be overtwisted in this construction, but for dimensions larger ...

53D05 ; 53D10 ; 53D35

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Research talks;Geometry;Algebraic and Complex Geometry

I will report on aspects of work with Sheridan and Ganatra in which we show how homo- logical mirror symmetry for Calabi-Yau manifolds implies equality of Yukawa couplings on the A- and B-sides. On the A-side, these couplings are generating functions for genus-zero GW invariants. On the B-side, one has a degenerating family of CY manifolds, and the couplings are fiberwise integrals involving a holomorphic volume form. We show that the Fukaya category implicitly "knows" the correct normalization of this volume form, as well as the mirror map. I will report on aspects of work with Sheridan and Ganatra in which we show how homo- logical mirror symmetry for Calabi-Yau manifolds implies equality of Yukawa couplings on the A- and B-sides. On the A-side, these couplings are generating functions for genus-zero GW invariants. On the B-side, one has a degenerating family of CY manifolds, and the couplings are fiberwise integrals involving a holomorphic volume form. We show that the Fukaya ...

53D37 ; 14J33

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Research talks;Geometry

The degenerate special Lagrangian equation governs geodesics in the space of positive Lagrangians. Existence of such geodesics has implications for uniqueness and existence of special Lagrangians. It also yields lower bounds on the cardinality of Lagrangian intersec- tions related to the strong Arnold conjecture. An overview of what is known about the existence problem will be given. The talk is based on joint work with A. Yuval and with Y. Rubinstein. The degenerate special Lagrangian equation governs geodesics in the space of positive Lagrangians. Existence of such geodesics has implications for uniqueness and existence of special Lagrangians. It also yields lower bounds on the cardinality of Lagrangian intersec- tions related to the strong Arnold conjecture. An overview of what is known about the existence problem will be given. The talk is based on joint work with A. Yuval and with Y. ...

53D12 ; 53C22

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Research talks;Geometry;Topology

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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Research schools;Dynamical Systems and Ordinary Differential Equations;Geometry

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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Research schools;Exposés de recherche;Dynamical Systems and Ordinary Differential Equations;Geometry

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

... Lire [+]

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Research schools;Dynamical Systems and Ordinary Differential Equations;Geometry

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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Research talks

We discuss interactions between quantum mechanics and symplectic topology including a link between symplectic displacement energy, a fundamental notion of symplectic dynamics, and the quantum speed limit, a universal constraint on the speed of quantum-mechanical processes.
Joint work with Laurent Charles.

81S10 ; 53D50 ; 81Q20 ; 81R30

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- x; 342 p.
ISBN 978-0-8218-4356-7

CRM proceedings & lecture notes , 0049

Localisation : Collection 1er étage

géométrie symplectique # variétés # théorie des champs

53D40 ; 53D45 ; 53D05 ; 53D10 ; 53D12 ; 53D35 ; 37J05 ; 58J05 ; 58J20 ; 34C25 ; 53-06 ; 53DXX ; 53Z05 ; 81T45 ; 00B30

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- xii; 203 p.
ISBN 978-1-4704-1693-5

CRM monograph series , 0034

Localisation : Collection 1er étage

géométrie symplectique # mesure quantique # quasi-morphisme # Poisson bracket # approximation # bruit quantique # théorie de Morse # théorie de Floer # invariants spectraux

53-02 ; 53D05 ; 53D17 ; 53D42 ; 53D40 ; 57R17 ; 81S10 ; 81P15 ; 53DXX ; 22E65 ; 20F99 ; 28A10

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