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Documents  Ono, Kaoru | enregistrements trouvés : 10

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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 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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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 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;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;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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- x; 266 p.
ISBN 978-1-4704-3625-4

Memoirs of the American Mathematical Society , 1254

Localisation : Collection 1er étage

homologie de Floer # sous-variété Lagrangienne # dynamique Hamiltonienne # déformation en masse # invariant spectral # quasi-état symplectique partiel # quasi-morphisme # cohomologie quantique # variété torique # théorie de Gromov-Witten ouverte-fermée

53D40 ; 53D12 ; 53D45 ; 53D20 ; 14M25 ; 20F65

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- vi; 340 p.
ISBN 978-2-85629-825-1

Astérisque , 0376

Localisation : Périodique 1er étage

cohomologie de Floer # symétrie miroir # variété torique # invariant de Gromov-Witten ouvert-fermé # théorie des singularités de Saito # modèle de Landau-Ginzburg # sous-variété Lagrangienne faiblement non-obstruée # fonction potentielle # anneau de Jacobi # variété de Frobenius

53D37 ; 53D40 ; 53D45 ; 14B07 ; 14M25 ; 37J05

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- xii; 397-805 p.
ISBN 978-0-8218-4837-1

Studies in advanced mathematics (AMS/IP) , 0046

Localisation : Collection 1er étage

cohomologie de Floer # géométrie symplectique # sous-variétés lagrangiennes # variétés de Calabi-Yau # opérades # théorie de l'homotopie # courbe pseudo-holomorphe # théorie de Morse elliptique # indexe de Maslov # symétrie miroir # structure de Kuranishi # transversalité # théorie des chaînes

53D12 ; 53D40 ; 14J32 ; 81T30 ; 37J10 ; 18D50 ; 55P62 ; 53-02

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- xii; 396 p.
ISBN 978-0-8218-4836-4

Studies in advanced mathematics (AMS/IP) , 0046

Localisation : Collection 1er étage

cohomologie de Floer # points lagrangiens # géométrie symplectique # sous-variétés lagrangiennes # variétés de Fano # variétés de Calabi-Yau

53D12 ; 53D40 ; 14J32 ; 81T30 ; 37J10 ; 18D50 ; 55P62 ; 53-02

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