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Documents  14J33 | enregistrements trouvés : 12

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Research talks;Algebraic and Complex Geometry

The remodeling conjecture proposed by Bouchard-Klemm-Marino-Pasquetti relates Gromov-Witten invariants of a semi-projective toric Calabi-Yau 3-orbifold to Eynard-Orantin invariants of the mirror curve of the toric Calabi-Yau 3-fold. It can be viewed as a version of all genus open-closed mirror symmetry. In this talk, I will describe results on this conjecture based on joint work with Bohan Fang and Zhengyu Zong.

14J33 ; 14N35

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- xvi; 294 p.
ISBN 978-1-4704-3515-8

Proceedings of symposia in pure mathematics , 0098

Localisation : Collection 1er étage

géométrie algébrique # théorie quantique # programme de Langlands # espace fibré vectoriel # fibration # espace modulaire # symétrie miroir # analyse globale # application harmonique # théorie des champs # théorie des cordes

14D24 ; 14H60 ; 14D21 ; 14J33 ; 58E20 ; 81T60 ; 81T30 ; 14-04 ; 81T13 ; 00B25

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- xv; 635 p.
ISBN 978-1-4704-3578-3

Proceedings of symposia in pure mathematics , 0097

Localisation : Collection 1er étage

géométrie algébrique # géométrie birationnelle # homologie # cohomologie # symétrie miroir # invariant de Gromov-Witten # algèbre modulaire

14E07 ; 14E18 ; 14E30 ; 14F05 ; 14F10 ; 14F30 ; 14J33 ; 14N35 ; 53C55 ; 14-06 ; 14Exx ; 14Fxx ; 14H10 ; 00B25

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- xv; 655 p.
ISBN 978-1-4704-3577-6

Proceedings of symposia in pure mathematics , 0097

Localisation : Collection 1er étage

géométrie algébrique # géométrie birationnelle # homologie # cohomologie # symétrie miroir # invariant de Gromov-Witten # algèbre modulaire

14E07 ; 14E18 ; 14E30 ; 14F05 ; 14F10 ; 14F30 ; 14J33 ; 14N35 ; 53C55 ; 14-06 ; 14Exx ; 14Fxx ; 14H10 ; 00B25

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- pag. mult.

Séminaire Bourbaki janvier 2017

Localisation : Séminaire 1er étage

conjecture de corrélation gaussienne # isomorphisme de graphes # groupe de Grothendieck-Teichmüller # complexe de graphe # inégalité isopérimétrique

62H20 ; 05Cxx ; 14J33 ; 53C23 ; 49Q20

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Research talks;Algebra;Algebraic and Complex Geometry

Homological mirror symmetry asserts that the connection, discovered by physicists, between a count of rational curves in a Calabi-Yau manifold and period integrals of its mirror should follow from an equivalence between the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. Physicists' observation can be reformulated as, or rather upgraded to, a statement about an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the above assertion would be to try to attach similar Hodge-like data to abstract derived categories. The aim of the talk is to report on some recent progress in this direction and illustrate the approach in the context of what physicists call Landau-Ginzburg B-models. Homological mirror symmetry asserts that the connection, discovered by physicists, between a count of rational curves in a Calabi-Yau manifold and period integrals of its mirror should follow from an equivalence between the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. Physicists' observation can be reformulated as, or rather upgraded to, a statement about an isomorphism of certain ...

14J32 ; 14J33 ; 14A22 ; 14F05 ; 16E40

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Research schools;Algebraic and Complex Geometry;Mathematical Physics

There are five superstring theories, all formulated in 9+1 spacetime dimensions; lower-dimensional theories are studied by taking some of the spatial dimensions to be compact (and small). One of the remarkable features of this setup is that the same lower-dimensional theory can often be realized by pairing different superstring theories with different geometries. The focus of these lectures will be on the mathematical implications of some of these physical “dualities.”
Our main focus from the string theory side will be the superstring theories known as type IIA and type IIB. The duality phenomenon occurs for compact spaces of various dimensions and types. We will begin by discussing “T-duality” which uses tori as the compact spaces. We will then digress to introduce M-theory as a strong-coupling limit of the type IIA string theory, and F-theory as a variant of the type IIB string theory whose existence is motivated by T-duality. The next topic is compactifying the type IIA and IIB string theories on K3 surfaces (where the duality involves a change of geometric parameters but not a change of string theory).
By the third lecture, we will have turned our attention to Calabi-Yau manifolds of higher dimension, and the “mirror symmetry” which relates pairs of them. Various aspects of mirror symmetry have various mathematical implications, and we will explain how these are conjecturally related to each other.
There are five superstring theories, all formulated in 9+1 spacetime dimensions; lower-dimensional theories are studied by taking some of the spatial dimensions to be compact (and small). One of the remarkable features of this setup is that the same lower-dimensional theory can often be realized by pairing different superstring theories with different geometries. The focus of these lectures will be on the mathematical implications of some of ...

14J32 ; 14J33 ; 81T30

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Research schools;Algebraic and Complex Geometry;Mathematical Physics

There are five superstring theories, all formulated in 9+1 spacetime dimensions; lower-dimensional theories are studied by taking some of the spatial dimensions to be compact (and small). One of the remarkable features of this setup is that the same lower-dimensional theory can often be realized by pairing different superstring theories with different geometries. The focus of these lectures will be on the mathematical implications of some of these physical “dualities.”
Our main focus from the string theory side will be the superstring theories known as type IIA and type IIB. The duality phenomenon occurs for compact spaces of various dimensions and types. We will begin by discussing “T-duality” which uses tori as the compact spaces. We will then digress to introduce M-theory as a strong-coupling limit of the type IIA string theory, and F-theory as a variant of the type IIB string theory whose existence is motivated by T-duality. The next topic is compactifying the type IIA and IIB string theories on K3 surfaces (where the duality involves a change of geometric parameters but not a change of string theory).
By the third lecture, we will have turned our attention to Calabi-Yau manifolds of higher dimension, and the “mirror symmetry” which relates pairs of them. Various aspects of mirror symmetry have various mathematical implications, and we will explain how these are conjecturally related to each other.
There are five superstring theories, all formulated in 9+1 spacetime dimensions; lower-dimensional theories are studied by taking some of the spatial dimensions to be compact (and small). One of the remarkable features of this setup is that the same lower-dimensional theory can often be realized by pairing different superstring theories with different geometries. The focus of these lectures will be on the mathematical implications of some of ...

14J32 ; 14J33 ; 81T30

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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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- 364 p.
ISBN 978-3-319-59938-0

Progress in mathematics , 0324

Localisation : Collection 1er étage

Maxim Kontsevich # commémoration # mathématiques modernes # géométrie algébrique # catégorie # géométrie différentielle # théorie quantique

14J33 ; 53D37 ; 18G60 ; 53C55 ; 14-06 ; 18-06 ; 53-06 ; 81-06 ; 00B30 ; 00B15

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- vii; 352 p.
ISBN 978-1-57146-322-7

Surveys in differential geometry , 0021

Localisation : Ouvrage RdC (SURV)

géométrie différentielle # physique mathématique # courbure

53A10 ; 49Q05 ; 53C42 ; 53C26 ; 14J33 ; 49Q15 ; 58A20

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- ix; 399 p.
ISBN 978-3-319-29958-7

Progress in mathematics , 0315

Localisation : Collection 1er étage

géométrie algébrique # module des surface K3 # théorie des treillis # système dynamique # théorie des nombres # conjecture de Tate # théorie des cordes # variété symplectique holomorphe

14J28 ; 14J15 ; 14J10 ; 14J32 ; 14J33 ; 14J50 ; 14N35

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