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Documents  Minasian, Ruben | enregistrements trouvés : 4

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Research schools;Mathematical Physics

This school consists of an array of courses which at first glance may seem to have little in common. The underlying structure relating gauge theory to enumerative geometry to number theory is string theory. In this short introduction, we will attempt to give a schematic overview of how the various topics covered in this school fit into this overarching framework.

81T30 ; 83E30

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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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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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Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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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