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Alessandro Chiodo - Towards global mirror symmetry (Part 2)
/ Fanny Bastien
/ 28-06-2011
/ Canal-u.fr
Chiodo Alessandro
Voir le résumé
Voir le résumé
Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathe-
matics and physics in the last twenty years; we will review here a number of results going from the enumerative
geometry of curves to homological algebra. These advances justify the introduction of new techniques, which
are interesting in their own right. Among them, Gromov{Witten theory and its variants allow us to provide a
re ned statement of mirror symmetry. Of course this leads to further open questions (despite much e ort and
progress, Gromov{Witten theory remains unknown in high genus for the quintic threefold). In this course, we
will illustrate the natural problem of moving beyond the local mirror symmetry statement and completing a
framework of global mirror symmetry which is gradually taking shape. We will show how the missing piece in
this picture comes unexpectedly from a classical subject in algebraic geometry: the theory of curves with level
structures. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, courbes, institut fourier, summer school, Gromov-Witten
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Accéder à la ressource
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Alessandro Chiodo - Towards global mirror symmetry (Part 1)
/ Fanny Bastien
/ 27-06-2011
/ Canal-u.fr
Chiodo Alessandro
Voir le résumé
Voir le résumé
Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathematics and physics in the last twenty years; we will review here a number of results going from the enumerative geometry of curves to homological algebra. These advances justify the introduction of new techniques, which are interesting in their own right. Among them, Gromov{Witten theory and its variants allow us to provide are ned statement of mirror symmetry. Of course this leads to further open questions (despite much e ort and progress, Gromov{Witten theory remains unknown in high genus for the quintic threefold). In this course, we will illustrate the natural problem of moving beyond the local mirror symmetry statement and completing a framework of global mirror symmetry which is gradually taking shape. We will show how the missing piece in this picture comes unexpectedly from a classical subject in algebraic geometry: the theory of curves with level structures. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, courbes, institut fourier, summer school, Gromov-Witten
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Accéder à la ressource
|
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