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Statut |
Confirmé |
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Série |
SEM-DARBOUX |
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Domaines |
hep-th,math |
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Date |
Jeudi 16 Janvier 2020 |
|
Heure |
11:00 |
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Institut |
LPTHE |
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Salle |
bibliothèque du LPTHE, tour 13-14, 4eme étage |
|
Nom de l'orateur |
Freixas Montplet |
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Prenom de l'orateur |
Gerard |
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Addresse email de l'orateur |
gerard [dot] freixas [at] imj-prg [dot] fr |
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Institution de l'orateur |
IMJ |
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Titre |
On genus one mirror symmetry |
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Résumé |
Classical genus zero proposes a duality phenomenon for Calabi-Yau (CY) manifolds, relating
the Yukawa coupling for a large structure limit of CY's and enumerative invariants of rational
curves on a mirror CY. For the higher genus counting problem, the corresponding conjectural
program was proposed by Bershadsky-Cecotti-Ooguri-Vafa (BCOV). In particular, they predict
that a combination of holomorphic analytic torsions of large structure limits of CY's
encapsulate genus one enumerative invariants on a mirror. In this talk I would like to present
and discuss a refined conjecture which bypasses spectral theory and pertains to the realm of
complex geometry, as for the Yukawa coupling. I will then explain a proof of this conjecture for
the mirror family of Calabi-Yau hypersurfaces in projective space, which relies on the
arithmetic Riemann-Roch theorem in Arakelov geometry. The result is compatible with the
BCOV predictions, as well as related work by Zinger. |
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Numéro de preprint arXiv |
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Commentaires |
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Fichiers attachés |
- Darboux-Freixas.pdf (391754 bytes)
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