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Status |
Confirmed |
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Seminar Series |
SEM-DARBOUX |
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Subjects |
hep-th,math |
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Date |
Thursday 16 January 2020 |
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Time |
11:00 |
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Institute |
LPTHE |
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Seminar Room |
bibliothèque du LPTHE, tour 13-14, 4eme étage |
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Speaker's Last Name |
Freixas Montplet |
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Speaker's First Name |
Gerard |
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Speaker's Email Address |
gerard [dot] freixas [at] imj-prg [dot] fr |
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Speaker's Institution |
IMJ |
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Title |
On genus one mirror symmetry |
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Abstract |
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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arXiv Preprint Number |
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Comments |
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Attachments |
- Darboux-Freixas.pdf (391754 bytes)
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