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