Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

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.
arXiv Preprint Number
  • Darboux-Freixas.pdf (391754 bytes) OPEN

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