Statut  Confirmé 
Série  SEMDARBOUX 
Domaines  hepth,math 
Date  Jeudi 16 Janvier 2020 
Heure  11:00 
Institut  LPTHE 
Salle  bibliothèque du LPTHE, tour 1314, 4eme étage 
Nom de l'orateur  Freixas Montplet 
Prenom de l'orateur  Gerard 
Addresse email de l'orateur  gerard [dot] freixas [at] imjprg [dot] fr 
Institution de l'orateur  IMJ 
Titre  On genus one mirror symmetry 
Résumé  Classical genus zero proposes a duality phenomenon for CalabiYau (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 BershadskyCecottiOoguriVafa (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 CalabiYau hypersurfaces in projective space, which relies on the arithmetic RiemannRoch theorem in Arakelov geometry. The result is compatible with the BCOV predictions, as well as related work by Zinger. 
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