Résumé : For a projective variety X defined over a non-Archimedean complete (non-trivially) valued field, and an ample line bundle L equipped with a semipositive metric, we consider the problem of metric extension for sections of Ln from a subvariety Y to X. Namely, for any given restricted section on Y, find an extended section on X with smallest possible distorsion of supremum norm. This problem is equivalent to the comparison of a quotient norm and a supremum norm on the restricted section algebra. We form normed section algebras and study their Berkovich spectra, relating them to the dual unit disc bundle of L with respect to the envelop metric. There are two methods for this norm comparison: one exploits the holomorphic convexity, another relies on special properties of affinoid algebras. Work based on arXiv: 1904.03696

15h15-16h45 – Dennis Eriksson (Chalmers)

"On an invariant for Calabi-Yau manifolds through analytic torsion"

Résumé : Recently a real-valued invariant of Calabi-Yau varieties was introduced by myself and my collaborators. This invariant borrows inspiration from theoretical physics,  is expected to play an important role in genus one mirror symmetry, and is principally built from analytic torsion. In this talk I will discuss recent results in this direction, with an emphasis on explicit computations. In particular I will highlight a mirror symmetry phenomenon in genus one for Calabi-Yau hypersurfaces in projective space and their mirrors, generalising results of Fang-Lu-Yoshikawa for the mirror quintic to arbitrary dimensions. This is joint work with Gerard Freixas and Christophe Mourougane