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Dennis Eriksson: Genus one mirror symmetry

Time: Wed 2020-05-27 13.15

Lecturer: Dennis Eriksson, Chalmers

Location: Zoom, meeting ID: 689 4480 8319

Abstract

Mirror symmetry, in a crude formulation, is usually presented as a correspondence between curve counting on a Calabi--Yau variety X, and some invariants extracted from a mirror family of Calabi--Yau varieties. After the physicists Bershadsky--Cecotti--Ooguri--Vafa (henceforth BCOV), this is organised according to the genus of the curves in X we wish to enumerate, and gives rise to an infinite recurrence of differential equations. In this talk, I will give a general introduction to these problems, and present a rigorous mathematical formulation of the BCOV conjecture at genus one, in terms of a lifting of the Grothendieck--Riemann--Roch. I will explain a proof of the conjecture for Calabi--Yau hypersurfaces in projective space, based on the Riemann--Roch theorem in Arakelov geometry. Our results generalise from dimension 3 to arbitrary dimensions previous work of Fang--Lu--Yoshikawa.

This is joint work with G. Freixas and C. Mourougane.

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Last changed: May 22, 2020