Dennis Eriksson: Genus one mirror symmetry

Tid: On 2020-05-27 kl 13.15

Föreläsare: Dennis Eriksson, Chalmers

Plats: 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.

Innehållsansvarig:webmaster@math.kth.se
Tillhör: Institutionen för matematik
Senast ändrad: 2020-05-22