Genus one mirror symmetry

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, 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 based on joint work with Gerard Freixas and Christophe Mourougane. I will explain the main ideas of the proof of the conjecture for Calabi-Yau hypersurfaces in projective space, relying on the Riemann-Roch theorem in Arakelov geometry. Our results generalise from dimension 3 to arbitrary dimensions previous work of Fang-Lu-Yoshikawa

number theoryrepresentation theory

Audience: researchers in the topic

Geometry, Number Theory and Representation Theory Seminar