Date(s) : 21/01/2020 iCal
11 h 00 min - 12 h 00 min
Dennis ERIKSSON (Chalmers University of Technology, Göteborg)
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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