An Enriques surface is the quotient of a K3 surface by a fixed point-free involution. Klemm and Marino conjectured a formula expressing the Gromov-Witten invariants of the local Enriques surface in terms of automorphic forms. In particular, the generating series of elliptic curve counts on the Enriques should be the Fourier expansion of (a certain power of) Borcherds automorphic form on the moduli space of Enriques surfaces. In this talk I will explain a proof of this conjecture. The proof uses the geometry of the Enriques Calabi-Yau threefold in fiber classes. If time permits, I will also discuss various conjectures about non-fiber classes.
For more information see: https://personal.math.ubc.ca/~jbryan/Zoominar-UBC-ETH/