Seminar in Algebraic Geometry and Number Theory

Abstract: An Enriques surface is the quotient of a K3 surface by a fixed point-free involution. Klemm and Marino conjectured a formula which expresses the Gromov-Witten invariants of the local Enriques surface in terms of automorphic forms. In particular, the generating series of Gromov-Witten counts of elliptic curves on the Enriques  is predicted to be the Fourier expansion of (a certain power of) Borcherd's automorphic form on the moduli space of Enriques surfaces (a quotient of a Hermitian symmetric domain of type IV). In this talk I will first give an overview over the conjecture and then explain how to prove it.