Speaker: Sean Keel
Title: Theta functions for K3 surfaces
Abstract: I will explain joint work with Gross, Hacking and Siebert where we
construct a distinguished toroidal compactification
of F_g = moduli of polarized K3 surfaces of degree 2g2, together with a canonical
formal family of polarized surfaces along the full boundary, endowed with canonical
theta functions  a canonical basis of sections of the line bundle, together with a
formula for the multiplication in the homogeneous coordinate ring determined by counts
of rational curves on the DolgachevVoisin mirror family. We expect that this
family glues to the universal family, and thus gives an algebraic universal family over the
compactification, and a proof of Tyurin's conjecture that the classical theory
of theta functions for Abelian surfaces extends to K3 surfaces, at least near the large
complex structure limit.
