Abstract

Building on work of Oh-Thomas, I will introduce invariants for counting surfaces on Calabi-Yau fourfolds. In a family, they are deformation invariant along Hodge loci. If non-zero, the variational Hodge conjecture for the family under consideration holds. Time permitting, I will discuss different compactifications of the moduli spaces of surfaces involved, and some (conjectural) relations under wall-crossing. Joint work with Y. Bae and H. Park.