Abstract: We study one-parameter deformations of Calabi-Yau type Fermat polynomial sin-gularities along degree-one directions. We show that twisted sectors in the vanishing cohomology are automorphic forms for certain triangular groups. We prove consequen-tially that genus zero Gromov-Witten generating series of the corresponding Fermat Calabi-Yau varieties are components of automorphic forms. The main tools we use are period mappings for quasi-homogeneous polynomial singularities, Riemann-Hilbert correspondence, and genus zero mirror symmetry.

This is joint work with Yongbin Ruan and Dingxin Zhang.