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We study one-parameter deformations of Calabi-Yau type Fermat polynomialsingularities along degree-one directions. We show that twisted sectors in thevanishing cohomology are components of automorphic forms for certain triangulargroups. We prove consequentially that genus zero Gromov-Witten generatingseries of the corresponding Fermat Calabi-Yau varieties are components ofautomorphic forms. The main tools we use are mixed Hodge structures forquasi-homogeneous polynomial singularities, Riemann-Hilbert correspondence, andgenus zero mirror symmetry.

Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms