The transcendental part of the regulator map for K_1 on a mirror family   of K3 surfaces
  We compute the transcendental part of the normal function corresponding to the Deligne class of a cycle in K_1 of a mirror family of quartic K3 surfaces. The resulting multivalued function does not satisfy the hypergeometric differential equation of the periods and we conclude that the cycle is indecomposable for most points in the mirror family. The occurring inhomogenous Picard-Fuchs equation are related to Painlev\'e VI type differential equations. 
Pedro Luis del Angel (Cimat, Mex.), Stefan M\"uller-Stach (Univ. of   Essen)