Modularity of Calabi-Yau varieties
  In this paper we discuss recent progress on the modularity of Calabi-Yau varieties. We focus mostly on the case of surfaces and threefolds. We will also discuss some progress on the structure of the L-function in connection with mirror symmetry. Finally, we address some questions and open problems. 
Klaus Hulek, Remke Kloosterman, Matthias Schuett