The modularity conjecture for rigid Calabi-Yau threefolds over Q
  We formulate the modularity conjecture for rigid Calabi-Yau threefolds defined over the field Q of rational numbers. We establish the modularity for the rigid Calabi-Yau threefold arising from the root lattice A_3. Our proof is based on geometric analysis. 
Masa-Hiko Saito (Kobe), Noriko Yui (Queen's)