Inspired by Kontsevich's homological mirror symmetry conjecture, I will show how to construct new classes of automorphisms of the bounded derived category of coherent sheaves on a smooth Calabi-Yau variety. The induced monodromy actions match the monodromy actions associated to general components of the discriminant locus in the moduli space of complex structures of the mirror Calabi-Yau. I will explain the 'local' character of the picture.