Abstract: I shall start my talk by attempting to explain how one would try to construct a counterexample to the generalization of Torelli to Calabi-Yau 3-folds, using Fourier-Mukai transforms and derived categories. This study will lead us to study sheaves of modules over Azumaya algebras and derived equivalences, and this will provide insights into why certain singularities appear in a way that is very similar to an example of Aspinwall-Morrison and Vafa-Witten.