Categories derivees et geometrie birationnelle
  Originally a technical tool, the derived category of coherent sheaves over an algebraic variety has become over the last twenty years an important invariant in the birational study of algebraic varieties. Problems of birational invariance and of minimization of the derived category have appeared, inspired by Kontsevich's homological mirror symmetry conjecture and Mori's minimal model program. We present the main conjectures and their proofs in dimension 3 and for particular classes of flops. 
Raphael Rouquier