M-regularity and the Fourier-Mukai transform
  This is a survey of M-regularity for coherent sheaves on abelian varieties and its applications, based on lectures given by the second author at the Seattle conference, in August 2005, and at the Luminy GAC workshop in October 2005. Section 3 contains some brief indications of upcoming work. 
Giuseppe Pareschi and Mihnea Popa