Sorin Popescu "Exterior algebra methods for syzygies" We use exterior algebra methods (via the Bernstein-Gel'fand-Gelfand correspondence, exterior minors, etc) to describe the structure and the geometry of the syzygies of various projective embeedings. We will discuss applications of our techniques among which to syzygies of Veronese and Segre embeddings, the failure of the Minimal resolution conjecture, the geometric content of property N_p or of its failure, etc This is joint work in progress with David Eisenbud, Mark Green, Klaus Hulek, Frank-Olaf Schreyer and Charles Walter.