Derived categories and applications

We will investigate many aspects of derived categories, and their applications in a wide swath of mathematics. The main part will focus on applications. Triangulated categories have been cropping up all over modern mathematics; we will work most on applications to algebraic geometry, to topology and to K-theory. We will develop further the exciting recent work on Grothendieck duality, by a string of authors, including me. My part of this has already seen one paper in Inventiones Mathematicae and one in the Annals of Mathematics. These are top-five journals; we expect to continue producing results of the highest calibre.