D-Branes on Calabi-Yau Manifolds
  We give an overview of recent work on Dirichlet branes on Calabi-Yau threefolds which makes contact with Kontsevich's homological mirror symmetry proposal, proposes a new definition of stability which is appropriate in string theory, and provides concrete quiver categories equivalent to certain categories of branes on CY.   To appear in the proceedings of the 3rd European Congress of Mathematics. 
Michael R. Douglas