Title: Graded matrix factorizations

Matrix factorizations, introduced by Eisenbud, provide a particularly useful means for studying hypersurface singularities. Since their introduction in commutative algebra, matrix factorizations appeared in algebraic geometry, string theory, and knot theory. In this talk, I will talk about the close ties, discovered by Orlov, between graded matrix factorizations and hypersurfaces in projective space. Our main focus will be on the idea of correspondences between graded matrix factorizations - or more precisely a categorification of a correspondence (in an appropriate sense). If time allows we will also discuss analogs for complete intersections.