ACM vector bundles on hypersurfaces

An Arithmetically Cohen Macaulay vector bundle on a hypersurface $X$ of projective space is a bundle $E$ for which $H^i(X,E(a))=0$ for any integer $a$ and any $i$ between $1$ and $\dim(X)-1$. We will discuss existence, constructions and applications of ACM bundles on smooth hypersurfaces.