Colloquium DATE 2017-10-05¡@16:10-17:00 PLACE ¼Æ¾ÇÀ]3174±Ð«Ç SPEAKER ¨ô¤h³ó ±Ð±Â¡]²MµØ¤j¾Ç¼Æ¾Ç¨t¡^ TITLE Iitaka Dimensions of Vector Bundles ABSTRACT To understand an abstract space X, one often tries to embed it into more familiar spaces such as the Euclidean space or the projective space. It has long been understood that giving a map from X to a projective space is equivalent to giving a line bundle L on X with nonzero global sections. A well-known result of Iitaka in algebraic geometry says that the maps from X to projective spaces given by higher and higher tensor powers of L eventually stabilize to a fibration. In a recent preprint, Mistretta and Urbinati generalize this when L is replaced by a vector bundle, which gives a map from X to a Grassmannian. I will explain their result and answer one of their questions.