Title: Bundles of rank 2 on algebraic curves and their sections
Abstract: Classical Brill-Noether theory is concerned with line bundles on
general algebraic curve and their spaces of sections. Since modern proofs
of the results were given in the 1980s, a similar theory has been
developed for vector bundles. However the results are much more
complicated and our knowledge is incomplete. In this talk I will give a
general introduction and discuss some recent developments, paying special
attention to the first case which is not fully solved - that of bundles of
rank 2 with 4 independent sections. I plan to set this in the context of
coherent systems (a generalisation of classical linear systems) and to say
something about the relationship with projective embeddings of the curve.