## Graduate Algebraic Geometry Seminar

Jay Kopper

Some problems in extending Brill-Noether theory from the classical case: the sky is the limit linear series

**Abstract:**Classical Brill-Noether theory asks how many global sections a line bundle on a (general) smooth curve can have. This was solved (completely, in some sense) by Griffiths-Harris several decades ago. A number of natural generalizations remain open: what if we ask about (semistable) vector bundles instead of line bundles? What if our curves are not Brill-Noether general but nonetheless lie in an interesting family? In this talk I will pose but fail to answer some of these very interesting questions.

Wednesday October 11, 2017 at 1:00 PM in SEO 712