Title:  Linear Systems on General Curves of Fixed Gonality



Abstract:  The geometry of an algebraic curve is governed by the maps it admits to various projective spaces.  While many curves exhibit bizarre and pathological maps, the general curve does not.  This is a consequence of the Brill-Noether theorem, which says that the space of maps of given degree and rank on a general curve has dimension equal to its expected dimension.  In this talk, we will discuss a generalization of this theorem to general curves of fixed gonality.  To prove this result, we use tropical and combinatorial methods.  This is joint work with Dhruv Ranganathan.