Bi-annual Algebraic and Tropical Meetings of
Brown and YaLE
(BATMOBYLE)

The geometry of an algebraic curve is governed by its linear systems. While many curves exhibit bizarre and pathological linear systems, the general curve does not. This is a consequence of the Brill-Noether theorem, which says that the space of linear systems 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. Our focus will be on an approach using tropical and combinatorial methods, but we will also discuss an independent proof, due to H. Larson. This is joint work with Kaelin Cook-Powell and Dhruv Ranganathan, based on prior work of Nathan Pflueger.