Student AG Seminar: The quest towards a tropical Brill-Noether Theorem

We will open with a discussion of the Brill-Noether Theorem, a statement concerning the topology of the Brill-Noether locus: the collection line bundles of degree $d$ and rank $r$ over a variety $X$. We then shift to discussing its conjectural tropical formulation and a recent attempt to attack the problem by mimicking the classical proof: developing a tropical Porteous formula and applying it to an analogue of the Poincaré bundle. This talk is largely based on the work of arXiv 2411.10578.