Wednesday, November 26, 2025

Time: 16:10-17:00

venue: Mathematics Building Room 527

Speaker: Dr. Chih-Wei Chang (Department of Mathematics, National Taiwan University)

Title: Linear series on tropical curves

Abstract:

Nearly two decades ago, M. Baker proved the Specialization Lemma, relating the ranks of divisors on algebraic curves to those on graphs via semistable degenerations. This initiated a program to prove results in divisor theory on curves—such as the Brill–Noether theorem—purely by combinatorial means. In the same spirit, G. Farkas, D. Jensen, and S. Payne introduced the notion of tropical linear series on metric graphs (=tropical curves), aiming to give combinatorial proofs of results that involve linear series on algebraic curves. In this talk, after introducing the basic notions, we will see that tropical linear series have a deep connection to matroid theory: their local structure and possible parametrizations are determined by matroids. We will then discuss how this matroidal perspective can be used to study tropical linear series further.