演講者：張志偉博士 (國立臺灣大學數學系)

日   期：2025 年 08 月 26 日（星期二）13:30

地   點：國立高雄大學理學院 408 室

講   題：Combinatorial Methods in the Study of Linear Series

摘   要：

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, aiming to give combinatorial proofs of results that involve linear series on algebraic curves.

In this talk, 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.