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# Matthew Baker : Riemann-Roch for Graphs and Applications

We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications (mainly due to other researchers) include new proofs of some important results in Brill-Noether theory, a generalization of the Eisenbud-Harris theory of limit linear series, and new bounds for the number of rational points on algebraic curves over number fields.

**Category**: Number Theory**Duration**: 01:14:50**Date**: February 20, 2015 at 1:25 PM**Views**: 121-
**Tags:**seminar, UNC-Duke Number Theory Seminar

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