RiemannRoch for graphs and applications
RiemannRoch for graphs and applications

Matt Baker, Georgia Institute of Technology
Fine Hall 314
We will begin by formulating the RiemannRoch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a RiemannRoch theorem for tropical curves, proved by GathmannKerber and MikhalkinZharkov, and a RiemannRoch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof by CoolsDraismaPayneRobeva of the BrillNoether theorem in algebraic geometry, a generalization by Amini and the speaker of the EisenbudHarris theory of limit linear series, and a new ChabautyColeman style bound for the number of rational points on an algebraic curve over the rationals, proved recently by Katz and ZureickBrown.