Currently the Riemann-Roch theorem is my nemesis, and I stumbled on Matt Baker’s math blog while I was looking for some help figuring out how to use it. The post I came across, Riemann-Roch for Graphs and Applications, was not what I was looking for, but I’m glad I found it! Baker, a math professor at Georgia Tech, describes the Riemann-Roch theorem for graphs in fairly straightforward language and also gives some background about how he and his coauthor Serguei Norine discovered it. At the beginning it was a theorem in search of a precise formulation: “I stumbled upon the idea that there ought to be a graph-theoretic avatar of the Riemann-Roch Theorem while investigating ‘p-adic Riemann surfaces’ (for the experts: Berkovich curves). At the time I didn’t know precisely how to formulate the combinatorial Riemann-Roch theorem, but I knew that the following should be a special case…” I like seeing the incremental development of the idea, and it’s nice to see how many undergraduates were involved at different points in the process. His explanation of the theorem involves a game you can play on a graph, and he includes an applet for the game created by REU student Adam Tart.
See the full post on the AMS Blog on Math Blogs.
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