How Quadratic Reciprocity Is Like Dealing Cards

Currently the Riemann-Roch theorem is my nemesis, and I stumbled on马特贝克的数学博客虽然我正在寻找一些帮助弄清楚如何使用它。我遇到的帖子,riemann-roch用于图形和应用程序,不是我在寻找的东西,但我很高兴我找到了它!贝克是格鲁吉亚科技的数学教授,以相当简单的语言描述了图形的Riemann-Roch定理,并且还给出了一些关于他和他的Coauthor Serguei Norine发现它的背景。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 anapplet对于Reu Student Adam Tart创建的游戏。

面包师的一部分是使用卡对二次互惠的解释。图片:Matt Baker。与许可一起使用。

Part of Baker’s explanation of quadratic reciprocity using cards. Image: Matt Baker. Used with permission.

另一个引起了我的帖子,可能是因为图片,是二次互惠和Zolotarev的引理。谁知道二次互动可以用一块卡片描述?Baker写道,“就在前一段时间我重新改造了Zolotarev的论点(如上所述)here)交易卡和我发了一点note about it on my web page. After reading my write-up (which was unfortunately opaque in a couple of spots),Jerry Shurman受到启发,返工争论,他提出了这种优雅的配方我认为这可能是“书中的证据”。以下博览会是我自己对杰瑞的论点。“我不会试图解释二次互惠性如何像交易卡。你应该只是读他的帖子。

贝克’s blog has several other posts that give background information and exposition for his research papers. I definitely appreciate reading about the motivation and false starts that usually get hidden away in the formal presentation of research. If that sounds like your thing, maybe you’d like to head on over and check it out.

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