October 2012


Last time on this series, I talked about the word manifold.  Today, we’re going to add a modifier.

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No substantive post today, because my grant application is due.  New post next week!

Last time, we discussed integration theory of functions along paths on Riemann surfaces, and then we decided that we wanted to talk about compact Riemann surfaces.  Unfortunately, there aren’t any holomorphic functions on them, and meromorphic functions are the wrong choice about what to integrate along curves.  Today, we’ll talk about the correct things to integrate, and some of their properties.

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So, I’m trying to learn Japanese, being as I live in Japan, so I’ve decided to start this series.  I’m armed with a mathematical English-Japanese dictionary, a kanji look-up website, and a willingness to be corrected if I happen to have any Japanese readers.  So, this post may not appear correctly if you don’t have Japanese fonts installed, just a warning, and if I explain anything incorrectly, let me know in the comments and I’ll correct the post.

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I’m back! And now, posting from Kavli IPMU in Japan.  Now, I’m going to start a series on theta functions, Jacobians, Pryms, and abelian varieties more generally, hopefully with some applications, with my goal being at least one post a week, and eventually establishing a regular posting schedule again.  But today, we’ll start with basics, something that should be completely understandable to graduate students and advanced undergraduates.

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