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

### October 2012

October 22, 2012

## Japanese for mathematics: Algebraic Variety

Posted by Charles Siegel under Japanese for Mathematics[4] Comments

October 15, 2012

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

October 15, 2012

## Understanding Integration II: 1-Forms and Periods

Posted by Charles Siegel under AG From the Beginning, Algebraic Geometry, Curves, Complex AnalysisLeave a Comment

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.

October 8, 2012

## Japanese for mathematics: Manifold

Posted by Charles Siegel under Japanese for Mathematics[4] Comments

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.

October 1, 2012

## Understanding Integration I: Riemann Surfaces

Posted by Charles Siegel under Abelian Varieties, AG From the Beginning, Algebraic Geometry, Complex Analysis, Curves[5] Comments

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.