On Instanton

Japanese version
I translated into Japanese the article titled "instanton" on en.wiki. Because there are no article titled so on Japanese version. The original is the following:

Instanton

On generalized complex structure

Japanese version
I translated into Japanese the article titled "generalized complex structure" on en.wiki. Because there are no article titled so on Japanese version. The original is the following:

generalized complex structure

On ADHM construction

Japanese version
I translated into Japanese the article titled "ADHM construction" on en.wiki. Because there are no article titled so on Japanese version. The original is the following:

ADHM construction

On Nahm equations

Japanese version
I translated into Japanese the article titled "Nahm equations" on en.wiki. Because there are no article titled so on Japanese version. The original is the following:

Nahm equations

On Hitchin functional

Japanese version
I translated into Japanese the article titled "Hitchin functional" on en.wiki. Because there are no article titled so on Japanese version. The original is the following:

Hitchin functional

What is Langlands Programme?

Japanese version

１、I have translated the description on the black board at the lecture "Knots and Quantum Theory" by E. Witten in Nov 2011.

"Knots and Quantum Theory"

The original lecture for the general audience is contained in the clicked page.

The Langlands correspondence is used in the meaning "Geometric Langlands" in Physics. As well known, it has an original in the number theory, class field theory. But I imagine they should have the common part, but of course it is not a established result.

3 years ago Witten published a article on arxiv titled "Mirror Symmetry, Hitchin's Equations, And Langlands Duality," which seems for me to explain to mathematicians about them. It is the most interesting for me and I had translated into Japanese as soon as published.

Mirror Symmetry, Hitchin's Equations, And Langlands Duality (translation)

Dr. P. Woit, Professor of mathematics (representation theory) at the Columbia university, posted a very interesting and educational article about Langlands Program on his BLOG. I had translated his article into Japanese.

The book "Not Even Wrong," written by him, is very famous, and in Japan its translation is published by Seito-sya titled "Is String Theory Science?"

From Woit's BLOG "Knots and Quantum Theory":

From Woit's BLOG "Knots and Quantum Theory"

Japanese translation I :

Dr. Woit's BLOG I (in Japanese)

The original BLOG :

Witten Geometric Langlands Talk and Paper

Japanese translation II :

Dr. Woit's BLOG II (in Japanese)

The original BLOG :

Geometric Langlands and QFT

Japanese translation III :

Dr. Woit's BLOG III (with my comments) (in Japanese)

２、The following article posted in Apr. 26 2010, But the article in it is in Japanese.

Langlands correpondence and physics

３、The articles from "n-cafe" on "Physics and Geometric Langlands"

Geometric Langlands and Integrable systems about "Hitchin system, Opers and Bethe Ansatz."

Kapustin on SYM, Mirror Symmetry and Langlands, I

Kapustin on SYM, Mirror Symmetry and Langlands, II

Kapustin on SYM, Mirror Symmetry and Langlands, III

the latter three article might be the simplest explanation of the paper "Electric-Magnetic Duality And the Geometric Langlands Program" by A. Kapustin and E. Witten.

４、The trace formula is very important for Langlands programme. And I have translated Arthur's little article "a very brief history of the trace formula.

Arthur's brief history of the trace formula (translation)

another old article "Hitchin system"

Japanese version
Before About 2007 on en.wiki there are an another old article titled "Hitchin system". I don't know the auther of it. Of cource, now there is a nice article of the same title in the modern view point. But the old article is rather available and I post it on my BLOG. Because I drove it from my notebook, It might contain some mistakes.

Hitchin System (old version)

But the new version is the following, which point out that Hitchin system plays an important role in geometric Langlands correspondence over the field of complex numbers; related to conformal field theory as certain limit of Knizhnik–Zamolodchikov equations.

Hitchin_system (current version)

21 Jun. 2012:I have added the old version as Appendix and the current version contains the old one.

An old article "Magnetic Monopole"

Japanese version
Before About 2007 on en.wiki there are an old article titled "Magnetic Monopole", which had the signature by N.J.Hitchin. Of cource, now there is a nice article of the same title in the modern view point. But the old article is rather available and I post it on my BLOG. Because I drove it from my notebook, It might contain some mistakes.

Magnetic Monopole (old version)

But the new version is the following, which starts with Maxwell equation and contains the recent applications, GUT theory and the condensed matter etc..

Magnetic Monopole (current version)