On major content update "mirror symmetry (string theory)" in the English version of Wikipedia

Japanese version

Since the beginning of this month, the contents of the article "mirror symmetry (string theory)" in Wikipedia's English version has been significantly updated. I think that its perspective is turned to the "mathematical" at all. The contents was different from the previous "mirror symmetry (string theory)" from the "physical" viewpoint.

I think that this article's not that bad and it is better to to change the title of the article (for example, "mirror symmetry (mathematics)" so on).

Already, I have been translated this new article into Japanese. In addition, the article from the point of view "physical" earlier remains as a "Appendix". You know immediately if you can see Japanese version.

Fortunately, behind the Japanese version, the English version of the article "Physical" earlier remains still now, so just is commented out, it is possible to revive without difficulty. Firstly, I will revive the former version as Appendix of English new version and after obtaining the consensus of the community I want to change the title of the new article.

I agree completely Mr. Polytope24, who update broadly this article. and I have revived the 1st Aug 2013 version on note in English version, as Appendix in Japanese version. Everybody might update the previous article.

14 Sep. 2013 I have moved the 1st Aug. 2013 version from "Appendix" to the "note" and have translated the whole of current article into Japanese.

I have comment this opinion on the notes column of the article both of Japanese version and English version. The URL of the article is the following.

Mirror symmetry (string theory)(in English)

Mirror symmetry (string theory)(in Japanese)

A Proof of the Full Shimura- Taniyama-Weil Conjecture Is Announced

Japanese version before half　Japanese version later half

Until read this article on AMS journal, Quadratic reciprocity law is of algebraic number theory, while Shimura Taniyama conjecture is of the number theory of automorphic forms, I think,,, As soon as I read it, found that Quadratic Rediprocity law is an example of Shimura Taniyama conjecture. There might be a lot of the same description on the other books. Although a little old, I think this article is very important and translated into Japanese．

The original URL by Henri Darmon：
A Proof of the Full Shimura- Taniyama-Weil Conjecture Is Announced

A translation into Japanese:
A Proof of the Full Shimura- Taniyama-Weil Conjecture Is Announced (In Japanese) before half
A Proof of the Full Shimura- Taniyama-Weil Conjecture Is Announced (In Japanese) later half

The Geometric Langlands Program with Edward Frenkel

Japanese version

Fields Medal Symposium will be held this October. Professor E. Frenkel's view to Langlands program is posted on the BLOG for the general public. He says that the origin of Number Theory is how many solutions algebraic equation has and Langlands program is harmonic analysis. I think this is very important and translate into Japanese．

The original URL：
The Geometric Langlands Program with Edward Frenkel

A translation into Japanese:
The Geometric Langlands Program with Edward Frenkel (In Japanese)

What is a symplectic manifold, really?

Japanese version

I have translated "What is a symplectic manifold, really?" into Japanese and posted on my BLOG. Because the article on ja.wiki about "Symplectic Manifold" is just only the mathematical definition and no its histories, no its future and no motives of researches. Such fact happens in Japan. Perhaps it is a wrong Japanese culture.

The original article:
What is a symplectic manifold, really? (in English)

A translation into Japanese:
What is a symplectic manifold, really? (in Japanese)

The cradle of arthmetic topology

Japanese version

Recently, on B. Mazur's home page, an article tilted "Remarks on the Alexander Polynomial" he presents that Alexander polynomials (modules) directly are related to Iwasawa theory, and that the origin of this idea comes from D. Mumford's idea. I was impressed by the paper is the introduction of Dr. Lieven "cradle of arithmetic topology."

The original preprint：
Remarks on the Alexander Polynomial

On Higgs field from the mathematical point of view

Japanese version

Higgs field is also important in Mathematics. Essays have been published in the Notices of the AMS Sep 2007. In Physics the Higgs field is a scalar field, while in mathematics 1-form. It appears in the application to number theory.

The original article:
What is a Higgs bundle? (in English)

A translation into Japanese:
What is a Higgs bundle? (in Japanese)

Reflection on arithmetic physics

Japanese version I Japanese version II Japanese version III

I translate into Japanese the main part of the essay "Reflection on arithmetic physics" in 1989 of Professor Manin. Posted on the blog in three divided doses. Unfortunately, the electronic media does not exist, can not be posted a link and cannot link to it.

The original document: Yu. I. Manin, "Reflections on Arithmetical Physics," in Conformal Invariance and String theory (Academic, Boston 1989), pp.293-303; Selected papers of Yu. I. Manin (World Sci, Singapore, 1996), pp. 518-528