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

Today is the day of discovery of the Higgs. What comes next?

Japanese version
Today, 4 Jul. 2012,is the day of discovery of the Higgs particle. And I post the related BLOG, which does not contain the official sites.


The Higgs particle

my list of wikipedia

Japanese version none
Here is my list of some articles that I have already corrected and created.


my list of wikipedia

On Alexander polynomial

Japanese version
In order to explain the analogy between Alexander polynomials (modules) and Iwasawa theory I will translate into Japanese the article titled "Alexander Polynomial" on en.wiki. The article titled so on Japanese version doesn't contain any explanation of Alexander modules.

The original is the following:

Alexander polynomial

a translation into Japanese:

Alexander polynomial (in Japanese)

More on 3D gravity by Witten

Japanese version

On "Quantum Gravity in Flatland" there are the topic on Witten and Maloney. There is a sensational described as "they has been suggested in the simplest version of the two-dimensional gravity, and does not seem to correctly predict the holographic principle. Since the original preprint is difficult, which is a little old. On the Japanese version I have been written on my notebook for the BLOG by Mr. Scott about it and post it with some comments.

Scott's BLOG：
Witten: More on 3D gravity

The preprint by Witten and Maloney：
Quantum Gravity Partition Functions In Three Dimensions

More on 3D gravity by Witten (in Japanese)

On "Quantum Gravity in Flatland"

Japanese version

On Scientific American April 2012 (and NIKKEI SCIENCE July (its Japanese translation)) Prof. Carlip had written an article titled "Quantum Gravity in Flatland." It is very interesting for me and I post its points and my questions on my BLOG. (There are likely to revision.)

On Quantum Gravity in Flatland (in English)

On Quantum Gravity in Flatland (in Japanese)

(2+1)dimensional gravity theory

Japanese version
1, the translations of some article on BLOGs.

P. Woit's "Witten on 2+1 dimensional gravity"
Witten on 2+1 Dimensional Gravity

2, L. Motl's "Monstrous symmetry of black holes: beauty and the beast"
Witten on 2+1 Dimensional Gravity II

3, Points and my impression for the article by Dr. Carlip on SCIENTIFIC AMERICAN July
On Quantum Gravity in Flatland

4, On the second item from the end of my article above:
More on 3D gravity by Witten

Mahler’s measure, hyperbolic geometry and the dilogarithm

Japanse version
Dr. David Boyd was a professor of Number Theory at British Columbia UNIV. for a long time. I had recently known his retirement. About 9 years ago I read his article on a journal and write it 1page as "shakyoh," which means copying the bible of Buddhism in Japan. After his retirement I knew the article remained on the net. And, the full text was able to be acquired. There is Nunber Theory to run freely about three fields of mathematics of algebra, geometry, and the analysis. I translated into the full text Japanese and to post it on my BLOG. It is fortunate if becoming a part of the motive of a young person.

The original articles are on p3,p4,p26,p27,p28 of the following journal:

Mahler's measure, hyperbolic geometry and the dilogarithm

and p15,p16 of the following journal:

Explicit formulas for Mahler measure

Its translation is decomposed to two parts.

The before half:
Mahler's measure, hyperbolic geometry and the dilogarithm I (in Japanese)

The after half:
Mahler's measure, hyperbolic geometry and the dilogarithm II (in Japanese)

Mahler's measure, hyperbolic geometry and the dilogarithm III (in Japanese only, my comments and explanations)

Mahler's measure, hyperbolic geometry and the dilogarithm IV (in Japanese) translate from "Explicit formulas for Mahler measure"

Mahler's measure, hyperbolic geometry and the dilogarithm V (in Japanese only, my comments and explanations)

Page of Dr. Boyd. There are some summaries of the conferennse at BIRS. In particular, the summary in 2003 titled "The Many Aspects of Mahler's Measure" is very suitable to explain the posted articles about Dr. Boyd. Then I will translated it, separating to 3 parts.

The original document:

The Many Aspects of Mahler's Measure

and Dr. Boyd's Home Page:

David W. Boyd

The first part of the translation:

Mahler’s measure, hyperbolic geometry and the dilogarithm VI (in Japanese)

Mahler’s measure, hyperbolic geometry and the dilogarithm VII (in Japanese)

Mahler’s measure, hyperbolic geometry and the dilogarithm VIII (in Japanese)

I will add some little comments so the Japanese versions are tentative.

Some Stories by Prof. Lieven le Bruyn on Arithmetic Topology

Japanese version
Recently, Professor Lieven le Bryun is describing about Arithmetic Toplogy on his BLOG, progressing now. The articles I'm interested in are listed as follows. I would like to translate them into Japanese with other topics.
I add the preprint "Remarks on the Alexander Polynomials" by B. Mazur. I translated into Japanese only the introduction of it.

An episode of arithmetic topology My original

Mumford's treasure map
　　　　　　Japanese version

Manin's geometric axis
　　　　　　Japanese version

Mazur's knotty dictionary
　　　　　　Japanese version

Gukov on Arithmetic Topology and Gauge Theory (extra)
　　　　　　Japanese version

Grothendieck's functor of points
　　　　　　Japanese version

What is the knot associated to a prime?
　　　　　　Japanese version

Remarks on the Alexander Polynomials by Barry Mazur

Who dreamed up the primes=knots analogy?
　　　　　　Japanese version

the birthday of the primes=knots analogy
　　　　　　Japanese version

Manin’s three-space-2000
　　　　　　Japanese version

On mathematical physics seminer

Japanese version
The fourth mathematical physics seminar was held on April the 1st. 4 times of the old contents are arranged and it is made a list. Regrettably, I cannot translate all of the contents into English. But I had already posted my explanation at the second time seminer into English.

The 1st time:
On the convergence of generating prime number on "purple circle" (Japanese only) by Mr. Konishi.

The 2nd time:
Zeta Function and Statistical Dynamics (in English) by Yokoyama.

The 3rd time:
Partition Function and Correlation Function (Japanese only) by Mr. Kohmoto.

The 4-th time:
Value, Money and Price (Japanese only) by Mr. Kondo.

An episode of arithmetic topology

Japanese version
Now, although this article does not relate to arithmetic topology, the beginning of Dr. Lieven's blog is the work of Dr. David Mumford, and he talked about the textbook of the algebra geometry. I was very astonishing because the figure on it are the ones that I studied in my youth from some pirate edition(?) of Mumford's textbook, which might be of mimeographed type and I post the following article.

An episode of arithmetic topology

two translations from en.wiki

Japanese version of Langlands Program
Japanese version of Local Langlands Conjecture

Because in Japanese wikipedia there are no items about Langlands program I translated them.

the original articles：

Langlands program

Local Langlands conjectures

The opportunity of geometric Langlands

Japanese version
About the opportunity which comes to write Mr. Kapustin, and "electricity and magnetism and geometric Langlands", E. Witten told in a lecture "Gauge Theory and the Geometric Langlands Program" at StonyBrook on August 10, 2005. The following report is based on notes by Ram Sriharsha.

The report:
Gauge Theory and the Geometric Langlands Program

I translate the part of it, which contains that Dr. Witten listened Ben-zvi's lecture, and I posted my Japanese BLOG restricted to the opportunity of geometric Langlands.

Quantropy Part3

Japanese version before half
Japanese version after half

Now, "Quantropy (Part3)," the series by Dr. John Baez and I translated them into Japanese.

the before half of Part3 (in Japanese)

the after half of Part3 (in Japanese)

The original article:

Quantropy (Part 3)

Quantropy Part2

Japanese version before half
Japanese version after half

Now, "Quantropy (Part2)," the series by Dr. John Baez and I translated them into Japanese.

the before half of Part2 (in Japanese)

the after half of Part2 (in Japanese)

The original article:

Quantropy (Part 2)

Quantropy Part1

Japanese version before half
Japanese version after half

I posted on my Blog "the zero-th talk" about my motivation to thermo-dynamics. I am interested in the article "Quantropy," series by Dr. John Baez and I translated them into Japanese.

the before half of Part1 (in Japanese)

the after half of Part1 (in Japanese)

The original article:

Quantropy (Part 1)

Introducing categorification into mathmatical finance

Japanese version

I told my motivation on the zeor-th talk. It is surprizing for me that Black-Scholes equation is related to Schroedinger equation by imaginary time transformation, which is posted on Phorgy Phynance as an article. In the previous post I told it with relating to Feynman-Kac formula, one of Feynman integral that is exactly proved by mathmatics. On BLOG n-cafe, Mr. Eric stresses the analogy that as just a particle is categorified into string price, option, is categorified into "price curve," bond.Namely, let consider some categorification of Black-Scholes equation．
The original article posted by John Baez in Aug 2008:

Classical String Theory and Categorified Symplectic Geometry

And I traslated into Japanese the comment part by Mr. Eric of it.

Classical Mechanics versus Thermodynamics (Part 2)

Japanese version The 4-th talk
Japanese version The 5-th talk

I post on my Blog "the zero-th talk" about my motivation to thermo-dynamics. The article "Classical Mechanics versus Thermodynamics" is posted on the same blog "AZIMUTH" as the previous "the first talk (translation): Max and Min Princeple in Classical, Statistical and Quantum dynamics." So I translated it into Japanese.

Classical Mechanics versus Thermodynamics 1 (Part 2)(tentative)(in Japanese)


Classical Mechanics versus Thermodynamics 2 (Part 2)(tentative)(in Japanese)

The original article:

Classical Mechanics versus Thermodynamics (Part 2)

Classical Mechanics versus Thermodynamics (Part 1)

Japanese version The second talk
Japanese version The third talk

I post on my Blog "the zero-th talk" about my motivation to thermo-dynamics. The article "Classical Mechanics versus Thermodynamics" is posted on the same blog "AZIMUTH" as the previous "the first talk (translation): Max and Min Princeple in Classical, Statistical and Quantum dynamics." So I translated it into Japanese.

Classical Mechanics versus Thermodynamics 1 (Part 1)(tentative)(in Japanese)


Classical Mechanics versus Thermodynamics 2 (Part 1)(tentative)(in Japanese)

The original article:

Classical Mechanics versus Thermodynamics (Part 1)

Now, on this article there is the idea that symplectic geomety should be introduced into thermo-dynamics.

The 1st talk:On Imaginary Time Tranfomation (Wick Rotation)

Japanese version

I am attracted in the charm of imaginary time transformation (Wick rotation). I had already indicated my motive of it in the 0-th talk. About imaginary time transformation there is various arguments for long time. On Dr. John Baez's blog, Mr. Mike Stay, perhaps who is a student of Dr. John Baez, posts a article and he proposes some very interesting ideas. Then I translated into Japanese.

Extremal Principles in Classical, Statistical and Quantum Mechanics（tentative）(in Japanese)

the original article by Mr. Mike Stay:

Extremal Principles in Classical, Statistical and Quantum Mechanics

In addition, there is very interesting comments but I will omit.

Imaginary Time Transformation (Wick rotation)

Japanese version
Because the subjecy is related to quantum gravity I make "Imaginary Time Transformation" a menu on my BLOG.

The zero-th talk: Why Wick rotation? My motivation

The 1st talk:On Imaginary Time Tranfomation (Wick Rotation)

The 2nd-3rd talk:Classical Mechanics versus Thermodynamics (Part 1)

The 4-th 5-th talk:Classical Mechanics versus Thermodynamics (Part 2)

The 6-th talk:Black-Scholes and Schroedinger

The 7-th and 8-th talks, Quantum Black Holes

Introducing categorification into mathmatical financial

The 9-th talk: Quantropy (Part1)

The 10-th talk: Quantropy (Part2)

The 11-th talk: Quantropy (Part3)

The zero-th talk: Why Wick rotation? My motivation

Japanese version

I decide that the zero-th talk is named "Why Wick rotation?" For a background I suspect in this talk why thermo-statistical dynamics can detect the crack of a physical theory.

Imaginary Time Tranformation (Wick rotation)

It is greatly based on the article of Professor Eguchi in Suurikagaku January, 2001 titled "The arrow of time."

Why do we expect a Higgs boson? Part II：Unitarization of Vector Boson Scattering

Japanese version

I translated the article posted on QuantumDiaries by US LHC F. Tanedo, "Why do we expect a Higgs boson? Part II: Unitarization of Vector Boson Scattering." This article is written intelligibly and in detail about the story of Higgs particle and the unitarization of vector bosons. It is expected from the end of last year PartI was posted.

Why do we expect a Higgs boson? Part II: Unitarization of Vector Boson Scattering (Japanese only version)

The original article:

Why do we expect a Higgs boson? Part II: Unitarization of Vector Boson Scattering

The 7-th and 8-th talks, Quantum Black Holes

The 7-th talk Japanese versionThe 8-th talk Japanese version

The imaginary time transformations(Wick rotations) play a very important role in the theory of Black Holes. Dr. Hawking Told the idea of the imaginary time transformation on the textbook "The Nature of Space and Time" published by Princeton and Oxford UNIV. press. I translated few parts that relate to the imaginary time transformation into Japanese from chapter III of it.

Quantum Black Holes I (in Japanese)


Quantum Black Holes II (in Japanese)

The original book：

"The Nature of Space and Time" Chapter III

The 6-th talk:Black-Scholes and Schroedinger

Japanese version

I was astonishing that the imaginary time transformation(Wick rotation) makes Schroedinger equation for an electron in the electromagnetic field to Black-Scholes formula in the famous formula in economics. I recognized by John Baez's blog azimath that it is described on Phorgy Phynance. It might be related to Feynman-Kac formula. I have translated it into Japanese and post my blog.

Black-Scholes and Schroedinger(tentative)(in Japanese)

The original article:

Black-Scholes and Schrodinger

Categorified Option Pricing Theory

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

Japanese version I Japanese version II
Japanese version III
I had translated Witten's paper, titled "Mirror Symmetry, Hitchin's Equations, And Langlands Duality" into Japanese and posted them my Blog. This paper may not be familiar for physicists and mathematicians but it contains very fruitful contents about mirror symmetry and Langlands dualities, which is my Blog's title.

The original paper :

Mirror Symmetry, Hitchin's Equations, And Langlands Duality

The first part :

Mirror Symmetry, Hitchin's Equations, And Langlands Duality I (in Japanese)

The second part :

Mirror Symmetry, Hitchin's Equations, And Langlands Duality II (in Japanese)

The third part :

Mirror Symmetry, Hitchin's Equations, And Langlands Duality III (in Japanese)

Implications of Higgs Searches (translation)

Japanese version 1 Japanese version 2
Although it published at September 2011 I had traslated Rutgers UNIV. Professor Matt Strassler's Blog article, titled "Implications of Higgs Searches" into Japanese and post it my Blog. This article contains the status at LHC for Higgs research now and why and how we look for Higgs particle. It is acceptable and intelligible.

The original blog :

Implications of Higgs Searches

The first part :

Implications of Higgs Searches 1 (in Japanese)

The second part :

Implications of Higgs Searches 2 (in Japanese)