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)
Witten's recent research is published on arxiv with compact style.
ReplyDeleteE.Witten:"Khovanov Homology And Gauge Theory”arxiv:1108.3103
At KITP Program: Nonperturbative Effects and Dualities in QFT and Integrable Systems (Jul 11 - Aug 26, 2011) E. Frenkel gave a lecture titled
ReplyDelete"What Do Fermat's Last Theorem and Electro-magnetic Duality Have in Common?"
I had listened to the lecture on Internet and taken my notebook of it. Very interesting!
Half the last question can be received with the joke and the game played in earnest.
Q1、What is Categoies (equivalence)?
A1、In SYM,,,
Q2、Then on integers \mathbb{Z} what would happen?
A2、There are some Hitchin system on \mathbb{Z} such as Geometric Langlands case,,,
Q3、What happens when one translate the geometry on CY on the integers？
A3、...
Once more let us listen it.