"Chern-Simons gauge theory and Witten's invariant"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
| 5번째 줄: | 5번째 줄: | ||
* [[Kashaev's volume conjecture|Kashaev Volume conjecture]] | * [[Kashaev's volume conjecture|Kashaev Volume conjecture]] | ||
| − | * action<br><math>S=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{2}{3}A\wedge A\wedge A)\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{ | + | * action<br><math>S=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{2}{3}A\wedge A\wedge A)=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{1}{3}A\wedge [A,A])</math><br> |
| + | |||
| + | |||
| + | |||
| + | |||
| + | |||
| + | <h5>Chern-Simons and arithmetic</h5> | ||
| + | |||
| + | The Chern-Simons invariants of a closed 3-manifold are secondary characteristic numbers that are given in terms of a finite set of phases in the unit circle. Hyperbolic 3-dimensional geometry links these phases with arithmetic, and identifies them with values of the Rogers dilogarithm at algebraic numbers. The quantization of these invariants are the famous Witten-Reshetikhin-Turaev invariants of 3-manifolds, constructed by the Jones polynomial. In the talk we will review conjectures regarding the asymptotics of the quantum 3-manifold invariants, and their relation to Chern-Simons theory and arithmetic. We will review progress on those conjectures, theoretical, and experimental. | ||
2011년 6월 8일 (수) 05:33 판
introduction
- 3D TQFT( Chern-Simons theory)
- CS is an invariant for 3-manifolds
- Kashaev Volume conjecture
- action
\(S=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{2}{3}A\wedge A\wedge A)=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{1}{3}A\wedge [A,A])\)
Chern-Simons and arithmetic
The Chern-Simons invariants of a closed 3-manifold are secondary characteristic numbers that are given in terms of a finite set of phases in the unit circle. Hyperbolic 3-dimensional geometry links these phases with arithmetic, and identifies them with values of the Rogers dilogarithm at algebraic numbers. The quantization of these invariants are the famous Witten-Reshetikhin-Turaev invariants of 3-manifolds, constructed by the Jones polynomial. In the talk we will review conjectures regarding the asymptotics of the quantum 3-manifold invariants, and their relation to Chern-Simons theory and arithmetic. We will review progress on those conjectures, theoretical, and experimental.
memo
history
books
- 찾아볼 수학책
- http://gigapedia.info/1/chern+simons
- http://gigapedia.info/1/wzw
- http://gigapedia.info/1/Wess+zumino
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Chern–Simons_theory
- http://en.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
blogs
- 구글 블로그 검색
expositions
articles
- http://journal.ms.u-tokyo.ac.jp/pdf/jms030310.pdf
- Rationality problems for K-theory and Chern-Simons invariants of hyperbolic 3-manifolds
- Walter Neumann, 1995
- 논문정리
- http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/
experts on the field