From Osher Doctorow
I mentioned earlier in this thread that Readers should think of the
200 series of Sections in the thread as "Graduate level" rather than
"Undergraduate" as in the 0-199 Sections, which is only relative since
all the ideas on Probable Causation/Influence (PI) and many others are
new, as are most of the relationships.
In a sense, we do come to a Graduate level now with the works of
Edward Witten (Institute for Advanced Studies Princeton and now also
CalTech USA), Edward Frenkel (U. C. Berkeley USA), David Ben-Zvi (I'll
have to look up his location), Yi-Zhi Huang of Rutgers U. USA, all on
or closely related to the Langlands Program in the topics that I'll
focus on.
Curiously enough, the best translation of the complicated concepts of
these people and others into ordinary physics intuition and simple
language seems to be Yi-Zhi Huang's Review of Frankel and Ben-Zvi's
2001 book, Vertex Algebras and Algebraic Curves, Math Surveys and
Monotgraphs volume 85, AMS (American Mathematical Society): Providence
Rhode Island USA 2001, 348 pages. Huang's review of the book is in
Bulletin of the AMS, 39(4), 585-591, Jul 10, 2002, also online at
www.ams.org/bull/2002-39-04.
You'll find there simple translations of the physical ideas behind
vertex algebras, vertex operators, CFT (Conformal Field Theory),
chiral algebras, their relationship to Laurent Series, Virasoro
algebras, Laurent polynomials relationships, Quasi-CFT, moduli spaces,
Knizhnik-Zamolodchikov equations, correlation etc.
Edward Frenkel's "Lectures on the Langlands program and conformal
field theory," hep-th/0512172 v1 [math-AG, math-Q] 15 Dec 2005, 128
pages, are intermediate in self-contained clarity and simplicity
between Huang and Witten, by a person (Frenkel) who has pioneered in
most related fields.
Witten's "Gauge theory and the geometric Langlands program", Aug 10,
2005, Talk at Third Simons Workshop in Math and Physics SUNY Stony
Brook New Your, July 25-Ag 26 2005, http://insti.physics/sunysb.edu/itp/conf/simonswork3/talks/Witten.pdf,
has already been mentioned and at times approaches Frenkel and Huang
in simplicity and clarity and intuition, with a mostly string and
brane theory and TQFT orientation.
Osher Doctorow
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