Comments on: A draft version of the blog book

By: Google, Wikipedia and blogosphere « What Is Research?

Google, Wikipedia and blogosphere « What Is Research? — Sat, 14 Jun 2008 22:58:36 +0000

[...] idea of what goes on inside mathematics, has experimented with a number of ventures, ranging from a blog book (a book in blog form) to making a contribution to Scholarpedia, a site that aims to aggregate [...]

By: hasan

hasan — Tue, 13 May 2008 15:01:42 +0000

thanks

By: Karlik

Karlik — Wed, 30 Apr 2008 14:51:56 +0000

page 183, line 6 from bottom
\alpha \leq maxflow -> 1/\alpha\leq maxflow
and in Menger’s theorem
max-flow -> maxflow

By: Terence Tao

Terence Tao — Fri, 25 Apr 2008 00:32:01 +0000

Thanks for the corrections! I’ve restored the last few paragraphs of the Tomb Raider article, which had mysteriously gotten lost earlier.

By: Gil

Gil — Wed, 23 Apr 2008 10:47:34 +0000

A couple more corrections:

1. p73, “that combination down on two piece of paper (one for Lara, one for Indiana),”
Should be pieces.

2. p103, under Algebra Homomorphism, the product limit equality is wrong (or rather, is right, but is the wrong equality).

I’m also rather interested in the conclusion of the wonderfully bright Tomb Raider article. It’s been snipped off in such a cruel way ;)

By: Emmanuel Kowalski

Emmanuel Kowalski — Tue, 22 Apr 2008 18:26:16 +0000

Harald’s comment (a) is correct, and is stated in various places when ‘generic’ is in the sense of algebraic geometry (or more concretely, in a semisimple group, there is an open dense subset of regular semisimple elements, in the Zariski topology). For instance, I’m pretty sure it’s in Borel’s book on linear algebraic groups, and I just checked it’s explicitly stated in Steinberg’s paper “Regular elements of semi-simple algebraic groups”, Publ. IHES 25 (1965), 49-80, which can be downloaded from http://www.numdam.org (see 2.14 there).

In fact, one can also ask the slightly stronger property of “strong” regularity, meaning that the centralizer of the element is a maximal torus (another standard fact being that regular semisimple elements are those with centralizer whose connected component of the identity is a maximal torus; see 2.11 in Steinberg’s paper). For a group like SL(n) - “simply-connected” being the keyword -, regular and strongly regular coincide (another theorem of Steinberg), but for SO(n) or PSL(n), it’s not necessarily the case. The genericity of strongly regular elements is 2.15 in Steinberg’s paper.

(Another comment about url’s: the LaTeX package url has a macro \url{…} which typesets long URLs with line-breaks; whether it’s a good thing to have line-breaks is debatable, but at least it avoids oveflowing lines).

By: Terence Tao

Terence Tao — Tue, 22 Apr 2008 17:48:09 +0000

Thanks for the comments and suggestions! I may upload a second revised version soon to incorporate them.

By: Harald Helfgott

Harald Helfgott — Tue, 22 Apr 2008 16:31:43 +0000

Two comments:

(a) I would not say that the fact that two elements that commute with a third one are likely to commute with each other is specific to SL_2. That fact is true for SL_n, and, if memory serves me correctly, for any semisimple group of Lie type: a generic element of a semisimple group is regular semisimple. (It would be nice to have a reference for this, actually.)

(b) Less importantly: my paper on SL_2 finally appeared last month.

By: tom

tom — Tue, 22 Apr 2008 13:16:47 +0000

In some URLs you mention at the end of each chapter a tilde is missing sometimes, for example in the one of Tim Gowers at paragraph 2.9.5. I think in the LaTeX code you should use \~{} instead of ~ to force it to print.

By: harrison

harrison — Tue, 22 Apr 2008 00:05:43 +0000

Various typos, grammatical inconsistencies, etc. (what I could find in part one while procrastinating on homework):

p. 4: In the parenthetical comment, “the implicit constants in the conclusion depends on…” should probably be “the implicit constants in the conclusion depend on…”

p. 11: Is the plural of PDE “PDE” or “PDEs?” You use both here and elsewhere. (Same for “ODE” vs. “ODEs.”)

p. 14: “repeats” is misspelled as “repeates.”

p. 18: “Simply sticking in the existing energy bounds into the Navier-Stokes
equation and seeing what comes out will provide a few more bounds…” “Sticking in into” is redundant.

p. 32: There is an open parenthesis that needs a complementary close parenthesis.

p. 33: “invariant” is misspelled as “invraiant.”

p. 44: There is a close parenthesis without an open parenthesis.

p. 44-45, elsewhere: There looks to be a formatting issue with “modp,” etc.

p. 47: There’s a parenthetical comment which should probably be in parentheses which is in brackets.

All page numbers refer to the pdf of the new version.

Best,

Harrison