User talk:R.e.b.

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2005 March-2005 October 2005 November-2006 June 2006 July-2006 October

Contents 1 q-series etc. 2 Fermat's last theorem 3 Zariski surface 4 geometrization theorem 5 Elementary proof 6 Abhyankar's conjecture and Abhyankar's lemma 7 AdS space 8 RE: Notation for groups 9 Missing Unsolved Problem Box 10 E8 story 11 Kazhdan-Lusztig polynomials, Hecke algebras

[edit] q-series etc.

Hi,

Just saw your article mock theta function; thanks, good work! Please note also we have articles on q-series and basic hypergeometric series which this article overlaps a little bit, in terms of notation and definitions. linas 17:09, 10 November 2006 (UTC)

[edit] Fermat's last theorem

You changed the article Fermat's last theorem to say that Wiles' proof can be carried out in second-order arithmetic. Do you know of anyone who has been willing to put such a claim in print? At the time of the FOM discussion formerly referenced from the page, nobody there seemed to believe the proof goes through in SOA. I am not familiar with the proof myself, but I carefully read the FOM discussion before writing the former version of the paragraph on set theory in Wiles' proof. I put a fact tag on the paragraph and a note on the talk page looking for references. CMummert 00:30, 20 November 2006 (UTC)

No, and I doubt that there is such a claim in print, though I heard that Angus Macintyre has been thinking about this. However it is reasonably obvious to anyone who knows what l-adic cohomology is. If you are feeling nervous about verifiability feel free to tone down my statement a little (or even delete all references to set theory, which may be the best thing to do). However it is not a good idea to imply that there is any difficulty in formalizing the theorem in ZFC, and I do not recommend using an internet discussion by people who appear to know little about etale cohomology or number theory as a reliable source. R.e.b. 01:30, 20 November 2006 (UTC)

[edit] Zariski surface

Hello. Have you noticed the discussion at Wikipedia:Articles for deletion/Zariski surface? It is proposed that this article be deleted because a now-banned user, Piotr Blass, was its original author. But he was not its original author; you were. (It makes no sense to me at all to consider that a reason to delete an article. Some say his edits to it were in some ways an abuse of Wikipedia editing privileges. But if he's banned, there's no danger of that, so that cannot be a reason to delete it, IMO.) (It does not appear that it will be deleted, however.) Michael Hardy 02:44, 22 January 2007 (UTC)

"Zariski surface" is an obscure and rather pointless topic that only barely passes the guidelines for notability. Charles Matthews added a redlink about them to Enriques-Kodaira classification, which surprised me as I'd never heard of them; after looking them up, I wrote a short note about them mainly to save anyone else from wasting time trying to find out what they were.

Blass's edits to the article are mostly harmless, though they need a lot of copy editing. (On the other hand they don't add much useful for general readers: if everything except the introduction and the reference to Zariski's paper were deleted, it would be no great loss.) The bans and blocks on him are an overreaction: he is (mostly) trying to help and is gradually improving, but is rather slow at understanding how wikipedia works. R.e.b. 04:05, 22 January 2007 (UTC)

Unfortunately for him: we are tightening up on autobiographical editing; and his way of appealing the ban is upper-case only, little coherence and less punctuation. Charles Matthews 16:39, 22 January 2007 (UTC)

That's a good reason for protecting his vanity page from re-creation, but if it is protected then blocking him seems unnecessary. (Though it does save time!) R.e.b. 17:08, 22 January 2007 (UTC)

[edit] geometrization theorem

Geometrization theorem is actually a common name for Thurston's geometrization theorem for Haken 3-manifolds. Nobody actually calls the geometrization conjecture "geometrization theorem". I don't know if you were aware of this; I don't think many people outside the subject do, so this ought to be straightened out somehow. I think the geometrization theorem is of sufficient importance for its own article, with the appropriate link from geometrization conjecture. --Chan-Ho (Talk) 01:08, 28 January 2007 (UTC)

The geometrization theorem is a special case of the geometrization conjecture, so a redirect seems fine until someone writes a separate article. R.e.b. 01:31, 28 January 2007 (UTC)

I've just added the "R with possibilities" template to that redirect page. Michael Hardy 01:39, 28 January 2007 (UTC)

[edit] Elementary proof

Do you have a citation that the distinction between elementary and non-elementary is precisely whether it is doable in Peano arithmetic? I don't think that's correct in that even Selberg's proof uses a small bit of real analysis and it isn't at all obvious to me that it can be converted to a proof that is completely in Peano arithmetic. JoshuaZ 03:20, 6 February 2007 (UTC)

My recollection was that Selberg in his paper carefully eliminated all real analysis. But on rechecking it at [1] I find that he says that he eliminates all real analysis except for the most elementary properties of the logarithm. These can be converted into Peano arithmetic in a standard way by replacing the logarithms with harmonic sums. So Selberg's proof can indeed be converted into a proof in Peano arithmetic, though verifying this not completely trivial. R.e.b. 03:42, 6 February 2007 (UTC)

[edit] Abhyankar's conjecture and Abhyankar's lemma

Thanks for clearing up the confusion over Abhyankar's conjecture, and for creating the article on Abhyankar's lemma. DFH 19:45, 12 February 2007 (UTC)

[edit] AdS space

Please see the discussion page about AdS space. Pierreback 16:26, 28 February 2007 (UTC)

[edit] RE: Notation for groups

Hi R.e.b

IMO the notation GL(n,•) is not outdated nor mathematically inferior to GL_n(•) (it is a functor this way too, like Hom(M,•) ). There is not much difference between the two but I think we should avoid subscripts and superscripts if we can, hence in this context I think GL(n,•) is better. —The preceding unsigned comment was added by Hesam7 (talk • contribs).

[edit] Missing Unsolved Problem Box

R.e.b., why did you remove the unsolved problem box in the resolution of singularities article? Giftlite 17:08, 16 March 2007 (UTC)

Because it just duplicated a sentence already in the introduction. R.e.b. 17:54, 16 March 2007 (UTC)

Then, if you don't mind, I'd like to add Category:Unsolved problems in mathematics to the article. Giftlite 18:02, 16 March 2007 (UTC)

That sounds like a much better idea. Categories dont clutter up an article in the way that navigation boxes do, and are easier to use. R.e.b. 18:45, 16 March 2007 (UTC)

[edit] E8 story

What exactly have they computed for poor old E8 (mathematics)? Is it some structure matrix for the representation ring? Breaking news, but the press stuff has all the vital words taken out!

Charles Matthews 22:34, 19 March 2007 (UTC)

Kazhdan-Lusztig-Vogan polynomials for the split real form of E₈ according to this. I'll wait until the fuss has died down before trying to clean up the article. R.e.b. 22:43, 19 March 2007 (UTC)

Yes, also here.[2] Charles Matthews 22:56, 19 March 2007 (UTC)

[edit] Kazhdan-Lusztig polynomials, Hecke algebras

Hi there, I've reverted some of your recent edits to these articles. Please, do not take it personally, but it seems that some of your contributions are a bit hasty, and sometimes introduce errors. For example, you've added references to Iwahori-Matsumoto, which is fine, but in the wrong place (for finite case instead of affine). Likewise, it may be argued what the true motivations of Kazhdan and Lusztig were, but they very explicitly state that their polynomials measure "failure of local Poincare duality", which is understood to be the non-vanishing of local intersection cohomology of Schubert varieties. I also feel that an encyclopedia is not a proper venue for fleshing out technical details; instead, we need to state the general picture as seen by experts. I would be interested to know your opinion on this. Best wishes, Arcfrk 02:52, 26 March 2007 (UTC)

I did indeed misremember which case Iwahori-Matsumoto did. On the other hand my comments about K and L's motivation that you removed were more or less copied directly from their first paper. I'm a little surprised that they make no mention of IH there if that really was their original motivation. But it's not important enough to spend further time on.

Please don't remove www links to papers that are used as references: they make it much easier to fix misprints, such as the ones in the original version of that section. R.e.b. 03:44, 26 March 2007 (UTC)

OK. Please, also take a look at my comments in Talk:Hecke algebra. Arcfrk 04:53, 26 March 2007 (UTC)

Hello again, in the article on Kazhdan-Lusztig polynomials you wrote

As of 2007, there is no known combinatorial interpretation of the coefficients of the Kazhdan-Lusztig polynomials (as the cardinalities of some natural sets) even in the case of the symmetric groups.

Are you sure that that's true? First, there are definitely formulas for Kazhdan-Lusztig polynomials in some cases, like Lascoux-Schützenberger formulas for Grassmanians, Lusztig's intertpretaion of certain affine Kazhdan-Lusztig polynomials in terms of q-weight multiplicities, etc. One of my goals in creating this subsection had been to expose some of the results from Section 6.3 of Billey-Lakshmibai, especially Deodhar's theorem, I just have not gotten around to that yet. From my perspective, it would not have made too much sense to say "there is combinatorial theory" in the article if there had not been combinatoriral formulas. And also, there was big progress made recently in related questions, this is not a topic for a discussion on Wikipedia, but I would cautiously only vouch for as of June 2006, there was no general bijective formula for KL polynomials for all y,w in the symmetric group. In view of the comments above (some nice formulas exist), however, I do not think such a negative statement should be included in this section. Arcfrk 03:25, 29 March 2007 (UTC)

I'm not absolutely sure; but I saw it mentioned somewhere in a recent publication (Bjorner and Brenti?) as an important and hard unsolved problem. Feel free to update it if you have more recent info about its status (or go ahead and tone it down or delete it if it really upsets you). R.e.b. 03:41, 29 March 2007 (UTC)