Talk:Daniel Quillen

Paper by Mathai and Quillen
User:128.135.227.154 removed the sentence "Amongst his collaborating mathematicians is his former PhD student Mathai Varghese", with the comment: "Removed reference to Mathai. The wrote one (not very important) paper together in the 1980's. Quillen has written many papers with a variety of coauthors." I do not see this as justified. First of all, yes, Quillen wrote many papers, with several coauthors (not that many of them, actually), but, as far as I know, the paper with Mathai (Superconnections, Thom classes, and equivariant differential forms, Topology, 1986) is the only one he wrote with one of his PhD students, and this is a good way to bring that aspect of Quillen's career in. And second, I also disagree with the assessment that that is not a "very important" paper: not among the very top papers of Quillen, to be sure, but quite a significant paper, nonetheless -- the basis for the "Mathai-Quillen formalism", it is listed on MathSciNet with 39 quotations from articles and 18 from reviews (which is quite a bit), while on Google Scholar it registers 161 citations (which is really a lot for a math paper). Turgidson 04:55, 18 March 2007 (UTC)

The reference was in the midst of a long discussion of Quillen's most famous work (right between the higher K-groups and the proof of Serre's conjecture). Though his paper with Mathai is certainly important in its subarea, it is not anywhere close to the level of the work mentioned (for comparison, the paper in which Quillen defines higher K-groups has 290 quotations from articles and 72 from reviews on mathscinet). Moreover, there are many unmentioned things Quillen did which are (by any standard) much more important than his paper with Mathai (for instance, his "Homotopical Algebra" paper and his paper on "Rational Homotopy Theory"). If we were going to discuss collaborations, one should first mention the strange fact that Quillen didn't collaborate much to put it into context. Next, we would have to discuss Quillen's more important collaborations (for instance, his collaboration with Cuntz which resulted in 6 papers, some of which are often-cited). One possibility if people are dead-set on mentioning Quillen's work with Mathai is to have a separate section on Quillen as an advisor, but I'm not really sure what would go there -- according to the mathematics genealogy, Quillen only has had 6 students, which is quite a low number. Perhaps we should make a list of students at the end of the article, with a link to the (already existing) article on Mathai, which goes into some detail about the Mathai-Quillen formalism (which, of course, has played a much larger role in Mathai's career than in Quillen's). 128.135.227.91 07:38, 18 March 2007 (UTC)


 * I fully agree, the article is far from finished -- it should be rated somewhere between a Stub and a Start -- and important information is still missing, for example, the paper on "Rational Homotopy Theory", which must rank among the top 10 most influential papers in Algebraic Topology, ever. But that's the idea of wikipedia -- one starts small, and builds up the article, with input from many editors. Deleting stuff because the perfect pitch has not yet been reached is not quite the way to go. Much better is to add content to the article, and, if an issue like this arises, talk about it first on the Talk page (like we're doing now) before taking drastic action. At any rate, this is one of the articles I plan to work on more when I get a chance, I will see what I can do.  Turgidson 15:08, 18 March 2007 (UTC)


 * Fair enough. I've done a rearrangement of the Quillen page and restored the reference to Mathai in a more appropriate context (a list of students).  I've also added references to the theory of model categories and rational homotopy theory.  Someone (perhaps me when I have a large block of free time, but I'm in the midst of writing several long papers right now, so it won't be soon) should expand each of the entries in the "Selected Mathematical Contributions" into a separate section. 128.135.227.91 16:31, 18 March 2007 (UTC)


 * Looking good. I'll add a selected list of papers when I get a chance -- basically the ones mentioned implicitly in the text, plus a few others (eg, the one in J. Algebra about the associated graded ring of a group ring, which I think is a little gem, also quite influential).  Turgidson 16:42, 18 March 2007 (UTC)

Assessment comment
Substituted at 12:47, 29 April 2016 (UTC)

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