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Oct
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comment first Chern class of complex vector bundles and first Pontrjagin class of quaternionic vector bundles
Regardless of this particular question, in my opinion, "standard characteristic class stuff" like "standard applications of spectral sequences" like "standard facts about Floer homology" etc. are research-level mathematics as far as mathoverflow is concerned.
Oct
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Oct
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Oct
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comment Proposals for polymath projects
One more remark regarding the level of problems. In four out of the five first polymath projects the problems were well known and central open problems in their field (while not among the famous problems of mathematics). Polymath2 was a more open-ended project but it also reflected a question that experts in the relevant field were thinking about for decades.
Oct
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Oct
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comment Proposals for polymath projects
Joel, John and all. I did find a very relevant link about the criteria for choosing the very first polymath project: gowers.wordpress.com/2009/02/01/why-this-particular-problem I think that they are very good (of course, with more projects different criteria can be experimented.)
Oct
1
comment Proposals for polymath projects
John, There could be divide and conquer aspect also when different people work on different avenues of attack on the conjecture which can split and merge during the project. (So this allows in theory sharply different "global view" on the problem.) So far, I think that most participants worked what was considered the most promising avenue. (With competing ideas how to proceed "locally"). Maybe Tim and Terry can say more about experiences from earlier polymath projects. (And perhaps also from the micro projects.)
Oct
1
comment Proposals for polymath projects
Dear Joel, I thing some criteria were proposed (what I meant that we do not know what makes a good polymath project). It is probably good to have that the problem/task itself will have general appeal. I will try to find links to relevant discussions. Dear John, most polymath projects so far did not have a clear divide and conquer nature. The experience so far is that the emerging set of main contributors was not large (5-15, or less, I would say, with a larger group of observers and occasional contribitors) and they all had some global view on the problem.
Sep
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Sep
30
comment Proposals for polymath projects
Dear Joel, I do not think we know the answer to your question. In fact, this is part of what is explored. But there were discussions about it in general and with regard to specific suggestions mainly on Tim's blog.
Sep
30
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Sep
30
comment Proposals for polymath projects
I am curious what could be good polymath projects in areas not represented in polymath projects so far which are amply represented over MO like algebraic geometry, algebraic topology, group theory, differential geometry, probability, representation theory, logic and set theory, mathematical physics and various areas of algebra and analysis, and, of course, in various areas of applied mathematics, and connections between mathematics and other sciences.
Sep
30
comment Proposals for polymath projects
This is indeed a very famous problem. Probably aiming to show that $\zeta (5)$ is irrational, or better perhaps improving quantitatively the results by Ball and Rivoal regarding values of zeta functions at odd integers would be a good project. It is not impossible that in the sequence $a_n$ with , $a_1=$Aperi, $a_2=$ Ball-Rivoal, ... some later terms will have relevance to Euler's constant.