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1500 questions
54
votes
5 answers
Why are the sporadic simple groups HUGE?
I'm merely a grad student right now, but I don't think an exploration of the sporadic groups is standard fare for graduate algebra, so I'd like to ask the experts on MO. I did a little reading on them and would like some intuition about some…
REDace0
- 677
54
votes
3 answers
Serre's FAC in English
Has somebody translated J.-P. Serre's "Faisceaux algébriques cohérents" into English? At least part of it?
In a fit of enthusiasm, I started translating it and started TeXing. But after section 8, I got tired and stopped.
However if somebody else…
Anweshi
- 7,272
54
votes
6 answers
What happened to online articles published in K-theory (Springer journal)?
As most people probably know, the journal "K-theory" used to be published by Springer, but was discontinued after the editorial board resigned around 2007. The editors (or many of them) started the new "Journal of K-theory" in collaboration with…
Andreas Holmstrom
- 5,517
54
votes
2 answers
Lawvere's "Some thoughts on the future of category theory."
In Lecture Notes in Mathematics 1488, Lawvere writes the introduction to the Proceedings for a 1990 conference in Como.
In this article, Lawvere, the inventor of Toposes and Algebraic Theories, discusses two ancient philosophical "categories":…
David Spivak
- 8,559
54
votes
7 answers
Why might André Weil have named Carl Ludwig Siegel the greatest mathematician of the 20th century?
According to Steven Krantz's Mathematical Apocrypha (pg. 186):
As was custom, Weil often attended tea
at [Princeton] University . Graduate
student Steven Weintrab one day went
about the room asking various famous
mathematicians who was the…
Jonah Sinick
- 6,942
54
votes
2 answers
Is primary decomposition still important?
On p.50 of Atiyah and Macdonald's Introduction to Commutative Algebra, in the introduction to the chapter on primary decomposition, it says
In the modern treatment, with its
emphasis on localization, primary
decomposition is no longer such a
…
David Corwin
- 15,078
53
votes
6 answers
Colimits of schemes
This is related to another question.
I've found many remarks that the category of schemes is not cocomplete. The category of locally ringed spaces is cocomplete, and in some special cases this turns out to be the colimit of schemes, but in other…
Martin Brandenburg
- 61,443
53
votes
8 answers
Analogue to covering space for higher homotopy groups?
The connection between the fundamental group and covering spaces is quite fundamental. Is there any analogue for higher homotopy groups? It doesn't make sense to me that one could make a branched cover over a set of codimension 3, since I guess,…
j.c.
- 13,490
53
votes
2 answers
Connections between various generalized algebraic geometries (Toen-Vaquié, Durov, Diers, Lurie)?
As far as I know, there are four possible ways to generalize algebraic geometry by 'simply' replacing the basic category of rings with something similar but more general:
$\bullet$ In the approach by Toen-Vaquié we fix a nice symmetric monoidal…
Martin Brandenburg
- 61,443
53
votes
3 answers
Grothendieck's manuscript on topology
Edit: Infos on the current state by Lieven Le Bruyn: http://www.neverendingbooks.org/grothendiecks-gribouillis
Edit: Just in case anyone still thinks that Grothendieck's unpublished manuscripts are (by his letter) entirely out of sight: Declared as…
Thomas Riepe
- 10,731
53
votes
8 answers
Physicist's request for intuition on covariant derivatives and Lie derivatives
A friend of mine is studying physics, and asks the following question which, I am sure, others could respond to better:
What is the difference between the covariant derivative of $X$ along the curve $(t)$ and a Lie derivative of $X$ along $y(t)?$ …
Igor Rivin
- 95,560
53
votes
5 answers
Motivating the Casimir element
Weyl's theorem states that any finite-dimensional representation of a finite-dimensional semisimple Lie algebra is completely reducible. In my mind, the "natural" way to prove this result is by way of Lie groups. However, as a student, I first…
Timothy Chow
- 78,129
53
votes
4 answers
Explanation for the Chern character
The Chern character is often seen as just being a convenient way to get a ring homomorphism from K-theory to (ordinary) cohomology.
The most usual definition in that case seems to just be to define the Chern character on a line bundle as…
Sam Derbyshire
- 5,440
53
votes
9 answers
What is the shortest Ph.D. thesis?
The question is self-explanatory, but I want to make some remarks in order to prevent the responses from going off into undesirable directions.
It seems that every few years I hear someone ask this question; it seems to hold a perennial fascination…
Timothy Chow
- 78,129
53
votes
17 answers
Computer science for mathematicians
This is a big-list community question, so I'm sorry in advance if it is deemed too soft but I haven't seen anything similar yet.
I've seen computer scientists post questions looking to learn things from pure maths. This is basically the other way…
Spencer
- 1,771