Eivind Dahl
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 Oct 8 comment Guide to mathematical physics? I couldn't really say. I mean, if you're interested in 1 dimensional field theory as described in Faria-Melo one could say that you don't really ever need to say "category," it's just a convenient way to think. Though if you're interested in d dimensional field theories, you should probably know about d (or at least d-1) categories. I couldn't tell you what mathematical physicists usually do because I'm not one of them. Maybe I'll be able to send one your way but I can't promise anything, heh. Oct 7 comment Guide to mathematical physics? Yeah well, principal bundles with their connections, vector bundles, lie groups and their representations, operator algebras for infinite dimensional stuff, Lagrangian and Hamiltonian mechanics for the dynamics of states (or the unifying frame work of symplectic geometry), and as always category theory. Cohomology becomes useful for understanding existence of spin structures etc. I'll let someone with more experience write a more comprehensive answer :) Oct 7 comment Guide to mathematical physics? My favourite book so far on gauge theory is "Mathematical Aspects of Quantum Field Theory" by Faria-Melo -- you might find it useful. Oct 5 comment In how many ways can you arrange all letters in the word MISSISSIPPI so that For 1, the symmetric group on 11 letters acts on the set of arrangements of these 11 letters. The stabilizer of any four letters is a copy of the symmetric group on 7 letters. A consecutive arrangement of four I's is determined by the location of the first I (there are 8 possible choices) and by a permutation on 4 letters. Hence there should be about $(11!/7!)\cdot 8\cdot 4!=1520640$ such arrangments. This is assuming two copies of a single letter are different; if not, scrap the copy of $\Sigma_4$ and some of the stuff in $\Sigma_7$. Oct 3 comment Why is one “$\infty$” number enough for complex numbers? By the way, you could consider a closed 2-dimensional disc a compactification of $\mathbf{C}$ with a full circle worth of infinities. Sep 30 comment A smooth non-stably trivial smooth vector bundle Yes so it would appear. I have no idea why I had convinced myself that it didn't. May 26 comment Combinatorics of the Zeta function of a variety 'May be' of course, not 'is' :-) May 26 comment Combinatorics of the Zeta function of a variety Qiaochu: I think what hilbert points out is that a closed point is of codimension $>1$. Nov 22 comment Intuition behind Matrix Multiplication @lhf When you extend multiplication to fractions or the real line like you do, I'm sure you agree that the intuitive 'counting' operation of multiplying integers extends to the intuitive operation of 'scaling'. May 31 comment Prove $\mathbb{Z}$ is not a vector space over a field Nice solution! Getting rid of the simplest (characteristic $2$) case as neatly as possible, and then using this directly to support the initial intuition: "fields have fractions." Om nom chomp. May 2 comment Why is one “$\infty$” number enough for complex numbers? I see your point of view as well; there are apparently many angles on a somewhat open question. My approach was to point out that the dichotomy between the case of $\mathbb{R}$ and $\mathbb{C}$ implied by the word 'instead' could be considered somewhat artificial o_O Apr 14 comment Which functor does the projective space represent? This got way clearer with time. Thanks again :-) Apr 14 comment Which functor does the projective space represent? Ah, the condition that the $r_i$ generate $R$ got much clearer when considering that this means that they do not all vanish at any point. This plugs nicely into thinking about projective schemes as looking for strictly non-trivial solutions to homogeneous equations. Neat :-) Mar 17 comment Which functor does the projective space represent? Thank you! Another good answer. Hard to know which one to pick, but I think I'll go for this one because it is closer to the generality I asked for. I also found this treated in a set of notes by Strickland on formal schemes. Mar 16 comment Which functor does the projective space represent? Thank you! I agree charts might not be all too great for understanding projective spaces, but the first thing I really understood and liked was the projective line, patched together by pieces of $k[t]$. It makes it clear to me why a meromorphic function on $X$ is the same thing as a morphism $X\to\mathbb{P}^1$. This complements nicely the notion of a regular function as a morphism $X\to\mathbb{A}^1$. If I was able to see from the definition of $\mathbb{P}^I$, that this was the case I would be every happy. At least you've told me what I need to stare at until it makes sense :-) Nov 20 comment cup products and smash products Ok, I have no Idea what this question is actually asking anymore, but I'm glad you managed to find a satisfactory answer for yourself. Oct 14 comment What's $F'(x)$ if $F(x) = \int_a^{g(x)} H(x,t) dt$? This is probably the favourite answer I've read on Stackexchange yet :-) So unbelievably natural, thank you! Aug 19 comment Why is one “$\infty$” number enough for complex numbers? I'd love it if that downvote came with a comment. Aug 10 comment False proof of $H_0 ( X) = 0$ That's it, Matt :-) Jul 18 comment intersection of two affine open sets of a scheme Is the union of the $U,V$ off the mark here? A lower bound would be the open set. Am I missing something?