I went to a talk a couple days ago that I told you about and while I didn't follow well, it has finally convinced me that the stuff is cool. I'm sorta wondering, aside from commutative algebra, what do you think one should know going in?
On the internet (read: reddit) there's back and forth about whether folk should know complex geometry going in, so I was wondering your take on that in particular, but also in general.
In fact, I think that to prove reading competence in French in grad school, Mo Hirsch might have given us Thom to read and translate. More words than symbols, but that didn't bother me.
@Balarka, does your starred comment suggest that in India there's as much drunken partying among college students as there is in the US? That surprises me.
I was reading a book, called "Academically Adrift", and I was surprised to see that what I am seeing in the student culture has been happening for decades in US
Oh but Hinduism is like, old. And historically it was way more liberal than the rest as well. Buddhism basically doesn't exist in any form in the current times.
So I think we on effect of Hinduism is not far off from people on effect of Christianity in the West. There's no religious ethics that's ingrained.
@TedShifrin I like the simile between US and India right now, even though the former is the rich capitalist first world and the latter is the pathetic third world. Both our societies are a wreck at this point, both of us have elected a neofascist government, both of us think of the country as a religious sanctuary of one particular religion(Islam is somehow a problem for both of us), and we're doing the best we can to convert democracy into imperialism of the industry
@ÉricoMeloSilva i need to read latin america literature though, thankfully most of them are translated
@TedShifrin this is actually a moon logic take from this person though bc the media (both in the anglophone and lusophone world) is largely uncritical of that absolute POS bc he’s great for transnational business interests, at best they’re tepidly criticizing his neofash style, but by and large the media has no interest in being honest about how bad he is (i guess cause he’s not bad for you unless you’re working class or marginalized in some way)
"Any two contact embeddings $j_i$, $i = 0,1$, of $B_{st}$ into a connected contact manifold $(M,\xi)$ (with $\dim B_{st} = \dim M = 2n + 1$) are contact isotopic."
Consider the minimization problem described this paper. Let $f_{\lambda}$ be the minimizer. As a part of extending my work, I am able to show the following facts
$$\lim_\limits{\lambda \to 0}\|f_{\lambda}\| = 0$$ and $$\lim_\limits{\lambda \to \infty}\|f_{\lambda}\| = 0$$
My problem now is (as ...
I don't know why but many books remove the necessary definition of a manifold being hausdorff. Hausdorffness is a very important condition. It removes in a certain sense all the wonky topologies you can give to it. But books don't even mention it. Do they inherently assume that the space they are working with is a subspace of R^n?
Sure, many books, including Guillemin-Pollack, define manifolds as subspaces of R^n
non-Hausdorff locally Euclidean spaces are not that important to pay attention to. They definitely do come up in literature (leaf spaces of foliations) but they're not the central object of study
Neither are non second countable guys
A manifold is a Hausdorff second countable locally Euclidean space. Period.
That is true. But like if I don't mention Hausdorffness then when it comes to the smoothness condition of the transition function, I can define my open sets in a certain way which will make a lot of not smooth things seem smooth. That's why I thought that the Hausdorff condition should be put. But again if you just say it as a subspace of R^n its all fine.
I woke up this morning to find that I suffered massive drop in points across network because of lots of users were removed .
What happened to those users? Was there a database cleanup?
Hello. If one wants to compute the integral of a two form, say $\omega = y dx\wedge dy + z dy\wedge dz$ on the submanifold given by $z=16-x^2-y^2$ and $z>0$ of $\Bbb R^3$, how one approach this?
Do I reduce this to a classic calculus type double integral somehow? Perhaps something like $$\int \int (16-x^2-y^2)y dxdy + \int\int (16-x^2-y^2)z dydz,$$ with the appropriate regions (and appropriate orientations by placing an orientation on the submanifold)? Or something else entirely
What can you say about your submanifold? And $\omega$?
Stokes' theorem is a general statement about integrals of a form and it's exterior derivative over a manifold with boundary, not just something which is to be used only when you see an exact form.
If $z$ is strictly greater than zero, my manifold is without boundary right? and if my form $\omega$ was exact (and it were $z\geq 0$), with $d\gamma = \omega$, I would be able to integrate the 1-form $\gamma$over the boundary circle
My submanifold is orientable, and my form is closed
I guess my region is closed and bounded and hence compact too, is the other thing you wanted me to observe
You're working with the wrong dimensions. Your submanifold doesn't have boundary, but is bounded by a domain. Namely, consider the interior of the paraboloid.
@F.White Not quite, you have $z > 0$ there. It's not closed, but forget about that for now.
Just suppose that you were given the submanifold $S = \{(x, y, z) \in \Bbb R^3 : z = 16 - x^2 - y^2\}$.
(1) I should have written $V = \{(x, y, z) \in \Bbb R^3 : z \leq 16 - x^2 - y^2\}$ up there (2) Remember to not forget that your submanifold is $S \cap \{z > 0\}$ when writing a solution for your problem (but that isn't a problem).
I have a question about sparse matrices on the Wikipedia page (en.wikipedia.org/wiki/Sparse_matrix#cite_note-5). Under the definition of IA, it says "Thus, the first m elements of IA store the index into A of the first nonzero element in each row of M..". I just can't make sense of that. It seems like this differs from so-called row pointers that I'm familiar with in a sparse matrix. The elements in IA add up the non-zero elements of M, but then I don't understand the thing with indices?
Scroll up or down in the article to "Compressed sparse row (CSR, CRS or Yale format)"
Consider the minimization problem described this paper. Let $f_{\lambda}$ be the minimizer. As a part of extending my work, I am able to show the following facts
$$\lim_\limits{\lambda \to 0}\|f_{\lambda}\| = 0$$ and $$\lim_\limits{\lambda \to \infty}\|f_{\lambda}\| = 0$$
My problem now is (as ...
I woke up this morning to find that I suffered massive drop in points across network because of lots of users were removed .
What happened to those users? Was there a database cleanup?
