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00:00
@Hippalectryon So I guess the format needs to be further improved, but for the lemma I tend to think that writing $lim_{a,b\to \infty}\frac{a}{b}$ should fine, no?
this proof on wikipedia that two disjoint open convex sets can be separated by a hyperplane seems to be incomplete, in that it doesn't explain why the sequence of hyperplanes must converge: en.wikipedia.org/wiki/Hyperplane_separation_theorem#Proof
I have to go eat some empanadas.
Be back in a while.
@UserX True story: I once gave my girlfriend a Sierpinski Gasket made from coloring squares in a graph paper red/blue according to even/oddness of the corresponding numbers on Pascal's triangle. This particular gasket was heart shaped (starts off as a triangle but later curves inwards). We're still together. Yeah, she's every bit as nerdy as I am :p
@VincenzoOliva What is g in the line before you define it ?
00:04
@Hippalectryon Perhaps I should replace $a$ and $b$ with functions of the same variable, but then it wouldn't really reflect my original situation.

A random function. My professor agreed with that, but I don't trust him at all... though I would tend to think that's right, but again, I'm asleep
Random is vague
Continuous ? $\mathcal{C}^1$ ? ... ?
Don't say yeah when I ask 'A or B or C ?' xD
Who else hates working with fractions (my homework atm :L)?
Fractions are cool
00:07
@Hippalectryon Everything here is defined on the naturals, so continuous/differentiable are trivially, automatically true.
I have to "show my work" with homework, so this sucks...
I don't have calculators
@MikeMiller I don't know the context :/
Me neither, @Hippa
@MrSquer You're in a math chatroom. There are good odds that we like fractions, and bad odds that we're sympathetic to your homework woes.
@MikeMiller Well then again, I'm in 5th grade (I don't make well with most people...)
@MikeMiller @Hippalectryon I'll try to introduce it to you in a momeny
moment*
by showing what my ultimate goal is
00:09
I'm okay without context, @Vinenzo.
To destroy the Earth?
@Mike Oh, well. Any remarks on that lemma?
@Hippalectryon lol
No. Just remarks on Hippa's remarks.
I see
My aim is to prove the limit equality:

https://scontent-b-mxp.xx.fbcdn.net/hphotos-xpf1/v/t1.0-9/10421338_846746548720988_2512930349729295820_n.jpg?oh=e49ba7a80d071593cdee5e7336724f31&oe=54DE034C
Where again, @Hippalectryon, $p_l$ is the largest prime factor of the $m$-th superabundant $SA_m$.
I'm not really into NT :/
00:14
:/
Still eating, @PedroTamaroff ? :v
@VincenzoOliva I'm back.
I must say, though, that I have little interest in pursuing the matter further.
And that I don't think it is of much benefit for you to keep pushing for a proof of the Riemann Hypothesis.
It will tarnish your work.
It's not that I'm deluded. I'm just working on something that I think it could work. Only because the odds are low, it doesn't mean it's better not to try. And after all, at the very least, I've improved since when I began
@VincenzoOliva I partially agree.
Besides, Karl did not find errors after that limit equality, if I'm not mistaken, so I believe I really should try to prove that.
Do you recall other errors?
@PedroTamaroff
I'm pretty sure he does not want to engage on the mathematical content here.
00:26
@MikeMiller Do you mean Mike or Pedro?
lol
*Karl or Pedro
Pedro.
I base this on the fact that he said he doesn't want to.
I've not reposted the lemma, indeed. I was following up a different matter.
But I guess @PedroTamaroff has little interest in it too, fair enough.
my homework contains this statement:
is the bottom or an $\oplus$, or is $\vee$ inended?
(the actual question is to prove prime implies irreducible in integral domains)
@GBeau: it's or.
00:40
@TedShifrin specifically, the question is rather $\oplus$ is necessary to prove the latter, since of course you couldn't divine his intended meaning otherwise
Yup, @Pedro, cool theorem. Love the hands-on way of introducing the convergence factors.
which is what you point out
I don't understand, @GBeau.
as in, if "or" is interpreted as $\vee$, then would what I'm being asked to prove actually be untrue?
I got beat by two minutes here but I have a little more detail in my answer. Should I keep it or delete it?
00:41
No, in math or means $\vee$ (this allows the possibility of $\wedge$)
@Mike: shrug
lol
I was surprised to see that I couldn't find this in Hirsch, which was where I looked first.
@GBeau Why are you trying to parse things in symbols?
though I suppose showing $C^\infty(M,N)$ is dense in $C(M,N)$ automatically gives the result
It's hidden, but it's there. He has all sorts of $C^k$ approximation theorems in chapter 2 (or 3?).
Prime is $p\mid ab\implies p\mid a$ or $p\mid b$. That's it.
00:44
2, yes.
He just never uses the word "homotopic" in there.
For example, $4$ is not prime since $4\mid 4$ but $4\nmid 2$.
@PedroTamaroff I thought only one way was true for the way I was trying to prove it but I was wrong
I can't parse that sentence.
@GBeau Have you ever been as far as decided?
@PedroTamaroff yes
00:45
@GBeau Good.
Hi all
lol
hi drust
@GBeau So, a prime element is one which satisfies Euclid's lemma.
@PedroTamaroff I think I have proven it
@GBeau What definition of irreducible are you using?
00:48
@PedroTamaroff the one posted above?
@GBeau OK.
does anyone know when arxiv gets updated?
So you want to show that prime elements are irreducible.
seem to remember being in the evenings EST? but don't take my word for it
(that's my writing, I just need to fill in the logic, but I think that method resolves it)
00:51
@GBeau Yes. $r=ab\implies r\mid ab$, WLOG $r\mid a$, $rc=a\implies rcb=ab=r\implies cb=1\implies b\in R^{\times}$.
eugh $q_a$
Of course your ring is actually a domain.
One defines factorization in domains.
with it being notable that I could only "cancel" because it was an integral domain
which was defined in the question as commutative rings without zero divisors
@GBeau IN-DEED.
@Pedro remembers when he was just learning this stuff :)
00:54
@TedShifrin Seems like too long ago.
hi pal @JasperLoy
@Pedro: What mod showdown?
hi @skull
@skullpatrol Hi, I just woke up.
hi @Jasper
:O didn't know Eugene Dynkin had died
00:56
Hello Professor @TedShifrin
@TedShifrin Two mods dropped by.
ah, yes, @DanielR, one of my former colleagues (who's now in GB) posted that on FB a few hours ago
@TedShifrin Hi. Don't worry, I am not ignoring you, lol.
for once it wasn't my fault, @Pedro :D
Yeah, I found out through facebook too. how sad
00:56
I was afraid they were going to battle like Groudon and Kyogre.
And kill us all.
Timely reference @Pedro
@DanielRust I happen to know of Dynkin diagrams, despite being a banana, lol.
@MikeMiller Ah?
They're remaking those
WHAT.
DID.
00:57
A Lie banana, no doubt, @Jasper. (No, not Lee.)
YOU.
JUST.
SAID?
I can have my childhood back?
"Remaking" is the wrong word, since they come out in three days.
My childhood was ruined and it will never come back.
Really brightening conversation in the room, @Jasper.
@JasperLoy Dang Jasper.
00:59
I hope to have a better one next life, hopefully in Germany.
You just dropped a blackstorm all over chat.
Buddhism gives you all hope. Believe! LOL.
He had a long life and career at least :)
01:02
I have no life and no career.
the speaker in our seminar today was even using the finite dynkin diagram calssification
The publisher Assimil did not reply to my email, sad. I was going to buy a few books from them, lol. Now they have lost a valuable customer.
what was the seminar on, @DanielRust?
cluster algebras and quiver mutations
get something out of it?
01:07
@DanielRust Sounds deep as fudge.
most seminar titles do
there's going to be one tomorrow called "Equivalent notions of high dimensional overtwistedness"
I'm not an algebraist so most of it went over my head, but there was some topology in the talk too which was interesting
what do you study?
kind of in the intersection of algebraic topology and dynamical systems
Care to elaborate? :)
01:13
haha sorry sure
so I look at the Cech cohomology of moduli spaces of aperiodic tilings
now you've sold me
so spaces where the points are, for instance, the penrose tilings of the plane
aperiodic tilings in what sense? I can't think of a way to formulate what an aperiodic tiling should be that permits a reasonable moduli space
ah, I was being silly
I was thinking of tilings by ominoes
if you take a single tiling T, and then consider all other tilings which are locally the same (so any two patches in one can be found in the other), then that's the 'tiling space' of T
patches*?
sure
01:16
some compact union of tiles
have you attended any lectures by penrose?
just commenting on patched vs patches; didn't understand if it was the former
no :( he gave a public lecture at my department the year before I joined apparently
oh sorry, typo :P
so yeah, for periodic tilings, the moduli spaces are boring. they're just a torus of dimension the space you're tiling
for non-periodic tilings they can be much more wild
sure, I believe that
if they're 'regular' for some definition of regular, then the spaces associated are fiber bundles over a torus, with Cantor set fiber
01:19
that's insane
they're fun :)
so they're connected, compact metric spaces, but with uncountably many path components
@MikeMiller Szemeredi is giving a talk at mi uni. =D
oh and good timing... the preprint for my first paper just went online :D
How far into your studies are you?
@PedroTamaroff When are you giving a talk?
I guess the comparison between UK and US might not be so cut-and-dry
@JasperLoy Give or take 3 years, when I defend my thesis..
in the UK you start a phd with a masters and it takes 3-4 years to complete
01:22
@DanielRust Congratulations.
I'm just over 2 years into mine
Why don't you go by Dan here?
haha I don't know.
you don't understand how long it took me to decide to go with Dan instead of Daniel :P
Article's got a lot of pictures and diagrams, which I dig.
Trust me, I understand that, @DanielRust
My full name's Stephen Michael Miller. :P
LOL @ Chacon
01:23
@MikeMiller :)
I think when the time comes to decide what I want to publish as, I'm probably going to as S Michael Miller
There are just too many of us to go by Mike Miller alone, I think
@MikeMiller That explains the email, lol.
yeah, I'm lucky that I have a fairly uncommon surname
@MikeMiller I will call you Stephen from now, lol.
01:24
although I did find a D Rust that works for CERN apparently
Please don't, @Jasper.
@MikeMiller OK, but I will edit my email records accordingly.
@PedroTamaroff kill it with fire
@DanielRust You never heard of "Steven", with "PH"?
Phteven.
01:27
@PedroTamaroff Am I missing an inside joke?
@DanielRust It's a meme.
Phteven. Google it.
here's me thinking reddit kept me up to date with memes
@DanielRust So what led you to get into this line of work?
@TedShifrin - Hi, are you familiar with stochastic differential equation?
I don't know the meme either, so.
01:29
I hope Chris comes back.
No, @Victor, sorry.
@MikeMiller I used a fair bit of algebraic topology in my masters thesis so I started looking in the UK for AT researchers that were looking for students
@Pedro: You're violating your own rules here!
ended up getting a funding offer from Leicester and a couple of other places
oh, hi @DanielR :)
01:31
and I felt my supervisor in Leicester was the best fit for me :)
Considering the first result when I googled moduli spaces of aperiodic tilings, I think I can guess who you're working with.
@TedShifrin Hey Ted
@MikeMiller Well my supervisor actually moved to a different uni last year :P, so I have a new supervisor now
though I'm working on the same sort of stuff
Ah
this was what I saw; really neat connections
Yeah, John was my supervisor
Now it's Alex Clark
01:34
LOL
he's not aged well apparently
I guess that's not him.
hahaha
'matchbox manifold' is an interesting name
yeah, tiling spaces are a subclass of matchbox manifolds
I guess foliation theory is still alive and kicking; Thurston's article (on proof and progress) had given me the impression it had sort of cleared out
@TedShifrin Where?
pictures above
01:37
@MikeMiller I think folliations of manifolds has slowed down quite a bit. But foliations of other kinds of spaces are starting to become trendy
@TedShifrin How so?
I guess I'm not quite sure what a foliation should mean in other contexts
I suppose it generalizes naturally if you've got a class of spaces... so you might study foliations of matchbox manifolds by matchbox manifolds?
Well for instance a solenoid carries a natural foliation by real lines
which are just given by the path components
so you're still foliating with manifolds?
you have to be a bit careful about how you define foliation of course
yeah
01:40
alright
tbh I don't know a great deal about that side of the theory though
hey, you're in good company
or maybe I'm bad company; but either way, you're in company
@MikeMiller always appreciated :D
@MikeMiller So what are your interests atm?
I suspect I might become a topologist
I'm a first year which in these parts means we don't have explicit interests or advisors yet
I'm taking a course on gauge theory next quarter though, and if it goes well I might approach the professor about a reading course on Heegard Floer stuff
@MikeMiller ooo nice, I attended a low dimensional topology workshop last summer
Heegard Floer stuff was everywhere
01:45
it's definitely hip
Do you know Jake Rasmussen?
I don't.
have you met robjohn?
I don't really have a good grasp on who works in the field
He's one of the big names in knot theory atm, although I guess he's more Khovanov Homology than Heegard Floer
01:46
I'm not convinced I care about knots yet, but I am convinced I care about 3- and 4-manifolds, so I guess I automatically have to care about knots.
Anyway, he lead one of the workshops
haha yes
I don't think I appreciated knots until I studied braids
xypic is good for typesetting knots, braids and links.
I guess he probably taught the 3-manifolds course my friend took at Part III last year
I've still not used xypic. I used tikz in my paper
The diagram on page 16 took me about 2 hours to make in tikz
I think pstricks is the best.
01:49
is your paper publicly available?
Yes. As of 15 minutes ago. arxiv.org/abs/1411.4991v1
2
yeah, it's a nice one @Daniel
so far I've gotten away with only needing to know some basic photoshop
@DanielRust thanks for sharing :-)
@MikeMiller tikz is really powerful, but the learning curve is steep. I'm still at the foot of the mountain
@skullpatrol np :) I'm just happy if people read it (and if it gets accepted)
tikz is the most popular these days. I think it is simply because it produces PDF directly and has a good manual.
01:51
Where are you sending it off to?
tex.stackexchange have a strong tikz community which helps
ps, re: your workshop; what were some sources you looked at during it? I'd like to amass some things to read :)
@MikeMiller that's a good question. A lot of it was just board work.
maths.dur.ac.uk/~ddmb48/LMS_Durham_Short_Course.html page for the workshop, though can't find slides
the lectures themselves look nice
weird question; do you know if every $2n$-manifold supports a symplectic structure?
it was a fun week
erm, I don't think so...
I don't know :P
01:57
seems odd to me but google's not supplying one that doesn't
haha
eh, whatever
found a wiki article that says no
Additionally, if $M$ is a closed symplectic manifold, then the 2nd de Rham cohomology group $H^2(M)$ is nontrivial; this implies, for example, that the only $n$-sphere that admits a symplectic form is the 2-sphere.
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold. == Introduction == A symplectic geometry is defined on a smooth even-dimensional space that is a differentiable manifold. On this space is defined a geometric object, the symplectic form, that allows for the...
ah, yeah, that was the guess I had that I deleted
that it might be stopped by homological reasons
there's a talk on Thurs that says that every $2n+1$-manifold supports a contact structure except for homological reasons; not entirely sure what homological obstructions there are but it inspired a reasonable guess for symplectic ones
02:02
I'm gonna be off but fun chatting!
@MikeMiller you too. And yes I need to go to bed now.
02:38
@BalarkaSen
@PedroTamaroff
Er. Why did ya ping me?
@BalarkaSen You wanted an exercise.
I don't recall but I'd be glad to have something to think about.
So where's this exercise?
OK.
So, take a metric space $X$, and a set of continuous functions $f:X\to\Bbb C$.
Call this set $F$.
$\mathcal{C}(X, \Bbb C)$ dude.
02:48
Suppose the following is true: for any sequence of functions in $F$; there is a subsequence that converges uniformly on every compact subset $K$ of $X$.
mmkay.
Prove the following holds:
For any $x\in X$; there is an open ball $B=B(x,r)$ and $M>0$ such that $|f(y)|<M$ for any $f\in F$ and $y\in B$.
Do you guys know where I can find a proof of a generalization of the Stone Weierstrass approximation theorem for $C(\Bbb T)$ and polynomials with negative exponents?
noted.
@BalarkaSen My help is as follows: negate the last statement.
Can you do this?
02:53
hint noted too. i need to go somewhere at the moment and i'll ping my approaches when i get back, @Pedro.
@KajHansen Wanna do that exercise?
03:13
@DanielRust Oh man :( Sucks to be a mathematician who dies one day after Grothendieck.
@Pedro I've told you that (given some extra structure on these algebras) $C(X) \cong C(Y)$ iff $X \cong Y$, yeah?
Where $X,Y$ are locally compact Hausdorff.
@MikeMiller Eh, no.
That shit cray dude.
We have a lot more than that, too. Spaces are the same thing as commutative algebras.
Stone stuff?
This is Gel'fand duality. Stone duality is related but different.
Birth of noncommutative geometry, by the idea that noncommutative C* algebras should then be like "noncommutative spaces", and we should investigate them with the same tools.
03:23
OK.
I'm telling you, this stuff is your jam.
There's group theory in there too.
hi other folks btw
04:10
@MikeMiller We'll see.
I don't know if I'll learn that in my uni, though.
You will. I know it.
04:28
What's $\displaystyle\lim_{\epsilon\to0}\left[\operatorname{Im}\left(\frac{(1+i)^ \epsilon} \epsilon\right)\right]$?
$\epsilon$ is real.
Got to go!
Bye.
Before I go: perhaps the generalized binomial theorem can help us here? Or Euler's formula.
@columbus8myhw Yes.
05:17
@DanielFischer how did op's comments get three upvotes I wonder...
@anon no need to wonder; sockpuppets
that's what the ... was for
don't I feel silly
05:33
@columbus8myhw Euler's formula
 
1 hour later…
06:55
@MikeMiller Hey Mike!
@MikeMiller Are the following spaces homeomorphic? $D^2/\sim$ where $x\sim -x$ for $x\in S^1$ and $S^2/\sim$ where $x\sim -x$ ?
Yup
They're both $\Bbb{RP}^2
Ok nice!
hellllllllllllooooooooooooooo
hi
who likes lady gaga?
07:14
@robjohn Could I ask you about something that just came up that's really bothering me? It's not a math question.
@RandomVariable okay
@columbus8myhw $\pi/4$
@robjohn I edited an old answer of mine because it had bad formatting. But then I learned my answer had already been posted on here. It has received a bunch of upvotes since it edited it. I don't want the upvotes. Could I possibly be dissociated from it? math.stackexchange.com/questions/725592/…
I already voted to close it as a duplicate.
@RandomVariable May I ask why you don't want the upvotes? That's strange.
@Twink Because the other person deserves them. He posted the answer 2 years before I did.
But you can't decide who are others' upvotes for
07:29
@RandomVariable so the question is a duplicate. It is not easy to find duplicates and it was only recently pointed out to be a duplicate. Simply voting to close as a duplicate is good enough. Since it is accepted, I shouldn't delete it, but if you can convince the OP to unaccept it, you can delete it. Otherwise I can look into removing your name from it.
@RandomVariable He got the votes for the old question and would not have gotten more votes had the duplicate question not been asked.
@robjohn The problem with deletion is that I'll keep the reputation. I'm just really bothered by the fact that I received a bunch of upvotes after I edited it.
Nice idea
I'm gonna start editing my old answers :p
@Twink A few of my old answers had atrociously bad formatting. This one wasn't as bad as some of others. I should have just stopped after I edited the really bad ones. I'm an idiot.
@RandomVariable I don't understand you, I'd be vey happy to get many upvotes
If you don't want them give them to me :p
07:44
@Twink I'm not easy to understand. :)
@robjohn Would it be a big hassle to get my name removed from it?
@RandomVariable I think to do that would require a community manager. I can change it to a CW post. That won't remove the votes you've gotten, but it will keep futuer votes from giving any reputation bonus.
What do I vote to close as for something that's a rant, not a question? Primarily opinion-based?
I suppose not, because if there's no question, it can't be opinion-based.

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