The h Bar - 2016-07-13 (page 3 of 4)

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6:06 PM

@ChrisWhite But can you provide a single reordering of $\sum_{n=0}^\infty a_n(y) x^n$ to match a given output function $f(y)$? I imagine (without having seen it) that their procedure is closer to that than a single set sum.

would $\frac{p^n - k}{k+1}$ be the next term if $k$ were incremented by 1 in ${p^n \choose k}$

like ${p^n \choose k+1} = \frac{(p^{n} - k)}{k+1} * {p^n \choose k}$?

@Obliv You should really begin to test such formulae for some cases before asking such questions.

A little background: I am an Economics and Mathematics at a college in Lahore, Pakistan. I, however, have been in the process of making a transition to physics over the last year. I have a handful of physics courses and I am also involved in a summer research project over the summer. Starting September, I'll be going into my senior year which means I would have had a total of 2 years to make the transition to physics with a mathematical leaning/focus.

While I'm also considering either taking a year off to do research or enrolling in college for another year to do both research and get a de…

Also, would it be an appropriate question on Physics SE?

@JunaidAftab It wouldn't be! You can't really ask about provincial things ("too narrow"). The point of the site is for questions to be used/referred to later.

@acuriousmind what do you mean

6:16 PM

@Obliv I'm sure he means plug in numbers

bc questions like that anyone can see whether they're probably true or definitely false with a calculator and a few seconds

^that

Oh look, a cat

@neurofuzzy that requires one to know the form of ${a \choose b} = \frac{(a - (b-1))(a - (b-2))...a}{b!}$ i don't see how using examples make sense in showing what would happen if $b$ was incremented by $1$. Just plugging in $b+1$ in the RHS makes more sense to me

Hi @0celo7

@NeuroFuzzy ...hello?

Why am I being greeted

6:19 PM

Also, you should be able to tell whether your formula is true or false by inserting the formula for the binomial coefficient - do the l.h.s. and the r.h.s. match or not?

@yuggib ???

@Obliv How do you expect to be able to tell anything about the binomial coefficient without using its definition?

Also, writing ${a\choose b} = \frac{a!}{b!(a-b)!}$ is usually better to deduce properties.

the extra term would be $\frac{a-b}{b+1}$ yeaaa

What's new?

user54412

@EmilioPisanty Well, I'm referring to physically chunking up space into volumes of uniform density and asking what the gravitational effect is. Except the gravitational effect depends on how you divide up space and what order you sum the volumes.

6:21 PM

@0celo7 IDK. Saying "oh look a cat" entertains me. probably because of xkcd.com/231

But it's also polite, I guess.

well the solution manual mistakenly said ${p^n \choose k} = {p^n \choose k} * \frac{p^n - k}{k+1}$ when he must have meant ${p^n \choose k+1}$ on the left side so I was just checking if it was correct

@JunaidAftab Career advice is off-topic on physics.SE proper. (I'm afraid I don't know enough about the general situation to be able to say anythign definite, but a "funded master's program" sounds rather unusual to me, if you mean that you want to be paid for doing a master)

and the multiplied term is in the form I described, not in the usual form @acuriousmind

@NeuroFuzzy Hello back.

Not many people have the decency to greet me.

@ACuriousMind Sees me every day and does not greet me!

Measure 0 of them.

6:23 PM

@NeuroFuzzy If proximity to 0celo7 and not only actual cats triggered inanity, that would mean this chat should be filled with...OH WAIT THIS EXPLAINS SO MUCH

@ACuriousMind Filled with math? :)

filled with inane statements? @acuriousmind

@ACuriousMind what?

@0celo7 I don't greet any other people except for ones I haven't seen here in a long time either.

@ACuriousMind ???

What kind of behavior is that

In the math chat there is always greting

6:26 PM

You haven't seen 0celo in, like, a second.

That's pretty long, relative to 0celo.

@BalarkaSen I greet myself when I see myself in the mirror!

@ACuriousMind Do you have a moment

I'm looking back over the "there is a smooth function with zero set = some closed set" proof in Lee

@0celo7 It's my behaviour. I guess I tend to think of the regulars and myself just as people who sometimes fall asleep at the table, but never actually leave the bar, so there's no need to greet them ;)

Don't we need $\operatorname{supp}h=\overline{B_1(0)}$, rather than $\operatorname{supp}h\subset B_1(0)$

@0celo7 Your username then should have been nar7isus, not 0celo.

else you might have some other zeros floating about, no?

@BalarkaSen I am very humble...

user54412

6:29 PM

@JunaidAftab In Europe masters is seen as more an extension as undergrad (in that some people do it at the same place) and I guess (@ACuriousMind ?) isn't funded. In North America masters is just the first part of a PhD program (in the sciences at least), so it will be funded but it's not like you generally apply to a masters program.

@ChrisWhite Engineering is disjoint from sciences, it should be noted.

It's typical to get the MS right out of undergrad, then go work and make some money, and come back in ~5 years to do the PhD.

In particular, I'm concerned about lee's statement that "the $i$th term is positive exactly when..."

@ACuriousMind page 47 in Lee SM.

@ChrisWhite Indeed, master's is part of the "school-like" education and not funded.

user54412

@JunaidAftab There is also a small but growing trend in the US for "post-baccalaureate" programs between undergrad and masters/phd, designed for people intending to switch fields at that stage.

I think you need $h\ne 0$ on the whole ball $B_{r_i}(x_i)$, right?

@ChrisWhite Would you know of any schools that offer these post bacc. degrees?

To others, by a "funded Master's program," I meant a Master's program that may offer a scholarship or something of that sorts.

6:35 PM

Hmm, I wanted to prove the transversality theorem as an obvious application of some version of Sard's theorem on infinite dimensional manifolds but apparently that cannot be done.

For example, Perimeter. But it's top notch; everyone knows that, and it may be a too big of stretch.

@0celo7 I'm inclined to agree

@ACuriousMind also, why do we need $h=1$ on $\overline{B_{1/2}(0)}$?

i think that's unnecessary.

user54412

@JunaidAftab My own does, but I don't keep track of much more than that. Google searching + visiting lots of department home pages is the way to go.

@0celo7 That puzzles me too.

6:40 PM

I think I have a good handle on the idea of the proof, but I think he's wrong about what we need $h$ to be.

@0celo7 Well, maybe he means $h_i(x)\neq 0$ on all of $B_1(0)$ by "supported in $B_1(0)$".

I'm not sure why the 1 on 1/2, though.

@ACuriousMind See the bottom of page 44.

He defines "supported in" there.

Ah

I've never understood why he uses $\subseteq$

What does that mean?

@0celo7 It means that it need not be a proper subset?

6:45 PM

@ACuriousMind Oh right

It would seem easier to just write $\subsetneq$ when there's some anomaly.

It's a matter of taste

But that ain't the case, see, it's a matter of taste. - Eminem.

@ChrisWhite Yeah, that does sound shady, particularly if taking an off-centre expansion (e.g. spheres about another point) will yield a constant gravitational field, or thereabouts.

@ChrisWhite Where do you study?

@ChrisWhite Do you have your PhD yet?

user54412

6:48 PM

@JunaidAftab Princeton. You can check profiles -- they often have this sort of thing (especially for those of us who use real names) ;)

@ChrisWhite Seriously though, what's the ETA on it?

user54412

Apr 7 at 18:59, by ACuriousMind

Oh, for god's sake, stop trolling.

@ChrisWhite ???

I'm not trolling

user54412

Also, I defend next month.

Ok, thank you

We just had a grad student get his PhD in our lab

3 years I think

Although he had a Master's

6:50 PM

@ChrisWhite Have you submitted yet?

So 5 is normal for grad school in engineering too

user54412

@EmilioPisanty I have 12 days left :/

@ChrisWhite goodness

I need to submit by early September

@ChrisWhite can I read it?

or is it really physicsy

... and yet here the both of us are on a Stack Exchange chatroom =P

user54412

6:52 PM

indeed

@0celo7 You ever read any PhD thesis? If you found one that wasn't 'really physicsy' then it sounds dodgy.

user54412

@0celo7 It's entirely components and heuristics and numerics and pretty pictures

@ChrisWhite Pretty pictures are nice

@EmilioPisanty I'm a math student, not a physics student

@0celo7 ah, fair enough

6:53 PM

I can fake understanding a PhD math thesis but I have clue what physics is about

@EmilioPisanty nevermind the fact I'm an engineering student first :P

@ChrisWhite btw, while we're on the pretty pictures business

user image

↑ does that qualify for fair use?

I'm halfway through figuring out who I need to write to to get permission to use it

Well, I say halfway

I hope it's halfway

user54412

In my amateur opinion that is fair (and excellent) use

@ChrisWhite Heh, thanks

Maybe I'll write to the library and ask what they think

user54412

if not, I'm sure there are Renaissance paintings of a similar nature

@ChrisWhite Yeah, but it's not the same, though, is it?

user54412

7:01 PM

not quite

might yet work for the online version if whoever the copyright holder is denies permission

(also, if I actually manage to get hold of the copyright holder)

7:12 PM

would $p^{n-1} (\mod p^n)$ be $1$?

if so please explain

@Obliv did you try it

yes

ive been thinking about it for 15 minutes now

only part left in this proof

what is $11^{241}\mod 11^{242}$

Is 1 = 2 mod 4?

^

7:13 PM

@BalarkaSen yes?

$1=2+(-\frac{1}{4})\cdot 4$

well then this makes no sense.

Nonsense.

Also, stop trolling.

wtf

@ACuriousMind Figure out the 1/2 thing?

@0celo7 Hm?

@ACuriousMind Bump function on a ball

7:16 PM

@0celo7 Yes, I know what you are talking about, but I already told you I don't see where he would use the 1/2

@ACuriousMind Actually, I need you to do something. Please read last night's discussion on covariant derivatives and tell me if I'm insane or bolbteppa was tripping hard

@ACuriousMind starting here : chat.stackexchange.com/transcript/message/30994866#30994866

I need a sanity check

$p$ is an odd prime and $k$ is an integer. $\frac{{p^{n-1} \choose k}p^k}{p^n} = C$ (where $c$ is an integer) is what i must show. In a lemma I proved, if $p$ divides $k$ $m$ times then $p$ divides ${p^n \choose k}$ $n-m$ times. So if $p$ divides ${p^{n-1} \choose k}$ $n-1-m$ times, we have $p^{n-1-m}*S = {p^{n-1} \choose k}$ and then $p^{n-1-m+k}*S$ and so $m$ is determined by how many times $p \mid k$ and $k$ increments in the sum. They all have a $p^n$ term in them (except $k = 0$ term?)

There must be a term in which $... \mod p^n $ is $1$ but I'm not seeing it. When $k = 0$ isn't it $p^{n-1 - 0 - 0} * S = p^{-1}*S (\mod p^n)$

@0celo7 I don't agree with bolbteppa's view of either mathematics or physics.

@ACuriousMind What is his view of mathematics?

gotta get to class ill think about this later .-.

7:24 PM

@ACuriousMind Are sheafs used in Atiyah-Singer type stuff?

@0celo7 Depends on what you mean by "used". I'm sure there are formulations that use them and those that do not

But I didn't see sheaves when you used it to explain the chiral anomaly in QFT, for instance

@ACuriousMind I mean is it used in the proof

@0celo7 Implying I know the proof :D

@ACuriousMind The book by Bleeker and Blooss is on my adivsor's "to read" list for me

Although the list is ridiculous

He basically has every book in his office on there

@ACuriousMind How does AS explain the axial anomaly

Or chiral anomaly

or are those the same?

@0celo7 They are the same

7:31 PM

@ACuriousMind Thought so

And AS "explains" it by relating the index of the Dirac operator - which is the difference between chiral and anti-chiral zero fermion modes - to the $\int\mathrm{Tr}(F\wedge F)$ that is essentially the Chern class.

...what does that have to do with triangle diagrams?

The anomaly "really" is the path integral not being invariant under the chiral symmetry, and you find that the amount of it being anomalous is the difference between the chiral and anti-chiral fermion modes (this is called the Fujikawa method of deriving the anomaly)

I never really understood those stupid diagrams.

@ACuriousMind Although I do recall the divergence of the axial current being like $F^2$

They're a way to compute the expectation value of the anomalous current directly, but I don't find that insightful in the least

7:35 PM

this was years ago, mind you

@ACuriousMind Oh, I read about this in Nakahara back in the day

but my memory...damn

yes, the difference in the modes is the chern class

@ACuriousMind Actually it seems to be a general chern class for $n$ dimensions

is it the first one in 4 or something?

@0celo7 Since the anomaly term is something that is integrated over spacetime, you take only the top-dimensional part or something.

it seems to be $\int \mathrm{ch}_{n/2}(F)$.

I thought $F^2$ was the first Chern class

no, that's just $F$

actually technically you just get the trace-free part of $F$ in $F^2$

er..

what am I talking about

@ACuriousMind help please

what the heck is the second chern class

@0celo7 Isn't it $\frac{1}{32\pi}\int\mathrm{Tr}(F\wedge F)$ (the prefactor might be off)?

@ACuriousMind that's what I thought

but Jost has another term

what's the definition of Chern class again?

your definition

not his

@0celo7 That there is the definition, as far as I'm concerned. I never worked through the mathematical theory.

7:45 PM

@ACuriousMind Yikes

Thought Chern class was the bijection between H^2(X; Z) and complex line bundles on X.

At least, I guess that's a special case.

Not in geometry

there might be a correspondence somewhere

@ACuriousMind No, I'm right

Oh, right, Chern classes are like 50 million different things in different places.

the second Chern class is actually $\mathrm{tr} F^2-(\mathrm{tr}F)^2$

looks familiar from string theory

Looks like standard deviation :P

7:47 PM

@ACuriousMind So I'm assuming one of those terms gets killed by the integral

@0celo7 Not as far as I know.

I've not seen a $\mathrm{Tr}(F)^2$ term for the chiral anomaly

It does appear in gauge anomalies, though

I know it appears in string theory anomalies.

Those are gauge anomalies, yes

I don't know what that means.

Just assume I know zero physics.

8:11 PM

@0celo7 So the truth

So the "0" in "0celo" is explained.

9:08 PM

@ACuriousMind The issue is, as far as all time travel models we have so far in the mainstream physics, none of them allow changing the past.

Thus for slereah's plan to be sucessful, he had to had already done that

Unless it is either branching timelines (where non scifi version will mean he end up in another quantum reality that does not interact with our own), or that there is something I overlooked in the literature that allow spontaneous generation of CTCs

(for those who might said I took a joke too seriously: Well I tend to overanalyse things, and time travel, being my favoirite, is tge worst suffering from this habit)

9:43 PM

@Emilio thx for the interest in the chat session(s). alas my SSD crashed on mon & it took until now to fix it :( ... consider this to be DZs & his assistant/ comods (JR/ CW) & defer to their judgement on inappropriate content.

@vzn I don't have time to chat, but note that the conversation I referred to above was brought to a head precisely because there wasn't quite enough capacity to handle the chat.

read the whole transcript & the post-analysis re the problematic question by newbie...

@EmilioPisanty "capacity"? nobody else raised an issue. agree the format can be awkward at times.

@vzn Specifically, a user asked a (vaguely valid) question, which a mod thought was interfering with the event, the mod deleted the question, and the user walked away with a bruised impression of what the second A in AMA means

Not a terrible outcome

a much more structured dialog/ format is possible but it will take more time commitment by someone/ volunteer. am open to handing that off. note @DanielSank has been out for awhile on vac etc

but not one you should be thrilled by

9:46 PM

@EmilioPisanty lol its somewhat regrettable but also mostly TBE

@vzn You're "open to handing that off"? I imagined you'd be saying "I'm perfectly happy to take charge of it"

we had a new random user show up in the 1st session also & ask totally unrelated question... & then you have typical peanut gallery comments by the resident jester(s) etc...

@EmilioPisanty it seems very/ unexpectedly timeconsuming just to line up guests. would like to see a very elite/ streamlined fmt but hey, this is cyberspace & SE chat is a highly unstructured part of the site (in comparison to elsewhere/ main site etc)

@vzn To be honest, if lining up guests is unexpectedly timeconsuming, I would blame it on the expectations.

Getting people to agree to take the spotlight is hard.

also in our 1st chat, Secret complained about not having his question answered etc. ... so some )( disappointment seems "natural/ unavoidable"...

@vzn In any case, as I said, I really have no time to chat now - I need to catch a tram home.

Just be aware that there is a need

9:49 PM

@EmilioPisanty so far it has not been overly difficult to find volunteers, working from site/ room regulars, its just tricky to coordinate everything

And that one of the mechanisms that you'd hope would help deal with that (moving comments between rooms) is probably too awkward to be of use.

So I would suggest that a better solution is needed.

@EmilioPisanty think you have valid concerns & would like to see the whole thing gain greater finesse/ polish/ smoothness but it needs more efforts by anyone willing to volunteer. am ok with the current level of attainment. we had 2 guests mainly without hitch, we had new faces in the last one, good questions, the guests are quite accomplished, etc.

Particularly if you want the events to scale up.

But anyway, I need to leave. Have a good one.

@EmilioPisanty there is a lot of expectation to call it an AMA because reddit AMAs are quite advanced at this point, they even have dedicated (paid) staff devoted to it etc... do like that model but its far from where we're at

@DavidZ/ @JohnRennie et al thx for your effort re moderating the guest session and don't want to overthink that too much right now unless more volunteers show up... think that nearly-random or laughable stuff may inevitably show up in transcript & think its fine to throw out worst offender stuff. DZ are you ok with another scheduled session in 4wk? should we have more discussion on fmt etc?

@DanielSank are you still interested in being guest speaker? can you do it in 4wk? ps could you update/ mark your meta post listing the sessions to point to the chat transcripts for 1st 2 spkers and maybe make it community wiki?

@ACuriousMind He wants me to have read the first 40 pages of Milnor by next week 😵

10:25 PM

@ACuriousMind I have been tainted by physics

@ACuriousMind Holy crapola, the price of Milnor Morse theory used to be $3

user image

Oh yeah all physics books used to be dirt cheap

HE was ten dollaridoos

@Slereah Is simple connectedness preserved by $h$-cobordism?

@0celo7 The covariant derivative thing is explained on P185 here in 2/3 short pages books.google.ie/…

I don't know what an $h$ cobordism is

@bolbteppa I'd prefer to stew in my ignorance

Now that I think about it, that's how Cahill does it

And it makes sh*t sense there too

Oh gosh @skullpatrol I'm sorry I said I bad word

10:37 PM

It's also here too taken from D'Inverno's GR book physicspages.com/2013/02/16/…

@bolbteppa They're just heavily abusing notation.

You guys are now disagreeing with vector analysis and general relativity books ;)

" Generalized solutions of the stochastic Burgers equation "

Hm

burgers

@bolbteppa I'll gladly disagree.

Me being correct has nothing to do with which books you cite.

Their notation $\partial_i \mathbf e^k$ is an abuse of notation.

They really mean $\nabla_i\mathbf e^k$.

You can test this in a vacuum by simply computing $\frac{\partial }{\partial r}(x^2 \hat{e}_x + y^2 \vec{e}_y)$ you don't need me or anybody to rely on, prove it yourself or prove it wrong or explain the mystery if it works and you don't see why

10:39 PM

If you make that change, I think it's correct.

For the last time, the partial derivatives on $\Bbb R^k$ agree with the usual LC connection.

You can get away with muddling the two concepts.

That's why vector calculus can be taught to sophomores.

@0celo7 What do you mean by that? That a h-cobordism whose one end is simply connected must have its other end also simply connected?

@ACuriousMind It's a cobordism where the cobordism can be deformation retracted onto the two manifolds.

I want to know if one manifold simply connected implies that other is too.

No you are still confusing things, vector calculus is taught this way in EM books too, go to the first chapter of Wangsness or Ida (if I remember correctly) and you'll see the same ideas

Do you know if this is true?

@0celo7 That's what I meant. Ok, so I understood you correctly.

10:43 PM

@ACuriousMind I think the $h$ is italic.

I picked up Milnor's book on it for fun.

@JunaidAftab Europe has a lot of cheap if not virtually free masters but they are usually 2 years long, usually people get an insanely large loan specially made for masters and just cry

Though the 2 years might benefit you in your situation

@0celo7 It sounds as if it should be true since the deformation retract would "rip apart" the other end while retracting it onto the not-simply-connected end, but I'm not sure.

@ACuriousMind So it's not trivial?

@yuggib Analysis books for next semester: amazon.com/Advanced-Calculus-Several-Variables-Mathematics/dp/… link.springer.com/book/10.1007%2F978-1-4684-9461-7

@0celo7 Hm. Doesn't the h-cobordism itself give a homotopy equivalence from one end onto the other, meaning that the fundamental groups of the ends must be the same?

@ACuriousMind Yeah, I guess that would work.

10:51 PM

Yeah, it's kinda trivial - for a h-cobordism $W$ from $M$ to $N$, compose the equivalence $M\to W$ with the equivalence $W\to N$ to get an equivalence $M\to N$, so if $M$ is n-fold connected, $N$ is too, since the fundamental group is homotopy invariant

Does that work for any cobordism?

No, you need the h-

Otherwise, the pair of pants is a counterexample

@ACuriousMind Oh right, deformation retraction is a homotopy equivalence. Derp.

What's new?

I see h-cobordism is being discussed.

I picked up Milnor's book on it.

Seems it will be accessible after Morse Theory.

The library has the original 1963 copy.

10:57 PM

There are not many interesting h-cobordisms.

If the cobordant manifolds are simply connected, and the h-cobordism is simply connected, then it's homeomorphic to a copy of M x I.

It proves the Poincare Conjecture in n>4.

In particular, h-cobordant simply connected manifolds are homeomorphic. This is the content of h-cobordism theorem.

Have you read the proof?

No, not really. How it proves the Poincare conjecture for n > 5 is easy.

@BalarkaSen One can strengthen it to diffeomorphism in the smooth category.

The proof seems long.

10:59 PM

For n>5. n = 4 is open.

Do you mean n>=5?

Well, it's false for n = 4.

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