Anyway I suggest The Lobster again @Balarka

WTF, I watched Lobster too, LOL.

@Alessandro I see. Disturbing surrealism is an interesting genre I have been meddling with for some time.

OK, one of the actresses in Lobster is really pretty, so I recommend it too.

(Ah yeah Lobster)

If you want to watch some very sexy movies with lots of double crossing, I recommend Wild Things 1,2,3,4. I watched all of them.

@JasonBourne Léa Seydoux?

And if you like deformed cannibals killing people one by one, watch Wrong Turn 1,2,3,4,5,6.

@AlessandroCodenotti Yes

And if you like the slasher film with some nice repetitive music, watch Halloween 1,2,3,4,5,6,7,8,9,10.

the thing is nice. watched that recently.

@BalarkaSen what are some (maybe not directed by Lynch) movies in this genre?

Of course if you like British spies, watch James Bond 1-26.

And if you like American spies watch Jason Bourne 1-5.

That's a pretty wide range of Bond movies.

@Daminark That one is J H Conway not the J B Conway who wrote the complex analysis text, LOL.

@Alessandro I think Mike can give you a better list than mine. Hellraiser is interesting (I watched it after reading Hellbound Heart, the original Barker novella), pretty much literally whatever by Cronenberg. Naked Lunch is more of a strange satirical drama than disturbing, but Videodrome is awesome cool.

by hellraiser i mean hellraiser 1

Lol, game theory Conway is wild

I was so ticked off at the definition of a game originally

At the onset it's like, how is this not circular?

I watched the drama series Hindsight (2015). Sad to say they cancelled Season 2, so I am left without an ending. =(

I don't think I can actually classify Naked Lunch into a genre lol

Then you realize the damn vacuous truth of the empty set is doing its mischief once again

The empty set trips up a lot of people except me.

That is because ...

I am the empty set

@BalarkaSen hm, I see, I've had videodrome and a few more Cronenberg movies in my list for a while

Alien Covenant is showing this week.

If you like women killing zombies watch Resident Evil 1-6.

Dead Ringers by him is v good: it's arguably the first successful movie about twins that's neither a comedy nor a good-guy-bad-guy thing. There's not much visually disturbing stuff in it but it's really paranoid

Not related, they released the trailers for Dunkirk and Blade Runner 2049 this week

I did not watch the movie Pi. I think it's pathetic.

... strange to make a comment about a movie without seeing it

I watched the first 5 min.

my point holds, even more strongly :P

at best you can stop watching and say "I don't want to watch it"

If someone talks to you a certain way for 5 min you never wanna talk to him again

which is what i do

The movie which I haven't (and won't) see is The Imitation Game.

As a story, it might be fine. But as any kind of depiction of Alan Turing my understanding is that it's just bad bad bad.

I watched a lot of Shane West movies too, because he is very handsome.

Pi was borderline too surrealist for my taste but it was not bad. They showed it in the uni's library as part of a series of movies about maths or mathematicians

Basically, I am a shallow guy who choose movies mostly based on the looks of the actors and actresses. =)

@Semiclassical I was in Germany when it came out so I went to see it in the cinema, but it wasn't available in English and I hadn't been in Germany for a lot of time...20 minutes in the movie I asked the guy sitting next to me and it turns out that Krieg means war, the dialogues made more sense afterward

I think it's possible to like a movie as a story while objecting to what conclusions it leads people to draw from it.

@AlessandroCodenotti My favourite German movie which I watched 9000 times if Sommersturm or Summer Storm.

To the extent that it's "The Imitation Game"'s Alan Turing, I can appreciate it. But that's not how people view it.

Hi @Ted

grump grump grump

Hi @Balarka

Hiya @Ted!

@AlessandroCodenotti yeah Pi is ok. I wouldn't call it great but ok.

I see everyone is still grumpy.

They all need some smacking.

Hi, @Fargle, @Alessandro, Mr. Bond, @Semiclassic

My grumpiness I suspect is a disguise for anxiety at this point.

Hi @Ted

Need to do my grading but uuuuggghhh

@TedShifrin I am Mr Bourne now, actually.

You can't change names every day, Mr. Bond. I'm too slow for that.

Did they take the final already, @Semiclassic?

No.

It's part of being an international spy.

I'm talking about the last lab report

@BalarkaSen agreed, that's why I called it not bad rather than good :P

And putting together my portion of the gradebook more generally.

Oh.

I -need- to get that done before the final exam is finished or it's going to go to hell pretty fast.

Because I'll also have to grade one of the problems on the final.

Now every time I eat duck I think of Ted's comment about duck fat, lol.

Yup. Get outta chat, @Semiclassic. Bye.

sigh. yeah.

speaking of surrealism I watched Cabinet of Dr Calegari finally

artistically very very good

@BalarkaSen Thaaaaaaaaaaaaaaaat's a weird one.

I actually watched 120 Days of Sodom. It was crazy.

Excellent, but weeeeeeird.

@Fargle haha

Just now I had a really strong alcoholic drink. Just taking a sip makes my throat all hot.

In fact, the whole container seemed to be at a very high temperature...

We should all get Mr. Bond drunk.

Vodka Martini, shaken, not stirred.

I can do that ... although I personally drink gin rather than vodka.

That's what Bond asks for in almost every movie, btw.

Ok, back to maths! Can I annoy you with PDEs @Ted?

Yes, I know.

You can try, @Alessandro, but I may fail.

The difference between try and triumph is that extra umph

Hi chat

I mean, Ted

LOL, Salut, @Astyx. How's Poitiers?

It hasn't moved since yesterday

But you have, I hope.

ok, so we're interested in solving the problem $\Delta\varphi=f$ in $\Omega$ which is a connected and open subset of $\Bbb R^n$with compact closure, with $f\in C^0(\Omega)$ known and $\varphi$ unknown (continuous in $\bar{\Omega}$ and $C^2$ in $\Omega$)

It seems like this room has turned into Procrastinators Unanonymous.

I'm not anonymous, I'm proud to procrastinate

I said un

@Alessandro: So, convolve $f$ with the fundamental solution?

@TedShifrin: I was calling you because I wanted to make sure that I was doing a problem correctly. I ended up figuring it out.

You did indeed

Oh, sorry, @Faraad. Maybe you called when I went to get the mail.

@TedShifrinL It's fine. Actually, it was probably best that you didn't answer since it forced be to think of another way interpret and do the problem.

We saw that there are $2$ kinds of initial conditions, we might ask $\varphi_{|_{\partial\Omega}}=\psi$ for some given $\psi$ or we might ask for $\frac{\partial\varphi}{\partial\vec{n}}_{|_{\partial\Omega}}=\rho$ (assuming enough regularity for $\psi,\rho$ and $\partial\Omega$ where needed)

What kind of problem, @Faraad?

Ted helps even when he's not helping

Right, @Alessandro. Dirichlet versus Neumann.

But I haven't taught this stuff in 30+ years, @Alessandro, so I'm very rusty.

(what's the proper way to write function restrictions in LaTeX?)

I use \big| or \Big|.

@TedShifrin:math.stackexchange.com/questions/2273451/…

@Faraad: Too much stuff there for me. Remember that if you make a conformal change of metric (multiply the first fundamental form by a constant), then angles are preserved. That's immediate.

I knew you could do it just by showing $\signa^*(ds^2) = \lambda(u,v) du^2 + dv^2$ i.e that $\sigma$ was conformal, but the OP said he hadn't seen differential geometry.

And the hyperbolic metric is conformally flat (i.e., a scalar function times the identity).

we saw that with Dirichlet's conditions everything is fine, that with both conditions the problem isn't well posed (there might not be solutions) and then the professor just remarked that Neumann conditions are problematic inside $\Omega$ but we used them when dealing with the "external" problem, looking for a $\varphi$ defined of $\Bbb R^n\setminus\Omega$

It's just linear algebra. No differential geometry.

P.S. You need parens after your $\lambda$.

I don't understand that comment, @Alessandro.

neither do I, which is my question

Oh, let's see. Does the divergence theorem (Green's identity) give us some necessary condition that has to be met?

@TedShifrin: See that was the issue. He didn't know any of these things. I thought that was the best way to do it.

it was only mentioned in passing so I probably misunderstood and wrote something stupid which I'm now trying to sort out

@TedShifrin: He didn't know anything about first fundamental forms and conformal maps.

@Faraad: I call bulls***. He's writing down the metric on the hyperbolic plane in diff geo notation.

@TedShifrin Yes, but they're conditions on $\partial\Omega$

@TedShifrin: Check the comments. He told me he didn't have a course in diff geo yet.

@Alessandro: If we're talking about a function harmonic on the interior of $\Omega$, then the integral of its normal derivative on the boundary must be $0$.

Oh, it's a relativity course, @Faraad. He needs to know how to compute angles using dot product. That's all the linear algebra I'm talking about.

But, anyhow, I've lost interest. :)

@TedShifrin o/

Hey @Ted!

hi chat

And @Eric!

Salut, @Hippa. Il faut te rappeler déjeuner le 10 juin!

Hi Demonark and @Eric.

@TedShifrin: Ah I see. And don't be a diva with me. Next time answer your phone.

I was out of the apartment, @Faraad. F*** off.

@TedShifrin Hm, wait, why is that?

@TedShifrin: hahaha

Language

@TedShifrin I've got it in my calendar :-)

Cuz that's what one of the Green's identities tells you, @Alessandro. Of course, you can't apply it on the complement, because it's noncompact.

@Hippa: We all need to pick a time and approximate place. I won't be in chat much once I'm in Paris!

Is harmonic analysis about studying harmonic functions?

In part, Demonark. Lots of Lie group actions, representation theory, too.

Sounds dope

Good to be excited about learning lots of different things, Demonark.

@TedShifrin Anywhere/anytime should be good for me

lie groups and lie algebras was tough for me when I took it

@Daminark ~~~~Fourier transforms~~~~

But you local guys should figure a reasonable place for us to meet. @Hippa @Astyx @LeGrandDODOM ... Astyx has that excuse, too.

I live on the outskirts of Paris, I'm not a true parisien :P

I know a nice little restaurant that just opened, I think it's called La Tour d'Argent

Haha @Astyx.

I live approx where Hippa is so same goes for me

Je connais bien les restaurants bien connus :)

Celui là de toutes façons on aurait pas pu y aller, il faut réserver plusieurs mois à l'avance :p

I didn't call you guys "true Parisians." I'm just asking the locals to make a choice.

@Astyx My wallet wouldn't allow me anyway >.>

@TedShifrin: Will you be in Athens at all this summer?

Et je sais même pas ce que ça vaut, n'y étant jamais allé

@Faraad: Not planning on being anywhere in GA in summer. Maybe later in the fall.

Mine neither @Hippalectryon

@Astyx @Hippa: With a reasonable choice of brasserie or small restaurant, I will treat you guys.

@Alessandro: Did you disappear?

@TedShifrin: aw man. I haven't seen u in forever it seems.

And you're so much happier, @Faraad :D

isee.jpeg @Eric

"The locals" it sounds like we're some sort of indigenous tribe

But I'm scared to be on campus now with all the legal guns, @Faraad. My Facebook friends on the faculty are totally freaking out.

@TedShifrin: Noo. I got to see Azoff last summer.

@TedShifrin: Oh wow, I didn't know about that.

@TedShifrin I think I'm missing somehing. I know that $\displaystyle\varphi(y)=\oint\limits_{\partial\Omega}\left(\varphi(x)\frac{\par‌​tial G(x,y)}{\partial n}-G(x,y)\frac{\partial\varphi}{\partial n}\right)\text{d}S(y)$

I wonder if MSRI lost some students due to the recent riots.

LOL @Steamy's Old MacDonald joke :P

@Daminark Use png, uploads easier on internet

@Daminark when Brian was trying to explain it to me this was my impression anyway. I don't really know anything about it.

So, @Eric, you sorted out the integration over the fiber stuff? Have you had alg top yet?

I'm out ! Bye all !

@Balarka Will keep in mind

Sya @Astyx

@Alessandro: I mean basic stuff with no Green's function. You know $$\int_\Omega \Delta\phi\,dV = \int_{\partial\Omega}\frac{\partial\phi}{\partial\vec n}dS.$$

A bientôt, @Astyx.

funny that message seems to render fine on MSE but there's a broken \partial here

Hi guys. I'm trying to get Maple to evalute to expressions of an equation there is the same. I 've tried to use evalb((sqrt(3)/4-3/2)*x^2+100x=x*(100-3/2*x)+1/2*xxsin(60)) but the output is false for some reason however I know it is true which wolframalpha also states...... Do you know what I'm doing wrong here?

no, it's not rendering fine, @Alessandro.

I mean it renders fine if I copy/paste it in an answer box on the main site

You can't use times in there, @Daniel.

@Eric When are we gonna upgrade to Fiveier transforms?

@DanielGuldbergAaes: Nor can you use angles in degrees. It won't evaluate that at all.

Anyhow, @Alessandro: Back to maths, as you appropriately said a while ago.

I've had an intro to alg top in my reading course with Benson, @Ted, I worked out how you could get a map of the $k + 1$-forms on $M \times [0, 1]$ to $k$-forms by integrating through $[0, 1]$, drew the de Rham complex of $M \times [0, 1]$ and $M$ and drew all the arrows and saw Cartan's magic formula drop out

and then was blown away

@TedShifrin Oh, I'm quite embarassed that I never thought to put a constant function in Green's first identity, which is usually stated with two functions, but I see what you meant now

@Te

@TedShifrin times? And it doesn't help if i subsitute Sin(60) wit sqrt(4)/3 which is again the same

@Daminark pls no

Oh, cool. The point is that integration over the fiber is adjoint to crossing with $[0,1]$. So the chain homotopy formula comes from integrating over $\sigma\times I$ and taking Stokes's Theorem and the boundary.

yup yup

@DanielGuldbergAaes: You have a weird x in front of the sin. And what are you saying $\sin(60º)$ is?

Cool @Eric

@Alessandro: So now I think we know what your prof meant by his comment. There's a constraint that must be met by the Neumann boundary conditions. (I've forgotten whether two n's or three. :))

howdy @ted

hi @PVAL

and @Daminarks prolly here too

It was very cool to see how the Lie derivative on forms satisfies that homotopy formula, I feel like it finally makes sense to me now

Yo @PVAL

chain homotopy rather

On so many things you can get intuition from Stokes's Theorem, @Eric :)

I know it's a chain homotopy formula but... I still don't get it

@PVAL: It seems Demonark is always here.

integrating things is one of my top five favorite things to do tbh

Did you see my remark yesterday, @Balarka, about interpreting $\int_\gamma \mathscr L_X\omega$ as differentiating the integral of $\int_\gamma\omega$ as the curve flows by $X$?

Yeah, I tend to work rather sporadically, so I end up being here quite a bit

@Ted Oh that was referred to me? Hm, I didn't think about it but let's see.

@TedShifrin yeah, and in general we can substitute $\Delta\phi$ with $f$. I'm probably going to office hours next week so I might ask him about the details, thanks for your help!

Demonark: It's as bad as a poker addiction.

@Eric Lel

To you and to Eric, I do believe, @Balarka.

(I am not that great at understanding the Lie derivative)

Sure, @Alessandro.

It's differentiating along a flow, @Balarka.

@Eric: You should derive the first variation of arclength following the lines of this discussion. For lots of bonus points, work on the second variation. :)

@Ted At any given time I have some poker addiction, I only lose one by developing another

No further comments, Demonark.

I mean in reality I usually just have this open and do other stuff in the meantime

Hiya DogAteMy!

Will do, I assume the formula in the language of moving frames is very nice as usual :P

Fair

@TedShifrin Hi!

Hey @Akiva!

Of course, @Eric, using appropriate adapted frames.

You can do it for surface area of a hypersurface, too, and see mean curvature appear, @Eric.

interesting, I'll do that too

variational formulae are actually like maybe my favorite thing in math

I like thinking variationally about things a lot

@TedShifrin Oh, sure, I agree. And Cartan's formula says $\int_\gamma \mathcal{L}_X \omega = \int_\gamma \iota_X d\omega$

The whole point is to use the formula we've just been discussing, plus Stokes's.

hmm i guess it's mathscr

Where did the other term go, @Balarka?

Oh, I was assuming $\gamma$ was a path with endpoints.

aren't you integrating along a closed integral curve

ah ok

No, no.

Definitely not integral curve of the vector field, either.

What is $\gamma$? You said it flows by $X$

@Eric: Re variational thinking. Here's a beginning calculus conundrum for you (and others).

@Balarka: Right, the points of the path flow by the flow of $X$.

Doesn't that mean it's an integral curve of $X$?

Back to Eric. We know that the derivative of area of a circle is the circumference. We try to explain that to every beginning calculus student. Why then is the derivative of the area of a square not the circumference of the square?

NOOOO @Balarka.

@Balarka: Imagine a line segment on the $x$-axis and $X = \partial/\partial y$. (Sorry about awkward letters.)

What do you mean by "points of the path flow by the flow of $X$", then? If I start at $(0, 0)$, $\partial/\partial y$ (the unit vector field parallel to y-axis) it takes it to $(0, t)$ after time $t$ by the flow. I don't get it.

Right. So the horizontal line segment flows vertically. This is not saying $\gamma$ is an integral curve of $X$ !!!

Oh, you're literally saying, differentiate $\int_\gamma \omega$ when varying $\gamma$ by the flow?

Right. I'm saying what I said. :)

Oh ok so for the variational formula of Arc-length, you take a frame adapted to your curve and then calculate $X\int_{\gamma}\omega = \int_{\gamma}\mathscr{L}_{X}\omega = \int_{\gamma} d(i_{X}\omega) + i_{X}d\omega$ first term drops off because Stokes, so you are left with the second term which is $\int_{\gamma}(\omega_{12} \wedge \omega_{2})$ which is $\int_{\gamma} \omega_{12}(\langle X, e_{2}\rangle)$

unless I made a mistake somewhere

$X = \frac{\partial \gamma}{\partial t}$

@Mike @Balarka Eraserhead is really only interesting because of how it influences The Elephant Man and Blue Velvet

I'm understanding what you're saying now. :) I was confused by why you're flowing the entire curve, but now I see. That's the variable of your differentiation.

@Eric: The first term drops out because you're doing an endpoint-fixed variation, presumably. And then you get $\kappa_g \langle X,e_2\rangle ds$. Yup.

Blue Velvet and The Elephant Man are Lynch's best in my opinion.

right right

Pretty cool, eh, @Eric?

@ted Do you know what happened to Mr Eyeglasses?

in my head endpoints were fixed

@PVAL Lynch, you meant. Interesting.

this is like waaaay easier than without forms

Yeah my brain no work gud sumtime

Mr. Bond, he reappeared once a few months ago. Life hasn't been too good. But I don't know what's happening now.

I should watch Blue Velvet. Wonder if I'll make it tonight.

Have you watched The Elephant Man?

Nope but Mike told me to see it too

@TedShifrin Oh dear. I hope he is OK. I am sending my positive energy to him now.

Glad to be brainwashing you a little, @Eric. Also, see my question above re variation of area = perimeter. :P

Mr. Bond, you remember that his mom burned all his math books and he was living in a church. But I don't think school went too well.

(i have watched only mullholland drive and lost highway by lynch. and his awesome sitcom rabbits on a whim)

Twin Peaks is good

though maybe falls off the deep end at some point

@TedShifrin That is the least of his problems, I think. Anyway, I am not OK myself, and there is nobody to send me any positive energy.

Wild at Heart is pretty good but very strange.

Well, we've always worried about you, Mr. Bond, and wished you very well.

Wait @Ted, is it not true? I feel like it secretly should be but we're writing the area in terms of the wrong variable or something

Dune was a complete failure

Thanks. Anyway, today is Vesak Day, commemorating the enlightenment of the Buddha.

given the quality of the source material.

I hated Dune. But I don't like sci fi.

The book?

I haven't met anyone who disliked the book.

@Ted You should watch Solyaris. Probably my favorite sci fi movie.

Wow, when this chat talks about movies, it's starting to become a real chat room again. =)

The books written by Frank Herbert (and not his son) are all phenomenal.

I also like Stalker but it's not truly sci fi

right yeah, write the area in terms of half the side length, and then the derivative is the perimeter @Ted :P

There you go, @Eric. I knew you'd get it. But that bothered me for a while when I first thought about it.

You need the same symmetry ... growing around the center.

Today I had a pie with rosemary herbs. I think rosemary is a lovely spice.

Rosemary, tarragon, and thyme are my favorites, with marjoram close behind. I also love cumin (not an herb).

@PVAL-inactive i saw it on his movie list while googling Lynch's movies. but nicholas cage with a chick on his arms instinctively repelled me a little

nic cage is great

yeah first thing I usually check in this type of problem is if the analogy is flawed to begin with @Ted, usually works out

He's pretty good in Wild at Heart

and amazing in things like Matchstick Men

Good @Eric :)

huh. guess i feel a little better about it then

Back to moving frames for you now, @Eric ... :)

most of the real films hes done hes been fantastic in my opinion.

It's just that hes done many things that seemed to barely have scripts.

lol true

I will think about doing the variation of area with moving frames later

for now I must eat

i have leaving las vegas somewhere in my list

farewell chat

Bye :)

Matchstick Men was a Ridley Scott vehicle

if you like him.

haven't seen anything by him but i have heard of Aliens

He directed Alien

and the cool story by Cronenberg about him (Scott) "stealing" his body horror from They Came From Within

@Ted Oh and when I said Solyaris I did NOT mean the american version

Cameron directed Aliens

ah yeah Alien. that's the one

He directed Blade Runner and Gladiator and Thelma and Louise

@BalarkaSen You should watch Blade runner

Assuming that $x \neq 0$, suppose we have that for every $\epsilon > 0$, there exists a $\delta > 0$ such that $|x| < \delta \implies |f(x)-x) < \delta \epsilon$. What would this tell us about the function $x$? That is behaves locally like $g(x) = x$? I can't quite figure out what it says about $f$.

Is there a simple test which can show that a three-coloring doesn't exist on a graph?

I have an 8-vertex (mostly connected) graph and I'm looking for a simple argument

I would like bring attention to a question I haven't had any progress with so far, hopefully someone here can help: math.stackexchange.com/questions/2260555/…

@PVAL @Alessandro Noted.

On a mathematical note, how would you prove the length function induced from the Riemannian metric is positive-definite? If $p \neq q$, I want to show $d(p, q) > 0$, so I start off from $p$ in a little chart around $p$, and make it hit a ball of radius $r$ around $p$ on that chart.

I want to show the length of the bit of the geodesic from $p$ to the sphere of radius $r$ is more than $r$.