We say that 0|0 so that gcd(0,0) is well defined and we dont have to deal with a few corner cases now and then

I disagree. We say that $0\vert 0$, because our definition just allows us to.

Would... Would $\gcd(0,0)=0$?

While $0/0$ doesn't give us a unique value, so we leave it undefined

Or $\infty$?

Hey sha

hi @Dodsy

@AkivaWeinberger yeah, but it's a matter of convention

How were the exams

semi said you had been studying.

haha true

well, I had 3 exams in physics. I passed one with a 10, I passed one with a 6.5 (which I'm going to redo, because it's easy) and I think I failed one, because I started too late

but I'll redo that one next year

@AkivaWeinberger nah it's 0, it is the greatest number when ordered by divisibility after all

Yeah I guess

$\langle a\rangle+\langle b\rangle=\langle\gcd(a,b)\rangle$, right?

Since $\langle 0\rangle+\langle 0\rangle=\langle 0\rangle$, I guess it makes sense that way too

The integers ordered by divisibility are a (insert adjectives here, probably complete and bounded) lattice

in any case, I have a good GPA. which I find important, because my social skills aren't thát strikingly amazing, and I don't really have some big talents, so I think having good grades is going to help me if I apply to some other university in the future.

That's good sha

how are you?

Is latex supposed to render on chat? Or do you guys just have that built in to your brains by now?

@ShaVuklia Making a good impression on your professors is going to be just as important, if not more

Recommendation letters are everything

@DavidVarela There's a script you can run that renders it

tinyurl.com/cfqcvpc

(It's in the room description, on the top-right of the chat)

So, no, we don't have it built into our brains :P

I am good!

Thank you for asking.

@Steamy Yea, I've definitely done that. I got a mail a couple of months ago from my astronomy professor who was impressed how I did on a test once:P And also doing a double major makes you "impressive" for free, because everyone thinks you have a hard life. But having social skills is hella important too. Those people who don't socialize but get great grades don't seem that loved by professors as opposed to the more "active" students. So it's really a lot of factors to think about

@Dodsy nice!

@Steamy but the pressure is high

Like, you constantly have to work your a** off, either on tests, or socially wise, or just in any regard

@AkivaWeinberger Thanks, I suspected it was something like that, can't believe I missed it.

but at least it's fun

@DavidVarela Test: $\displaystyle\sum_{n=1}^\infty\frac1{n^2}$

@AkivaWeinberger yeah and $\langle a\rangle\cap\langle b\rangle=\langle \text{lcm}(a,b)\rangle$, if you apply the second isomorphism theorem to the ideals of $\Bbb Z$ you just get the identity $ab=\gcd(a,b)\text{lcm}(a,b)$

(If you set it up right the above should render)

$\frac{\pi^2}{6}$

@AlessandroCodenotti Remind me what the second isomorphism theorem is, again?

(It's annoying how there's a LaTeX command for $\gcd$ but not $\rm lcm$)

$\frac{B}{B\cap I}$ is isomorphic to $\frac{B+I}{I}$ where $B$ and $I$ are respectively a subring and an ideal of some common ring $A$

We read in Latex, @David. It's our side language now

(sometimes one also puts the facts that $B+I$ is a subring of $A$ and $B\cap I$ is an ideal of $B$ in the conclusions of the theorem)

@Avantgarde $\phantom{Secret message!}$

and the isomorphism is the function $x+B\cap I\mapsto x+I$

So $\frac{\langle a\rangle}{\langle{\rm lcm}(a,b)\rangle}=\frac{\langle\gcd(a,b)\rangle}{\langle b\rangle}$

:P

@Akiv

@AkivaWeinberger Sweet, got it working. That's way cool

I should do something about this though. I don't have mathjazz enabled or whatever. All I see are hieroglyphics

yeah, and then you show that $\left|\frac{n\Bbb Z}{m\Bbb Z}\right|=\frac mn$ whenever $n|m$

Nice! @DavidVarela $\phantom{Avantgarde, we attack at dawn}$

Now if only there was a script to convert thoughts straight to latex..

@EricSilva I summon thee! (just joking, I have a PDE question)

Someone on the math discord is complaining about math

i have been summoned, although unsure of how well i will be able to answer, having a slow day @Alessandro

but go ahead

do you know about Green functions (and Poisson kernels)?

What? I thought they were Red functions! Need to have my eyes checked

yeah

Lel @Akia

@ShaVuklia In my experience, what catches most attention is doing well during exercise sessions (professors definitely hear from TA's), and especially asking good questions during lectures. Most of all, though, these things should be consistent. Doing well every week and asking good questions every now and then, leaves a better impression than having one stellar exercise session and nothing remarkable the rest of the year.

How do I see these equations on a chatroom? I remember there was a meta post on it.

ok, so we saw in class how to calculate the Green function for a ball in $\Bbb R^3$ when dealing with the Poisson equation

Also, helping out voluntarily on, like, open days.

@Avantgarde Do you have mathjax?

It's on the right

@Avantgarde I posted the link above... and also it's on the top-right

where it says "latex in chat"

@Dodsy I have no idea

If you see dollar signs rather than equations, you don't have MathJax

@DavidVarela That scares me, because I can only stay concentrated so long and suddenly my latex document would be filled with random stuff

@Avantgarde Are you on mobile?

@Dodsy @Akiva Great, let me fix this right now.

No, browser.

on laptop

OK

@Alessandro ok

so basically those functions only depend on the domain $\Omega$ (which is an open subset of $\Bbb R^n$ with compact closure) in which we want to solve the equation $\Delta\varphi=f$, with $\varphi|_{\partial\Omega}=\psi$

Oh, it works!!

Thank you!

Grea

t

yes

for which kind of $\Omega$ does a Green function exist?

@SteamyRoot My notebooks are already filled with random stuff! It's kind of weird to look back on old work: "What the hell was going in my head!?"

wrt which operator @AlessandroCodenotti ?

the laplacian

I dont know much about this, but I think there are greens functions for $\Delta$ on annuli. I dont remember if this was a difficult or suprsing result though

Other than that you might like this ams.org/journals/proc/1952-003-04/S0002-9939-1952-0051380-0/…

hmmm @Alessandro i dont know what's necessary

@Steamy That's absolutely true. As far as TAs go: I am known for "doing my own thing" in class, usually against the advice of a lot of TAs and fellow class mates. So while that is a bad thing right now (they keep telling me I don't study "right"), I think it will actually turn out very well for me later, because it's just another instant of me showing I'm confident in doing things my way, and I can also do it right.

i imagine you need to be able to somehow make sense of normal to the boundary or have something that makes that issue go away

But just any involvement is going to count, just what works for you. I think one of my "attributes" is that I actually enjoy math/physics outside school, which surprisingly many students don't. Most students would tell me I'm crazy/boring if I continue reading on a subject we've had in class, so I'm guessing that's just good news for me, because obviously the competition is less then. But I already know who the people are I should either 1) collaborate with, or 2) watch out for.

So it doesn't matter that the bulk of the people aren't even highly passionate in the first place. In the end, I just count on the fact that I love math/physics a lot, for when that love dies out, everything I've built will be lost anyways, because I won't be able to pursue it any further without a genuine interest.

if you have a regular enough boundary i think you can prove the existence. iirc i read this somewhere but im not sure if im remembering correctly

@s.harp interesting, and thanks for the other link, I'll see if it's not too advanced. Sadly this was just a first course in PDEs so we saw how to use Green's functions to solve the problem, assuming they somehow descended from the sky, we never discussed their existence

@ShaVuklia I agree and disagree with this. Or, at least, I'm ambivalent about whether that's a good attribute.

the thing is that green's functions are really hard to find unless you have a very nice geometry

@Semi lol me too probably, but tell me why

@EricSilva orientable boundary seems like a reasonable request if you want to have at least the green identities

the professor who taught me what i know about PDE said it's kind of an old way to think about PDE @Alessandro

yes

Why I agree with it is being interested in a subject makes one naturally more willing to put more effort and attention into it.

Why I disagree with it...well, not everything you'll have to do is interesting :/

@EricSilva yeah the professor mentioned that. Our calculation for the green function of the ball heavily relied on its symmetry

@EricSilva he mentioned that too, but he also said we don't have the tools at this point to get into more advanced PDE theory

yeah similarly the other easiest domain to calculate for is like a half space which requires reflection symmetry, so like without loads of symmetries you can't do much, as with lots of math

Smart? @EricSilva

@Semi I don't think a person has to be "interesting" at all:P just involved and passionate and genuine (towards themselves). I think such a foundation ensures a good enough future

And if you get sick of a subject, it's hard to invest as much energy into it even if you once really found it interesting.

Schlag and smart have both expressed these things to me @Daminark

Nah, I didn't mean that the person wouldn't be interesting.

Schlag talking about the "old" way of doing things... interesting...

@EricSilva half space sounds like its doable with the method of image charges as well

@Semi you mean doing interesting activities right? like I dunno, setting up their own project, or arranging something?

no, it's not that either

@Alessandro i imagine it amounts to doing a similar thing, havent done that though

Also I'm starting to get the vibe that Schlag likes probability a good deal

he does

Apparently the RTG projects with him feature it prominently

@Semiclassical also, I'm not sure why you said this, beause I don't think I referred to something like this. I'm guessing I'm miscommunicating, but my point was kind of "do what you want", which is the opposite of continuing a subject you're sick of. But alright, there kinds of conversations are vague/hard anyways maybe

More like: even in research, not everything you do will revolve around "how do I figure out this interesting problem"

@Daminark, i think they're about probability and harmonic analysis or whatever

Practically speaking, one can't always do only the things which you like

of course, we have to stay realistic:d

yeah

I donno. I threw out a lot of scattered opinions out there, but I don't really think them through a lot. It's just what comes to my mind.

@BalarkaSen and @MikeMiller do you know the book on Fibre Bundles by Husemoller? Do you think this is a good book?

I will say, of the people I know, Schlag seems to be one of the more broad ones in terms of what he likes

stay complexistic

i dont know books @s.harp

So I think there is something to be said for being able to learn a subject even when you don't find it fascinating

are you looking for anything specific?

Im just sort of wondering what the general opinion on this book is

@Daminark Neves told me he wants to teach galois theory at some point

@Semi yea I agree with that.

he's pretty broad in terms of likes too

I have seen the book on a bookshelf

but that's it

There is something to be said for approaching learning as work rather than play

It looked good, the binding

we're basing a seminar on it

Lol I do remember when I was asking him quite some time back about what he thinks is good to do, his suggestions were wide

That's what I highly disagree with @Semi, here's why

so far the talks have all been so incredibly dry and boring and I wonder if its coming from the book itself

Number theory, do we have a class on curves and surfaces? Algebraic topology, geometry, make sure you know analysis, etc

@Balarka it's that inviting shade of springer yellow that makes us folk feel at home

actually I don't. I misread what you wrote

all I want to say is:

Heh

@EricSilva Hey, true!

@EricSilva lol

@Daminark he has given me a lot of advice to know things broadly cause the skill he thinks has been most useful in his career is just recognizing when shit looks familiar

I got the vibe that Schlag was broad since, like on one hand he likes probability, on another he's a harmonic analyst, then he seems to very much believe in teaching complex via algebraic topology, and he's also geometric

All that's left for him is diagram chasing

anyone good with graphs ?

@Semi Many students consider learning/studying "work", and therefore associate it with something negative. Of course you have to put in effort (which is pain, at times), but I think the trick is to find a joyful way of learning, if you're heading for a more theoretical career anyways. And that was kind of my point of "doing my own thing". While a lot of students study for test results, I think it's helpful if you can find a way to enjoy your learning too, which I can when I study "my own way"

@s.harp what does the book cover

@Ali.B I know a bit of graphs?

Sure. There's a balance

@EricSilva i shopped some of those GH ideas around; no bites yet though

But yeah I mean, he's fun for sure, it's sad that he won't be around much next year

@Daminark he has said to me "I love geometry, it is one of my favorite subjects, I just don't know enough examples"

I see

did Schlag say this

where he said examples with his unique Viennese emphasis

yes

i did

so the one example is the potato chip

Ideally, yes: any career should admit a degree of play room, so to speak

what's the other?

Hahahahaha

Oh, speaking of

I've perfected my pringle manifold over the course of this year, I'm quite proud

I never did solve that potato chip problem

@MikeM cool, should I read over the things you sent me on background? I haven't found time to look at them

But one shouldn't rely on being able to do tyat

with the $S^1$ in $\Bbb R^3$ thing

nah

@Balarka he says to look at the hyperbolic plane a lot

mmk

just keep doing your thing

part 1 is basic bundles which moves into fibre bundles and a bit gauge groups. He does most of it without assuming local triviality and a bundle is just a surjective map between topological spaces. part 2 is k theory and part 3 characteristic classes

@Eric he likes negative curvature eh?

most curvature is negative curvature

But yeah I do agree with that philosophy. Laci also said to do the same, I did this one problem and he was telling me about a way to modify my solution by thinking about signed measure and making it an integral

@s.harp sounds boring

the style seems so super dry to me

@EricSilva i'll let you know if the background stuff i suggested is actually worth reading

i guess he does @Balarka, never talked to him about what he likes specifically, we've mostly just talked about what i like tbh

thats what bothers me the most, he somehow manages to make things that should be obvious seem technical

mmk @MikeM sounds good

broadly, though, just keep doing what you were gonna do before

and maybe you can teach me about $\Delta$ as it happens

i need to start reading salamon seriously

The other qualm I have is that it's an attitude that can be taken advantage of. Namely: if you've been persuaded that you're doing X because you love it, then it's easy to exploit that by introducing things that you don't agree with and saying "if you really love this, you should be willing to make any sacrifice for it"

i've had to run too many errands lately to settle into my new place

hope to start picking it up this week

i need to start eating salmon more seriously

That's an attitude I think is endemic in grad school

@Ali.B Oh, that unfortunately goes beyond what I'm familiar with :(

lmao

in my mensa we have salmon. You pay per gram, so it costs the same as rice, and indeed the grad students go nuts when its available (connecting @Mike and @Semiclassical statements :P)

@Daminark no problem :)

@s.harp do they go nuts or do they go salmon? :P

It makes it impossible to address stuff like working conditions because, if you object, it's because you don't love what you're doing enough / aren't cut out for academia

har har, triple entendre

Though I'm not familiar enough with grad labor stuff beyond my department to speak too generally

@Semiclassical yeah, and they accuse you of "unhealthy salmon addictions" and "covering the lab with salmon"

but these are more or less basic workplace rights

Right.

Plus there's the context of "everyone who really likes their field is trying to get into grad school"

Aka "if you're not willing to put up with it, someone else will"

Which is a pretty classic way of making sure people don't question things