@MatheinBoulomenos Hi mathein

@MatheinBoulomenos Could you explain to me the idea behind the quotient group?

@Jacksoja so seems like he isn't quite around right now so I'll try and probably fail to say

You should have the integers mod $n$ in mind

Yo @Adeek

hiiii @Daminark

@Daminark I want a small cabin in the woods so I can go isolate myself and do math :D

gets megaphone NEEERRRRDD

haha

But yeah idk might be helpful for concentration

yeah without all the noise

@Adeek I find it useful to always place my desk facing a window, so I can look out when I'm thinking! Failing that, set your desktop background to some nice nature pics and pretend it's a window when you need to concentrate... depressing look at modern life

Dingo dingo Ding

howdy, Faust

Hows Ted?

trying not to get the 'flu that everyone has ... but about to go out to dinner.

nice

im thinking about going to sleep

been up since 3

G'night, then.

know of anything related to number theory thats geometric?

@TedShifrin :(

@Faust, there's this sort of question.

i have to write a report ona research paper or write someonething intresting related to number theory

Proof

@TedShifrin interesting thats more my area of interest than number theory

It ties in to all sorts of number theory stuff.

@LeakyNun You may be interested in the above ^

@Faust: Look up geometry of numbers.

@TedShifrin you call?

Inb4 "Would I ever page you purposely, Demonark?"

Would I ever page you purposely, Demonark?

wow such savagery

heya Eric

yo yo yo

Wow I predicted your statement perfectly

l m a o

a deft edit, there

probably more daft

tfw revisionist history happens in front of your eyes

those are the times in which we live, Eric

sad but true

much recent news has made me very very angry

oh hell, yeah

the country has to rise up in revolt soon

which country>

the one Eric and I inhabit

oh its full of crazy people that won't happen

the crazy ones are about 35% of voters ... that leaves plenty.

see that i Trumped ya...

Ted I officially revoke my claim to the worst punster

:P

lol

Is someone complaining about american politics!?!?

@TedShifrin the ones who are ok with the really crazy ones are also bad

im just making terrible puns...

honestly im pretty much perpetually angry about american politics (and brazilian politics)

i guess my leanings are fairly transparent

Maybe I shouldn't encourage this kind of punning. Solution: pun so hard that no one else can bear to do so

they're so transparent that you've fallen over, Eric

lol

I honestly don't even have leanings anymore, aside from wanting people to be reasonable.

@Antonios-AlexandrosRobotis crucify him tbh

Anyway thanks ted im sure i can find something intresting to do

The only things I really think are non-negotiable are the various common sense social issues. Economically I am more dubious.

economic issues are social issues

actually, @Faust, trying to decide which PIDs are Euclidean domains has some interesting basic geometry in it!

There's discussion of that in Hardy & Wright.

i had an example of one that wasnt the other but i forgot it

@TedShifrin wait really?

I believe I remember so, Demonark.

That's pretty nifty

ok i resign

resign from the world?

lol from being awake

ill ttyl

night

True @EricSilva but in a less direct way than obvious things like gay marriage etc. The economic solutions are far harder to come up with (as far as I know)

See you!

I need to go out to dinner, anyhow. All these JMM folks in town.

night

See ya later, Eric, Demonark, Antonios.

@Antonios-AlexandrosRobotis i agree

Hope you're still enjoying my exams, Antonios :)

See you Ted!

I sure am @TedShifrin

see ya @Ted

have a good evening!

Night (for now, anyhow).

i feel like i have option paralysis with all the different kinds of math i should be doing rn

let's hear the options :)

i have to read about the heat kernel for compact riemannian manifolds before thursday

i have to read some diff top and do some problems also before thursday

and i have to read minimal surfaces generally all the time for lots of reasons

well diff top would be my choice :P

but to each their own

it is probably the least involved of those

i could also do none of those and eat ice cream and cry

Heat kernel for DCal?

yup

well fwiw, when I'm stressed and I have too much stuff to do, it's best to start with the easiest

tangible progress is a great motivator

that is a very valid point

You should do communist algebra instead

are you making a pun about commutative algebra or should i do algebra while reading marx

The former

i can do either i have capital and jacobson on my nightstand

lolol

i do want to learn commutative algebra properly but that's a project for another time

this quarter is way 2 busy

Drop DCal's class tbh

:P

nah that's the best one

other than Neves' class those are tied for being the raddest

i figure ill just take the winter quarter of gralgebra next year @Daminark

But you have to sit through a quarter of geometry!

ah yes what a tragedy

a geometer sitting through a quarter of geometry

oh shit i just remembered

at the end of minimal surfaces on thursday Neves' looked at his watch and saw he went ten minutes over and turned to the class and said "You know I'm like a tragic greek hero, like Oedipus. Everything i do to prevent going over time causes me to go over time, like oedipus and dating his mom"

such gold

@Antonios-AlexandrosRobotis ive decided to listen to your advice

I hope it helps!

@Faust faust my man ! am alive and well thanks, I did finish algebra exam long time ago =p was just repeating it for myself wbu?

@anon Anon :D how are you ? :D

@Daminark dami :D

@Daminark long time no see

@Adeek what is up karim ?

what the hell is this. no one here to talk to kasmir?

:O

Yo @Kasmir, sorry I was doing work

@KasmirKhaan We also got a new cat at home

sorry for my late reply as well.

how are you

@Daminark I got a new cat :D I have now 2 cats at home

@Adeek that's amazing! :D

@Balarka how go the memes?

@Daminark the memes go skrra

@LeakyNun (and @Daminark) Now figure out the fundamental group of $S^3 - K$ where $K$ is a knotted circle in $S^3$.

Arbitrary knot. Maybe assume it's a tame knot.

It's tricky for me to decipher knots because in all of $\mathbb{R}^4$ I think you can undo any knot

Yup. Do you see why it is so?

I have an idea that I don't see but can sorta believe in words

"You have an extra dimension of movement"

That's the idea. Would you want to listen to a perhaps better picture?

It does make sense that given that much freedom, you can sorta play a kind of game of undoing it without self-intersecting. But actually processing $\mathbb{R}^4$ at all is beyond me

Sure

"Listen to a picture"

Without context it feels like level 7 drugs

I write excellent r/nocontext material

Ok, think of the extra coordinate of $\Bbb R^4$ as a "color coordinate"

$\Bbb R^3$ sits inside $\Bbb R^4$ as $(x_1, x_2, x_3, 0)$, and the $0$ in the last coordinate is represented by say the white color

So the knot $K \subset \Bbb R^3 \subset \Bbb R^4$ is all white.

Okay maybe even context can't dispel the notion of drugs now, but proceed

loooool

So now think about a crossing in $K$ where the overpass is $\ell$ and the underpass is $\ell'$, and both are white.

Is this a good knot image or is it knot?

Yep, that would do.

That's better

I'm looking at a specific crossing right now, so say the bottom-most crossing

$\ell$ is overpass and $\ell'$ is underpass

Aight

Now, "move them in the color coordinate". So $\ell$ slowly changes color from white to navy blue to finally deep blue. The position stays the same!

$\ell$ and $\ell'$ have the same position, but now have different color coordinates

One is white and the other is blue

Alright

Now make $\ell$ and $\ell'$ pass through each other. NO intersection happens, because they have different colors.

$\ell$ becomes the underpass and $\ell'$ becomes the overpass. $\ell$ is still deep blue, but bring it back to white coloredness

I buy that

You have flipped the overpass-underpass pair to underpass-overpass pair

Do this to all the crossings and you have unknotted your knot

So how badly does being in $S^3$ constrain this process?

I can't change color :)

The whole process was happening because every point not only had a position coordinate but also a color coordinate

$\Bbb R^4 = \Bbb R^3$ (position) $\times \Bbb R$ (color)

Is there no way to shift it around, that changes both colors nicely and do at least partial gypsy witchcraft?

Actually you know what, that sounds like a dark rabbit hole

@BalarkaSen interesting

So I'm gonna once again do the stereographic projection and let a point be infinity

@Daminark Right, you can do that. The knot would miss a point at infinity anyway!

Oh fuck I wanted to stick it there

Such is life

I see. You wanted to make it go around the point at infinity

So, $\mathbb{R}^3$ minus the knot

We have winding number considerations and then we also have overpass/underpass considerations

Initial guess is $\mathbb{Z}^3$ or $\mathbb{Z}^4$

(Either based on the over passes or based on, well if you project to 2-d like the image above, there are 4 regions you might be in trouble in if you stick a circle through

You'd be pleasantly surprised by how complicated those groups can be :)

@BalarkaSen so that is how you think about R^4

Occasionally

There's a lot of ways to visualize high dimensions. That's one of them.

@SimplyBeautifulArt I mean, it isn't actually that big

Hey @Ted!

Hi, Demonark and Balarka.

Hey @Ted!

How goes the struggle?

@Daminark maybe avoid using the ethnic slur

Ah, poor judgment on my part. Apologies

No worries

interesting...

...TIL: Gypsies are believed to have arrived in Europe from northern India in the 1400s. They were called Gypsies because Europeans thought they came from Egypt. This ethnic minority is made up of distinct groups called “tribes” or “nations.” Most of the Gypsies in German-occupied Europe belonged to the Sinti and Roma tribes.

Egyptians

the group refers to themselves as romani and the term gypsy is usually seen as pejorative

That, sir, would be politically correct :-)

i think it's just correct

using exonyms for people is kind of weird

"witchcraft" on the other hand...

especially when they're actually wrong

politically correct

i dont know anything about the romani except that they exist. my ignorance about the various cultures and subcultures of the world is tremendous :p

@BalarkaSen there are a lot in Brazil (in part because of the portuguese inquisition)

Ah

so ive had a little exposure but not much

Rio?

my family is from BH mostly

i live in the states though :P

i just am in brazil frequently

@Balarka might read chapter 9 of eliaakfnaskvbkdjsbarg masnjvcakdjsbvaksdjfhaskdfhchev tmr

woo cool

i got ahead of my work so i have time to think about these too twisty guys

there should be a generalization of manifold called too-many-folds

cc @Daminark

i have been writing out some notes as an accessible introduction to the h-principle

@EricSilva an excellent work of literature

or maybe we can call manifolds with a contact structure too-many-folds

i spent a month on trying to understand it

i guess that's not a good name tho

@BalarkaSen hmu i like accessibility

ill send it to you if i end up finishing it

mmmmmmk

1-fold, 2-fold, red-fold, blue-fold

im bored

I need to study physics :S

F

same tbh

did you just press F to pay respect literally

wasnt that from call of duty

a game which i cannot picture Amin playing ever

the origin of that meme has been lost in time

knowyourmeme.com/memes/press-f-to-pay-respects

meme saab?

"did you just link knowyourmeme unironically"

maybe?

I care so little that i cant tell how many layers of irony im working on

lol

im worried there might be torsion so it wraps around and becomes unironic again

@Eric I've played some call of duty

doesnt strike me as ur style

Never found that scene but I know of it

Daminark only plays waifu simulators

Yeah I'm more into Smash

@Balarka for fuck's sake

smash sucks

smash is definitely a waifu simulator

(what is a waifu)

it's a pejorative for anime wife

anime was a mistake

Daminark and I got an inside joke going because he played Doki Doki Literature Club so much

So much?

I played one round

enough for so much

you were really into it dude

And you know yourself that it ceases to be a waifu simulator rather quickly

im an analyst so i can tell you 1 is a huge number

I mean the game is disconcerting as shit because they give you so many warnings

$\varepsilon \ll 1$

Uhm I guess I'll come back later

hHAHAHAH

So you're expecting things to go to shit almost immediately and then it just doesn't happen

@AlessandroCodenotti Good idea

@Alessandro kek

Im going to watch a playthrough of the new Resident Evil 7 DLC

it's so different from the base game

Hmm

I really liked the base game

i like re7 a lot

the dlcs are good but not base game good

mm i see

still worth watching/playing

end of zoe is just re7: street fighter

I'm watching not a hero rn

urbandictionary.com/define.php?term=skullpatrol

We all know that re4 is the best one

looool

not a hero is just re7: every other resident evil game that isnt 7

@AlessandroCodenotti fight fight fight

@Eric yeah so far it just seems like a lot of gunnery

RE7 is unique because it's a survival horror game

unlike previous RE's

2017 had a lot of good survival horror going man

RE7, Outlast 2, ...

I don't know if anyone disagrees with you but we've gone for far too long without a slap fight so let's go

I'm out. you clearly are trolling

@BalarkaSen re7 is unique cause it's good

Leaky: $$$$

lol

idk how i feel about outlast 2

$$\frac{1}{0+\frac{1}{0+\frac{1}{0+\frac{1}{0+\frac{1}{0+\frac{1}{0+\frac{1}{0+\‌​frac{1}{0+\frac{1}{0+\begin{pmatrix}Glitch \\ 0 & 1/0, 0/0 & re7 \\ System & glitch & 243422322\end{pmatrix}}}}}}}}}}$$

lol

I loved the storyline

the highs were really high for me but sometimes it felt kind of disjointed

For me the complaint is that it's fast paced

you have things happening way too fast

The claustrophobia of Outlast 1 is not really present

I think I would agree

And now... some geometry:

Better

hai, secret. nice to see fractals.:)

@Mathein seems like a nerd just joined the chat

@Daminark indeed

How's it going?

pretty good thanks

I'm thinking about choosing my bachelor thesis advisor

And for you?

Oh I didn't know those were a thing

Doing aight on my side, still early quarter so things are more smooth

Borderline analytic even

ba dum tiss

@Daminark don't you have a bachelor thesis?

I mean in some majors yeah, not in math though

Ah I see, so you just finish your exams and move on to grad school?

Yup

Cool

I mean the bachelor thesis isn't a big deal here, it's worth 6 credits out of the 180 you need to graduate

The master thesis is worth 30 credits out of 120 and it's the important one

I should also choose a topic and an advisor, but I already have an idea so it's fine

Hi. My full problem is too long to describe here, but suppose that I'm dealing with $\sum_{k=1}^K a_{k,K}$ ($a_{k,K}$ are nonnegative) and I want to show that, as $K\to\infty$, it's only terms $k\propto K^{1/2-\delta}$, $\delta>0$, what matter (i.e., the others sum to zero). My problem with proving that is separating such terms from those of a higher order, since there is no first term of order $K^{1/2}$. Any suggestions?