point-set-topology

[sleek thicket]

chm

[tough imp]

It took me a year to become evil Hartshorne memer

[cedar pebble]

yea i grew out of it after a while

[sleek thicket]

you are literally

Taking a stacks class

And doing simplicial stuff

Right now

[tough imp]

It took me 2 years to get there

[cedar pebble]

but first few years of undergrad when I was DEEP into nlab/topos theory/type theory/categorical logic

[sleek thicket]

I'm taking functional analysis and a diff geo course

[cedar pebble]

we don't talk about those blunder years

[sleek thicket]

which one of us is evil???

[tough imp]

[obtuse meteor]

instead I talked to my prof for a long time about my idea for volume differentials on topological spaces equipped with a borel measure

[tough imp]

Sham you have background in PL theory

Who is evil

[obtuse meteor]

lol

[sleek thicket]

you

[obtuse meteor]

sham is evil

[tough imp]

Yes

[cedar pebble]

sham: haha you people are evil I would never do such masturbatory mathematics
also sham: the problem about vector bundles in terms of 2-functors

[sleek thicket]

None of you are free of sin

[tough imp]

Tfw trying to category pill Jack Lee

[sleek thicket]

I brought up yoneda the other day

[tough imp]

☘️

[sleek thicket]

In OH

[tough imp]

Lol

I recall

[cedar pebble]

Yoneda is unironically good tho

[tough imp]

He said

[obtuse meteor]

the idea of this is if you have f : X -> Y and these are both equipped with a measure and you choose an appropriate sequence of neighborhoods U_1, U_2, ... around a point x then you should be able to define |Df(x)| = limit as n -> infty of mu(f(U_n))/mu(U_n)

[tough imp]

“We will do this directly”

Right?

[sleek thicket]

but in my defense it's literally a thing about a natural transformation between representable functors

yeah

[obtuse meteor]

should be something like determinant of jacobian

[cedar pebble]

trying to remember the person that uses the Japanese Yo (よ) to denote the Yoneda embedding

[obtuse meteor]

yoneda is good

[cedar pebble]

this is unironically good notation

[tough imp]

No it’s evil

[sleek thicket]

Hom(yoneda is good, —)

oh?

[tidal cedar]

I like that notation

[obtuse meteor]

I have sunk way too many hours thinking about this idea and what properties you want the sequence to have

[sleek thicket]

why is it evil

[tough imp]

I don’t

[obtuse meteor]

despite not knowing any measure theory

[tough imp]

Because why bring in a kana

[cedar pebble]

honestly people should use more nonstandard symbols in math

[sleek thicket]

Do you think it should be Kanji or something?

[cedar pebble]

I use cyrillic symbols in my math if I get the chance and it's not too gross

[obtuse meteor]

[tough imp]

No

Idk

It probably isn’t that bad

But it feels weird seeing Japanese on a math thing

[cedar pebble]

I mean it's bad because LaTeX has the WORST support for characters like this

[sleek thicket]

I was just trying to understand if it's the kana or the Japanese

[tough imp]

Oh

Yeah no

[sleek thicket]

And yeah idk we use Greek and Cyrillic and Hebrew

[cedar pebble]

qed symbol replaced with chmonkey emoji

[tough imp]

Ultra

[obtuse meteor]

I'm gonna write a paper that uses

[tough imp]

Indeed

[obtuse meteor]

mark my words

[sleek thicket]

hell yeahhhhh

[tough imp]

Dan

Just put

[sleek thicket]

☘️

nabe????

[tough imp]

:dan:

[cedar pebble]

actually I did use as a qed symbol in a math shitpost I wrote up for someone

[obtuse meteor]

nice

[sleek thicket]

lmao

[tough imp]

Gabe said he quit math but he’ll be back in 1 month with a new topic to learn for 2 months

[sleek thicket]

oof

[obtuse meteor]

I use this for my qed symbol on all my homeworks

[sleek thicket]

nice

[obtuse meteor]

"don't you think it's kind of ... to drag mathematics down to ..."

[tough imp]

Which flag is the wario colors?

The like purple and black one

[obtuse meteor]

who has this shitpost on hand?

[sleek thicket]

Alex and my friend Jessie uses a sad cowboy emoji

[tough imp]

I do

[sleek thicket]

Aly does

hel yeah

Animated papers

[cedar pebble]

post on twitter
Aly likes the post before I even hit tweet

[obtuse meteor]

yes

[sleek thicket]

l o l

[obtuse meteor]

this person is my TA
-1000 pts

[tough imp]

Seriously???

[cedar pebble]

platonic math
why not non-platonic math

[tough imp]

Yeah

That’s my favorite part

[sleek thicket]

actually math isn't transcendtal at all. It fucking sucks. Have you ever been stuck on a math problem? It's gay as hell and i hate it

[obtuse meteor]

true

they're not

they just don't know it yet

[sleek thicket]

Tfw they stopped taking my bait

😢

[tough imp]

WAIT

[obtuse meteor]

lol

[tough imp]

I never saw that one

Or at least remember it

Lmfaoooo

“These indignities”

At that point I want to believe they were trolling

[sleek thicket]

Yes

[tough imp]

Hahaha

“Sheafs”

[cedar pebble]

Litt is getting in political arguments on his alt again

[tough imp]

Down to the little details

[obtuse meteor]

with who

[cedar pebble]

with a handful of people, he made some post about the NYT article about SSC

and it started a thread

[sleek thicket]

I pretty much agree with litt's take. Ssc is p bad but the nyt behavior seemed sketch

[cedar pebble]

yea I agree too

[obtuse meteor]

oh Juliette bruce and dlitt arguing

that's spicy

[tough imp]

What is SSC

[sleek thicket]

It seemed pretty cordial

[cedar pebble]

I think the contents of the article were perfectly fine if not in bad faith, though obviously the author is entitled to their opinions and that's fine

[obtuse meteor]

yeah it is cordial lol

juliette bruce gave a talk at my school's math club recently actually

[sleek thicket]

as far as Twitter arguments go

She seems neat

[cedar pebble]

but I feel like the actual doxing added no content to the article and was kinda gross to do

[sleek thicket]

I went to her zoom oh

A while back

[obtuse meteor]

she went to the same uni as I do for ug

[cedar pebble]

yea Juliette is super nice

for those not in the loop: SlateStarCodex is (was) a blog by some rationalist guy that posted some slightly spicy opinions although he is generally milquetoast liberal and I don't think anything on that blog is particularly abhorrent

the author was anonymous though

NYT wanted to do an article about the blog and insisted on publishing the full name of the author

the author, a practicing psychiatrist, said that he really did not want his name out there because he did not want his patients knowing his online name as this would interfere with actual psychiatric practice

NYT said no, we're publishing it anyways and there's nothing you can do about it

idk it was kinda gross and I don't think revealing the name added anything to the article and at best seemed to be an effort to dox and shame the author, consequences be damned

[obtuse meteor]

yeah

[cedar pebble]

the actual content was totally fair but yea the doxing was kinda :/

[tough imp]

That sux tho :/

[cedar pebble]

Litt's post definitely got ratio'd by the replies lmfaoo

[sleek thicket]

related tweet:

https://twitter.com/NintendoUpd8s/status/1360417211043639299?s=19

Nintendo of America (@NintendoUpd8s)

Meow meow meow! Nothing feels better than the inside of a cat!

Retweets

1265

Likes

7703

Twitter · Feb 13, 2021, 2:35 AM

[cedar pebble]

SHAM HOW IS THAT RELATED

[obtuse meteor]

jgfkjh,g

[sleek thicket]

it's related

[tough imp]

Unofficial Nintendo account

Kreygasm

[sleek thicket]

yeah it's not real lol

Just funny

[tough imp]

https://tenor.com/view/monkey-pog-pog-poggers-monke-pog-monkey-poggers-gif-19560507

[obtuse meteor]

another great thing about my exam--scheduled in the hour and 30 minutes between two other things

also due the same day as the draft for another midterm presentation thing in my research class

[cedar pebble]

https://twitter.com/antisisyphus/status/1360739626751778825?s=21

otaku entropy complex (@antisisyphus)

italians when you ask whats for dinner https://t.co/xMcYJd7ruz

Likes

516

▶ Play video

Twitter · Feb 13, 2021, 11:56 PM

important tweet

[sleek thicket]

Wow that's pretty fucked

Do not like

[obtuse meteor]

it's okay we like barely have a research question yet

But my portion of it will be easy

bc I just show off the program I made

for a few minutes

[sleek thicket]

I'm trying to remember what you're doing and feeling bad that I can't

Since I edited your statement and you talked about it

[obtuse meteor]

Game of Life stuff

[cedar pebble]

I should maybe finish grading my students' quizzes so they can figure out what they did wrong before the exam

[sleek thicket]

Oh yeah nice

[obtuse meteor]

probabilistic extensions

[sleek thicket]

I'm considering TAing next quarter

Applications are due Friday

[cedar pebble]

student: sorry I haven't turned things in I'm doing bad lately
me: yea thanks me too

[sleek thicket]

but last spring was so fucking bad

[obtuse meteor]

and whether you can have nice behavior despite having probabilistic rules

and what's a good set of probabilistic rules

the grad students were very miffed a few Wednesday's ago

bc like

[tough imp]

Almost a year of this shitty online school thing

[obtuse meteor]

there was this very simple paper which implemented like a very not interesting probabilistic extension of GoL in 2019

and it was a conference like keynote paper for a computer science / math thing :P

and they were like "aha, so this is what I need to do to get a conference paper, great"

[tough imp]

Sham if I get into Columbia you’ll receive a very excited phone call

[sleek thicket]

L o l

Bro if you get in

Call me immediately

Like

You can tell your family first or whatever

[obtuse meteor]

columbia reu?

[sleek thicket]

but I want to freak about it with you

[tough imp]

No

[cedar pebble]

no not family first

[obtuse meteor]

grad?

[tough imp]

Like grad school

[cedar pebble]

chmonkey first

[obtuse meteor]

ah

[tough imp]

Chmonkey first

[obtuse meteor]

is it your app cycle?

[sleek thicket]

I mean like

[tough imp]

Yeah I’ll tell my Chmonkey magnet

[sleek thicket]

yall know who I'm telling first about grad school admissions

[tough imp]

Twitter

[cedar pebble]

[tough imp]

😎

[sleek thicket]

absolutely

[cedar pebble]

beat me to it

[obtuse meteor]

lol

[cedar pebble]

omg the flooshed magnet

[pastel linden]

printed out discord emotes

[sleek thicket]

It was not supposed to be subtle!

[tough imp]

Also Faye, i only applied to Columbia this year

Also bacono this was a xmas gift

Hahaha

[cedar pebble]

just apply every year until they say yes

[obtuse meteor]

lol

[tough imp]

They actually cap it

Lmfao

[sleek thicket]

Woah

Fucked up

[tough imp]

I think it’s like 3 or 4 times

[sleek thicket]

Idk where to apply

-uw

[obtuse meteor]

I'm going to apply to JH

[pastel linden]

wait

[cedar pebble]

damn 5th time's the charm

[sleek thicket]

-Columbia if chm gets in this year

I'm thinking about it Faye

Riehl is really cool

[pastel linden]

I have a poster that is weirder

[obtuse meteor]

and if I get in we'll know that I'll become a true gct

graduate ct

[sleek thicket]

lmaoooo

[obtuse meteor]

worse than ugct

[sleek thicket]

hey everybody let's play a fun game

[cedar pebble]

go to JH and work with Jack Morava and write even more insane papers than he does

[sleek thicket]

It's called

[sleek thicket]

Figure out where sham should apply to grad school

[obtuse meteor]

now I pester whole research areas with ct

[pastel linden]

jar jar 🥰

[cedar pebble]

Morava's papers are the funniest shit to me

if you've seen his arxiv posting

[sleek thicket]

Jonathan shit talked him a little lol

(in a nice way)

[cedar pebble]

yea lmfao

yea I mean he's brilliant he just takes uhhh

[sleek thicket]

like apparently his meetings were just not helpful

[cedar pebble]

a lot of creative liberties with his arxiv postings

[sleek thicket]

Jack is too galaxy brained

[cedar pebble]

this is like

THE iconic Morava paper

[sleek thicket]

I thought you were already in grad school??

[cedar pebble]

what an abstract

[sleek thicket]

That is so based

[obtuse meteor]

HUGE BRAIN

[sleek thicket]

Not meming

[tough imp]

I thought slim was in grad school too

[sleek thicket]

Guess I got mixed up with someone else

[tough imp]

I think

Yeah

[cedar pebble]

it's an unironically good paper he just starts his papers like that to meme on people

[sleek thicket]

nice

[tough imp]

Hmmm

[obtuse meteor]

If only it got put into like

the crank section of arxiv

[sleek thicket]

Send me the list

[obtuse meteor]

for a bit

[tough imp]

General mathematics

[sleek thicket]

we can apply to the same places and then be buddies

[obtuse meteor]

to complete the meme

[tough imp]

Hahahaha

[sleek thicket]

:^)

this channel is now

Brainstorm zone

[tough imp]

:^)

[sleek thicket]

okay so grad schools

Chm is applying to

• Columbia

• anywhere with AG

ez clap done

slim where are you applying

[tough imp]

Apply to Columbia, MIT, Mich, Brown, UW, and other

[sleek thicket]

That's why we're brainstorming!

Also yes Chicago good

OKAY SO

• chicago
• uw

Is my list

[tough imp]

Isn’t Chicago stipend

Like

40k or sometbinf insane

[sleek thicket]

Woah

[tough imp]

I heard it gives money money money

[sleek thicket]

@tepid depot ???

is this true???

okay so

[tough imp]

I think Dami said they give fat stacks

[sleek thicket]

I'm planning to apply to either Oxford or Cambridge

idk which

[tough imp]

Oh also Stanford

[sleek thicket]

I don't know the difference

[cedar pebble]

yea Chicago gives fat stacks

[sleek thicket]

Hmm maybe I should apply to Stanford since my parents are here

[tough imp]

NG

What Japanese schools are not trash for AG

Or is it not worth even bothering

[sleek thicket]

oh yes I was thinking about uga too

[cedar pebble]

everywhere except where Mochizuki is

[sleek thicket]

Unrelated to anything

[tough imp]

Kyoto

Okay

[cedar pebble]

nah a lot of them are good

[obtuse meteor]

whenever I look at brendan and chm I'm like "ah, I will never get into grad school" lol

[sleek thicket]

Faye you're doing fine lol

[tough imp]

^^

[cedar pebble]

although most of the Japanese universities that specialize in AG are very heavy on arithmetic geometry iirc

if that's what you're into

[tough imp]

Yeah :/

[sleek thicket]

You're taking a grad AT class in your sophomore year

[cedar pebble]

also jfc Faye you're doing fucking great STOP

[sleek thicket]

And got into a great reu

[obtuse meteor]

if you don't red Hartshorne by your freshman year

[sleek thicket]

Doing a ton of research

[tough imp]

Lol

[obtuse meteor]

you're not getting into grad school

[sleek thicket]

Look this worked out terribly

For everyone in our group but chm

[obtuse meteor]

lmao

[sleek thicket]

And he didn't even read it in that group lmao

[tough imp]

TRUE

Lmfao

[sleek thicket]

like literally he was the least into Ag until spring 2020

[tough imp]

I mean in moments like this just think

“Did Gauss read Hartshorne”

No

[obtuse meteor]

fhdlsajk

[cedar pebble]

Euler did tho

[obtuse meteor]

lmao

[sleek thicket]

lmfao what

[tough imp]

I mean

[obtuse meteor]

Sorry imposter hard

[sleek thicket]

It's okay and a valid feeling

I feel that way with people in this server

[cedar pebble]

no the feeling is invalid, if you're feeling it you should just beat yourself up more for having it

[tough imp]

Brofibration moment

We need a pensivecat

[obtuse meteor]

the one thing I do know is that I have done so much in my department it's honestly ridiculous :P

not math math

just like

[sleek thicket]

Anyways Faye I was really impressed by your statements and like

[obtuse meteor]

doing things and outreach

[sleek thicket]

Was a tiny bit intimidated lol

[cedar pebble]

outreach is very good

that will help you a lot in the long run

[obtuse meteor]

which one was intimidating???

btw that prof hasn't gotten back to me

[cedar pebble]

lmfao in my NSF application when I got to talk about outreach and I got to talk about being an AGS mod except without using the word discord because that would tank my application

[sleek thicket]

I don't do math club stuff, I didn't do research before my REU

[obtuse meteor]

very unbased

[sleek thicket]

Seems like you're doing a lot more outside your classes than me

[obtuse meteor]

ah

[sleek thicket]

This is not to say like

[obtuse meteor]

I just have a lot of connection to the two people who basically run the undergrad program

and so I acquire jobs

by being around them

[sleek thicket]

I didn't go "wtf Faye is so much better than me and I will not go to grad school"

it's just

[obtuse meteor]

ye

[sleek thicket]

We all spend our time and energy in different ways

[cedar pebble]

we all spend our time in the same way: on twitter

[sleek thicket]

you are competing against some prodigies though lol

[obtuse meteor]

yes

[sleek thicket]

Just not many of them?

Oh yeah I agree

I have a friend who's a prodigy

and the more math I do the less intimidated I am

[obtuse meteor]

I am gonna watch shows with gf now

[cedar pebble]

it's been a contant meme on [redacted] that I need to get off twitter and someone offered me money to delete my twitter

[obtuse meteor]

and forget impostering

[sleek thicket]

When I met him I was like "wtf this dude knows so much more than me"

But that's because he was a 4th year and I was a 1st year

[cedar pebble]

should I delete my twitter forever for $1000

[sleek thicket]

Not because he was intrinsically better at math

yeah

[sleek thicket]

yeah I would

If someone offered this to me

[cedar pebble]

yea I might actually if he doesn't pussy out lol

[sleek thicket]

Twitter is fun but $1K is nice

There are other sites

[cedar pebble]

I dunno I don't know if he's actually serious but he has a stupid amount of money and really wants me to stop posting on twitter lol

[sleek thicket]

okay but slim

Now that I know you have a Twitter

Do you follow me?

follow me you fucking coward

[cedar pebble]

sham doesn't follow me so I couldn't comment on the penis post

[sleek thicket]

idc

[cedar pebble]

me: I should keep my twitter professional
sham: penis

[sleek thicket]

You'll find out when we both get into Chicago yeah

I fluctuate ng

[cedar pebble]

what, about penises?

[sleek thicket]

I'm also an undergrad and not really a professional in any sense

I've thought about cleaning it up in time

[obtuse meteor]

I should keep my twitter professional

lesbian sex

[sleek thicket]

lol

[obtuse meteor]

liking porn posts

[cedar pebble]

yea I tried keeping it professional for a while but that ship sailed long ago

[sleek thicket]

Okay at least I've beaten Faye at this

OH FUCK I WENT BACK INTO MY ROOM HALF AN HOUR AGO TO DO MY FRENCH EXAM

[obtuse meteor]

it's ok at least my alt doesn't have an onlyfans link

[sleek thicket]

AHHHH

[obtuse meteor]

do your exam

[sleek thicket]

okay goodbye I'm going to throw my phone at the wall

night

[tough imp]

Bye

[obtuse meteor]

(yet)

[cedar pebble]

math twitter has two cool posts:
horny on main
bad puns

[tough imp]

Faye I feel like this is a specific callout

[obtuse meteor]

who has one?

I need to know now

[tough imp]

¯_(ツ)_/¯

I mean I don’t know

I was saying it feels like u were referencing someone in particular

Lol

[sleek thicket]

Wait wtf why didn't you talk abt this one https://twitter.com/NintendoUpd8s/status/1360417211043639299?s=19

Nintendo of America (@NintendoUpd8s)

Meow meow meow! Nothing feels better than the inside of a cat!

Retweets

1378

Likes

8288

Twitter · Feb 13, 2021, 2:35 AM

This is so much worse

[tough imp]

True

[cedar pebble]

okay yea it is lmfaooo

on the other hand

[sleek thicket]

okay exam started officially

[cedar pebble]

the penis post has a certain efficiency to it

[sleek thicket]

Timer is running

Goodbye for real

[cedar pebble]

good luck!

[shut moat]

OMG

[feral copper]

https://math.stackexchange.com/a/154585/259363
Hi ! I don't understand the argument in the answer here : "[...] is constant since X is complete", can someone give a helping hand please ? 🙂

[rugged swan]

imo by def complete means that its glogal section ring is trivial

and imo it is true for any projective variety

like for instance it is true for all projective space P^n_k

[feral copper]

Oh... I guess that's a theorem we didn't see in our lectures... Thanks !

[rugged swan]

I'm not sure of that tho

I don't know a lot about algebraic geometry, I've read some things via wikipedia lol

[feral copper]

Would you happen to have any reference about complete varieties ? In my specific case, I'm only interested in compact complex manifolds, as we're doing differential complex geometry

[rugged swan]

On wikipedia we have https://en.wikipedia.org/wiki/Complete_variety. It mentions the fact that every projective variety is a complete one but does not state the fact that its global sections ring is trivial. So maybe it is false that it implies that I've said. The projective variety page does not mention it either : https://en.wikipedia.org/wiki/Projective_variety. (Is O the structure sheaf on your link ?) Maybe you could look for any references on these webpages.

[feral copper]

(Sorry, I had to go away from the computer for a moment)
On the webpage, I saw as a corollary of Chow's theorem :

Every holomorphic line bundle on a projective variety is a line bundle of a divisor.

Is this usable with the group morphism Div(X)->Pic(X) ?
Also, in the MSE I linked, I suspected O to be the trivial line bundle, since L (x) L* = Hom(L) is itself trivial

[rugged swan]

oh if it's the trivial line bundle it makes sense then

it is X x L and since the projection map XxL -> X is closed I think it makes sens to say that Gamma(X,O) = k

[feral copper]

You mean X x k ?

But still, I don't see why we cannot take any holomorphic map f:X->C and call it a section of the trivial bundle by taking s(x)=(x,f(x)) then, so Gamma(X,O)=O(X) in this case :/

So this makes me think I'm missing something ! 😄

[rugged swan]

ok, ig if f : X -> C is holomorphic then it is a constant since X is projective x)

that's like the fact that O(P^n) = k x)

[feral copper]

Omg *facepalm

[rugged swan]

but idk

[feral copper]

Tyvm 😄

[tepid depot]

extremely false, it's more like 30k @sleek thicket

[tough imp]

Sadge

[tepid depot]

you do get a free laptop tho

so that's cool

(iirc you get a $1.4k budget for whatever you want, tablets are also cool)

also biden is president now, so maybe we'll get a union??

[tough imp]

U guys don’t have a union?

Rip

[tepid depot]

private school :/

so this is a whole story if you're curious

i'll give you the shortest version i can

in 2015 the NLRB ruled that grad students are private unis can unionize through the usual process

(get a majority of the unit to sign cards, do a yes or no election)

this happened for us, and after much litigation from the uni trying to stop it, the election happened

students voted in favor of unionization 2:1

the uni did more litigation to try and stop it until trump got in office

at that point, we had to pull back from the NLRB process to prevent the precedent from being overturned

cause trump appointed his people to the NLRB

so now that biden is president, he should be able to get his picks on the board, and if we won another election we should have a union that the uni would legally be required to bargin with

but that's gonna take some time

but basically students on the ground are overall quite supportive of having a union. especially in math lol

in math we TA second year, and teach calculus courses year 3+, so it'd be pretty great to have a uni to negotiate those sort of teaching conditions more

and also to have third party arbitration to deal with stuff like bad advisors

and of course pay, hyde park is gentrifying even more than before due to the obama library that's being built here

so yeah that's basically the story

ok i went and did the math, gross pay is $30,550. they increase it a little for each incoming cohort so you'd have a little more if you came here

but they won't increase it year to year

my partner is in geosci, and he gets around $35k if i a remember right. that $30k - $35k range is pretty typical for STEM here

[tough imp]

I see

[tepid depot]

if you have roommates, you're paying $700/month or less in rent

studio is closer to 1k

so depending on finances/debt, it is pretty manageable

(this is assuming you live in hyde park, the neighborhood of the uni)

yeah lol

[gritty widget]

BUNDLES

[sleek thicket]

Bundles good

[gritty widget]

what kind of bundle are you?

[trail ibex]

Not sure if this fits this channel as this is more algebraic geometry, but does there exist a "normalization sequence" similar to the localization sequence for Chow groups (say of varieties over a field) ? I'm trying to compare cardinality of the Chow group of an affine curve and the Picard group (=Chow group) of its normalization but it's going nowhere

[sleek thicket]

AG is appropriate here (although I don't know it well enough to help, sorry)

[sleek thicket]

-> ->

[little hemlock]

0 -> -> -> -> 0

[shut moat]

the differential topology proof of the fundamental theorem of algebra is so much prettier than the first one I've seen

[tight agate]

how does the argument go?

[shut moat]

identify the complex plane with$ \mathbb{R}^2 \times \qty{0}$, and consider the stereographic projection from $S^2 - \qty{(0,0,1)} \to \mathbb{R}^2 x \qty{0}$. The polynomial map P induces a map from the sphere to itself via
$$ = h_{+}^{-1}\circ P \circ h_{+}$$ when $x \neq (0,0,1)$ and $(0,0,1)$ at the pole

[gentle osprey]

~S^1

[cedar pebble]

0 -> -> -> -> 0 yields a long exact sequence in catmology
H^0()->H^0()->H^0()->H^1()->H^1()->H^1()->...

[shut moat]

the + subscripts to distinguish it from the other stereographic projeciton which is coming soon

i can spell I promise

so f has finitely many critical points, because P' is not generically zero. The set of regular values of f is then S^2 with finitely many points removed, so it's connected. The function that counts the cardinality of f^{-1}(y) for a regular point y must then be constant on S^2

it can't be zero everywhere, so it must be zero nowhere, so f is onto --> P has a zero

[tight agate]

[gritty widget]

[shut moat]

the full version is in milnor's topology from the differentiable viewpoint

[tight agate]

the nicest proof is the open mapping theorem proof

imo

[trim cypress]

damn, posted this in #discussion and no one responded to me

but would anyone like to go through coxeters projective geo with me

[frigid patrol]

Resolution

Hahah I get it

[sleek thicket]

Is any simply connected open subset of $\C$ homeomorphic to a disk?

[gentle osprey]

Shamrock emoji ☘

[tight agate]

no

C

oh

[obtuse meteor]

lol

[tight agate]

homeomorphic

[obtuse meteor]

not holomorphic

[tight agate]

homeomorphic

[gritty widget]

In complex analysis, the Riemann mapping theorem states that if U is a non-empty simply connected open subset of the complex number plane C which is not all of C, then there exists a biholomorphic mapping f (i.e. a bijective holomorphic mapping whose inverse is also holomorphic) from U onto the open unit disk

🤔

[pastel linden]

why is there a special name for bijective analytic maps

[tight agate]

shamrock was baiting

no, I misread homeomorphic (I assumed they were asking for a conformal map)

C is not conformally equivalent to the disk

[tight agate]

holeomorphism

[gritty widget]

holeomorphism = same no. of holes

[tight agate]

implies it, sure

[pastel linden]

who, me?omorphisms: preserves the ending of a mystery novel

owch tough crowd

[fading vale]

homieomorphism is just the natural extension of the concept of erdos numbers

[sleek thicket]

sham wasn't baiting sham has forgotten all of complex analysis

But yeah uniformization or whatever

classification of covering spaces/simply connected surfaces

[tight agate]

2D poincare

like ultra said

[sleek thicket]

yee

[fading vale]

anyway i came here to say that i will never learn what a 2-category is and you cant make me

😌

[pastel linden]

hsct

[sleek thicket]

Any noncompact simply connected surface is homeomorphic to R^2

[pastel linden]

[gritty widget]

y'know now that i look closely at my copy of lee's IRM there are some parts where the text is squished really close together and it's making me angry

[fading vale]

also i finished a chapter of tom dieck which is nice

[tight agate]

esct

[fading vale]

one more before i finally hit totally new material for me

[sleek thicket]

more like tom dick

I got really really bored so I'm working out scheme theory problems

[pastel linden]

preschool category theorist, e.g. new math

[fading vale]

nvm i think most of ch3 is going to be new material

i only learned covering theory the normie way but this is all like

[tight agate]

what's ch3 on?

[fading vale]

fiber transports connected groupoids memes

[obtuse meteor]

similar to Generalized Generalized Flat Earth Theorem

[fading vale]

covering theory

[sleek thicket]

Ooh nice

[obtuse meteor]

all manifolds homeomorphic to R^2

[sleek thicket]

hell yeah

[obtuse meteor]

not as good as Generalized Generalized Generalized Flat Earth Theorem

All CW complexes homeomorphic to R^2

[sleek thicket]

I believe in simply connected earth

Can't we all get along?

also that's not a generalization

[fading vale]

but it has like "let TRA_B = [Pi(B), SET]" sooooooo i assume this is going to be an uh

alternative approach

[sleek thicket]

YOOOO

That's so based

I read that equivalence of cats before seeing stuff about like, lifting maps (not homotopies) in terms of covering spaces

I think it may have been the first equivalence I ever saw

[fading vale]

scary

but this looks pog

i will do more tmrw

[sleek thicket]

It is very cool

[fading vale]

rn i am sleepy

[sleek thicket]

goodnight moth

[gritty widget]

mfw earth is not locally path connected

[fading vale]

sadge

also this chapter doesnt have many problems until the very end

[sleek thicket]

non semilocally simply connected earth

[gritty widget]

semi quasi locally simply connected

[fading vale]

something something path connected locally path connected semilocally simply connected

those r the 3 conditions right

[sleek thicket]

¯\_(ツ)_/¯

I think so

[tight agate]

"nice spaces"

that's the condition

[sleek thicket]

"smooth manifolds"

that's the condition

:smug:

[fading vale]

thats not even that unbelievable a name brofibration

i still cant believe someone was just like "oh lets just call them 'good pairs'"

[sleek thicket]

isn't it like secretly cofibrations

[tight agate]

yes

[sleek thicket]

there is a real name (unfortunately)

[tight agate]

ndr pairs are cofibrations

[fading vale]

wtf is a ndr pair

[sleek thicket]

Neighborhood deformation retract

I assume

[fading vale]

is that just the good pair condition

[tight agate]

sniped

yes

[fading vale]

ok that makes sense i guess

but thats not as good a name

[sleek thicket]

yeah but it's more cofibration of a name

[tight agate]

I get to read the proof of Quillen's theorem on MU this week

petthecat

[cedar pebble]

@sleek thicket re: twitter
This semester I think I have shown up to homological algebra maybe twice, and those two times I have asked incredibly annoying questions

[sleek thicket]

i showed up to homological algebra on friday and wednesday which is good

[cedar pebble]

it's also at like 9am and I'm not going for the lecture I'm literally just there so I'm forced to do exercises

the lectures aren't useful at all I feel like

[sleek thicket]

same lmfao

except i have no hw

[cedar pebble]

oh rip lmfao

yea this class has a lot of homework

[sleek thicket]

but same on having it at 9:30

I was here to learn about group cohomology and derived categories

and we are progressing very slowly

[cedar pebble]

I was thinking of taking a course on birational geometry from one of the top people in the minimal model program

[sleek thicket]

so i will hit maybe 1 of them

[tight agate]

what are yall doing right now?

[cedar pebble]

except it was also at 9am

and supposedly uhhh

if you miss one (1) class from this professor

[sleek thicket]

yoneda product in Ext

[cedar pebble]

you're instantly dead to him

[sleek thicket]

and there's no class on monday or wednesday

[cedar pebble]

so I decided not to even try lmfao

[sleek thicket]

so fucking slow lmao

yeah i would not uh

i would not succeed in that class

[cedar pebble]

yea lmfao

[sleek thicket]

70% is a super high attendance rate for me

[cedar pebble]

friend of mine took a course from this professor and missed two classes in a row (otherwise perfect attendance)

[sleek thicket]

idk if I've ever hit it

[cedar pebble]

and from that point on he would like

ask the professor a question and the professor would go

"why should I take your question seriously if you don't take my class even half as seriously?"

[sleek thicket]

that is extremely frustrating

[cedar pebble]

complete dickhead lmfao

yea lmfao

[gritty widget]

should hvae beat the professor on the spot

[sleek thicket]

i'm kind of done with like

professors

[cedar pebble]

yea that professor is uhhh

dreadful

insanely intense older Russian man which explains part of it

one of my friends is his only student and their student meetings are typically 3-4 hours long

ran into this friend when I was leaving the office super late

when he was leaving an advisor meeting

like drenched in sweat

[tight agate]

my hom alg prof is an older russian man, and he's super nice

[cedar pebble]

and I was like hey Nolan how's it going

I get a blank stare

and he says

"I'm going to go drink now"

[tight agate]

wait wut

typical??????

wtf

[cedar pebble]

I mean yes lots of grad students have borderline/high functioning alcoholism

I drink after every advisor meeting
ng your advisor meetings are at 10am

[tight agate]

we're done with the group cohomology section in my class

[sleek thicket]

if i were a grad student i would simply develop healthy coping mechanisms

[cedar pebble]

nice

uhhh what have we been doing lately

[sleek thicket]

@tight agate we're doing fucking ext and tor computations

or finishing them up

which is extremely frustrating since

this course has a ""prerequisite""

first year grad algebra

which does tor and ext

except half the class is taking grad algebra concurrently and they haven't gotten there yet

[cedar pebble]

we've been going kinda slow but we finished up delta functors and spent a while talking about resolutions of complexes in general rather than resolutions of particular objects

[tight agate]

I think the next section is on spectral sequences

and then "applications"

[cedar pebble]

I mean we've also been doing everything in terms of bare Abelian categories instead of using the FM embedding theorem

okay now diagram chase
HOW

[tight agate]

masochists

[cedar pebble]

I mean we occasionally use it

for diagram chases

otherwise no

[sleek thicket]

we're doing the chad strat

do everything in R mod and then say it generalizes

[cedar pebble]

carefully

[sleek thicket]

@limpid vault aluffi actually has a good section on this

[cedar pebble]

I mean you can do it it's just a giant pain

[sleek thicket]

in his homological algebra chapter

[cedar pebble]

but e.g. Harry has access to an unpublished note that does the salamander lemma (and hence every diagram chase) without using FM embedding

it's uhhh

harder

than the standard proof

Harry what's your favorite algebraic curve
I dunno a wedge of circles

[obtuse meteor]

yes

[sleek thicket]

idgi just take the torus an elliptic curve and remove a point?

bam wedge of circles

[cedar pebble]

no he said wedge of circles first

which got a laugh out of everyone

I think the funniest Harry related thing I've seen lately is the like

online quiz where you have to guess who said which MO post

and Harry's post was like

by far the one that everyone got correctly

like 70% got it correct

https://www.sporcle.com/games/Xedi/mo_users/results

I HAVE A PRETTY GOOD UNDERSTANDING OF

[obtuse meteor]

🧠

[cedar pebble]

yea he isn't

it's just typical

lmfao when Litt joined old [redacted] for a few days

Harry (under a fake name) was posting

and Litt just immediately goes

"Harry you dox yourself every time you type"

[sleek thicket]

holy shit lmao

evis

[cedar pebble]

utterly DESTROYED

also at Litt posting in the general [redacted] chat

"wow this is epic: Z->Q"

like right before he left

iconic

[obtuse meteor]

fdadksdfh

[cedar pebble]

aside: I like how #point-set-topology inevitably becomes #ng-sham-chmonkey-ultra-tt-shitposting

[sleek thicket]

tterra erasure

[obtuse meteor]

this is accurate

[cedar pebble]

I like this new AT discord (replacing the MO homotopy chat)

[cloud owl]

LIGHT MODE

[cedar pebble]

yes

[cedar pebble]

yea it's really nice I enjoy it a lot

[obtuse meteor]

I have to resist the temptation to become a homotopy theorist

[cedar pebble]

especially since I live on discord and can't be bothered to check a whole separate chat like MO

don't resist

[obtuse meteor]

and do real math

[tight agate]

why

oh

[obtuse meteor]

t. my undergraduate advisor

[cedar pebble]

homotopy theory is real math though

[tight agate]

understandable, have a nice day

[cedar pebble]

ding ding ding ding we are now half way through February already

[tight agate]

not here

[obtuse meteor]

that's good

also nG we're in same tz :o

but yes that's really good

[cedar pebble]

😮

[obtuse meteor]

bc it means

less time in semester

it's also really bad

bc

3 days till AT exam

strap in

it's about to get rough

[cedar pebble]

bad because it means the arrow of time inevitably inches forward; regrets pile, opportunities diminish

[tight agate]

the quarter is almost done

4 weeks left

[obtuse meteor]

4 weeks hmmm

that's when the next AT midterm is

[gritty widget]

hhhhhhhhhuh am i being cancelled?

[obtuse meteor]

always tterra

always

[gritty widget]

[obtuse meteor]

🧠

[gritty widget]

i said i'd burn their houses, not eat them.

i only wish to cause property damage

not human damage

[cedar pebble]

based

[gritty widget]

(for official reasons this is a joke)

[cedar pebble]

I like asking conservatives if they think the wealth that has been sucked away from local businesses and redistributed to large multinationals because of bad lockdown policy should be redistributed after all this because it makes their heads explode

[obtuse meteor]

lol

damn I really just wanna be in the reimu x marisa relationship. Be able to do my special interests for 80 hours a week and gf come wack me on the head with a magic broom to do other things

narrator: she was already living this way

[cedar pebble]

I just want to be in a functioning relationship

[obtuse meteor]

aren't you???

[sweet wing]

ng jus date me ill bully you daily

[cedar pebble]

still here dying at the adorable chmonkey valentine's day twitter romance

[sleek thicket]

I had no idea lmfao

[cedar pebble]

yea me neither omg

Marta's insanely nice and wholesome

[sweet wing]

owo

i see elliptic curves crypto pinned i like

[obtuse meteor]

wait give me the tea

[sweet wing]

see chmonkey twitter is cute

[obtuse meteor]

I know I follow him but finding it is so hard

damn this is pretty fucking cute

[sleek thicket]

https://twitter.com/alexscheffelin/status/1361057724453150720?s=19

Scheffy Xorn’s Lemma Fan (@alexscheffelin)

It was Chmonkey the whole time!!!!

First Valentine’s Day in 4 years I am spending with someone @computer_dream ❤️❤️❤️❤️

Twitter · Feb 14, 2021, 9:00 PM

The tea is just he's dating Marta

[cedar pebble]

yea omg this is the cutest shit

[sleek thicket]

For of all sad words of tongue or pen, The saddest are these: 'tfw no bf'

i amv ery lonely

[obtuse meteor]

Sham you are so small why don't you have a big bf to hold you

:)

[sleek thicket]

this is a lie

[obtuse meteor]

sham

[sleek thicket]

why am i being

[obtuse meteor]

you are tiny in my haed

[sleek thicket]

assailed

always

my gremlin pfp is not helping

[obtuse meteor]

you cannot be tall

[sleek thicket]

faye i s2g i am 6 foot 1 inch tall

[obtuse meteor]

yes you are a 5'4" baby :)

sham being taller than me is illegal

[sweet wing]

ultra will you help me buy groceries daily

and help me cook

[cedar pebble]

what the fuck sham is taller than I am

[obtuse meteor]

It's so unnatural

[sleek thicket]

why does everyone think I'm a manlet???

I'm too soft spoken online

I need to be edgier

[sweet wing]

[cedar pebble]

it's the baby face in your old twitter pfp

[sleek thicket]

brb buying a gun so I can tweet about it

[obtuse meteor]

it's the baby face

and also just like

[cedar pebble]

awlkdfjlksjdfglksjdfg

[obtuse meteor]

sham you're soft

[sleek thicket]

lol

[sweet wing]

owo

sham being smal and cute is ok

[obtuse meteor]

^^^^

[sleek thicket]

I need to fix my street cred

[sweet wing]

jus need to be cute

[sleek thicket]

commit minor arson

[cedar pebble]

idk I picture sham as smol and nice and polite

[obtuse meteor]

wrong

[cedar pebble]

although sham being less smol and still nice and polite works

[obtuse meteor]

I can barely buy clothes without having a breakdown lmao

[sleek thicket]

I'm logging off this is slander

[sweet wing]

queue too long zzz

[obtuse meteor]

(groceries are ok)

[sweet wing]

istg at my place

[obtuse meteor]

(clothes shopping is not)

[sweet wing]

the queue for groceries is like

30 mins long

[sleek thicket]

ultra gift me nitro

[sweet wing]

[sleek thicket]

come on

[cedar pebble]

you may not like it but this is what peak math twitter looks like

[sleek thicket]

[cedar pebble]

[sweet wing]

[sleek thicket]

@limpid vault where is my nitro

give me nitro

[sweet wing]

give me as well uwu

[sleek thicket]

no

Fuck off

I'm trying to mooch over here

[sweet wing]

[cedar pebble]

Harry did the worst thing to me which was gift me a year of nitro

and then it ran out and I had already grown accustomed to using nitro

[sweet wing]

[cedar pebble]

😢

[sweet wing]

rip

[sleek thicket]

I got it at the start of the pandemic but then cancelled bc I stopped using discord as much

[cedar pebble]

I basically live on discord so lol

[sleek thicket]

But the wheel has turned

[sweet wing]

all i want is to use

[sleek thicket]

yes I need to use pet the cat emotes

see like

I'm missing out on the memes

[sweet wing]

go bully someone into giving you nitro

[sleek thicket]

:petTheCat: :honkhonk: :chickenwalk:

[sweet wing]

like me

[sleek thicket]

not the same

I'm trying smh

[gritty widget]

when you get a job in academia, please send the salary to me then 🙂

[sleek thicket]

@gritty widget hello gift me nitro

[sweet wing]

try harder

start a of

[sleek thicket]

☘️

I belive in you ultra

You will get a job

at like cvs at least

[sweet wing]

the sham of payment in nitro

[sleek thicket]

I believe in you ultra

You will drain society's resources successfully

I believe in you ultra

You will shave the barber who shaves all people who do not shave themselves

[obtuse meteor]

I mean basically

[cedar pebble]

sorry the clothes shopping was no fun 😦

[obtuse meteor]

It’s okay I really like the skinny jeans I got

Gf also really likes them because [REDACTED]

[cedar pebble]

W

glad you came away with a good haul, despite the shit you had to go through

[obtuse meteor]

@cedar pebble did you know Harry went to my undergrad

[cedar pebble]

no, because I didn't know you went there!

[sweet wing]

clothes shopping is fun

[cedar pebble]

man I have not bought new clothes in ages

[obtuse meteor]

I know some of his old professors

[cedar pebble]

lmfao do they have any stories?

[obtuse meteor]

I mentioned him and they said he was an arrogant piece of shit at michigan

Nothing more lol

[cedar pebble]

[sweet wing]

[cedar pebble]

yea I mean he was going through some shit as he continues to

lot of addiction issues started for him at that point

and I do think a lot of that arrogance is mediated by some of the drugs he takes

love the guy to death in the sense that I really wish he would stop being his own worst enemy and get past some of the shit that he's clearly still struggling with

(he's an ass, obviously, but there's a human in there that I get the feeling is really deeply hurt in some way)

[obtuse meteor]

Oop

[gritty widget]

you went to hogwarts???

[obtuse meteor]

I have a theory that a particular part of the first day lecture was created specifically because of him

[cedar pebble]

tell me more

[obtuse meteor]

The 295/296ers like lecture about how they used to be really arrogant and exclusionary from any of the other math majors and how it hasn’t been that way in X years

[cedar pebble]

[obtuse meteor]

And also quoting the thing about arrogant young men in math

As being intolerable

[cedar pebble]

yea

[obtuse meteor]

I was like “huh wonder where that—ah aha “

[cedar pebble]

[obtuse meteor]

I actually applied here on a whim solely Bc he told me to

[cedar pebble]

oh huh

[obtuse meteor]

Weird vibes

[cedar pebble]

actually wholesome moment, he added a certain homotopy theorist to [redacted]

and while we were chatting Harry told him

"you know, you were actually the single person that got me back into math and got me to apply to grad school. We had a conversation once where you motivated me to get back into things and here we are"

and he was like

"I didn't realize that conversation had so much impact on you, I'm really glad"

[sweet wing]

awwww

[cedar pebble]

[sweet wing]

[sleek thicket]

reading a proof

hmm okay i think I was being stupid

ty everybody

question is resolved

[gritty widget]

yw

glad to have helped

[sleek thicket]

i was confused but it is not resolved

say $X = \mathrm{Spec} A$ is affine and $g \in A$

[gentle osprey]

Shamrock emoji ☘

[sleek thicket]

we have a point $x \in X$ and a corresponding prime $\mathfrak{p} \subseteq A$

[gentle osprey]

Shamrock emoji ☘

[sleek thicket]

assume $g_x = 0$ ($g_x$ denoting the germ of $g$ in $\mathcal{O}{X, x}$, equivalently $g/1 = 0$ in $A\mathfrak{p}$)

[gentle osprey]

Shamrock emoji ☘

[sleek thicket]

oh no this is more complicated than I thought

so im reading the proof that closed subschemes of affine schemes are the same as ideals

having trouble understanding why we can choose a cover satisfying (1) and (2)

proof has so far wloged it so that the underlying continuous function is a homeomorphism and the sheaf map is injective on global sections

we know $(X, \mathcal{O}_X)$ and $(Z, \mathcal{O}_Z)$ are both schemes and that $X = \mathrm{Spec} A$ is affine

[gentle osprey]

Shamrock emoji ☘

[sleek thicket]

$\varphi : A \to \Gamma(Z, \mathcal{O}_Z)$ is the map on global sections coming from the immersion $i : Z \to X$

[gentle osprey]

Shamrock emoji ☘

[sleek thicket]

i see why we can find a U but not why we can find the Ui

[trail ibex]

I'm not sure it can be done, for instance consider the case where X is irreducible and x is its generic point. Then {x} is dense so intersects every nonempty open subset.

[sleek thicket]

Yeah, this is what was getting me. I don't see why everything in the closure would have φ(g) zero in their local ring

Seems like it goes backwards

[median glade]

lol

based or not?

"Modern Classical Homotopy Theory"

unironically I think this is actually a cool approach for a graduate level text

well as a reference text you just read the statements

and accept them as true

then you write the proof down

what's the big deal?

8^)

[viral atlas]

For the expert, reproducing the proof shouldn't be a big deal.

If it's laden with hints, someone using it as a reference might just convince themselves of the proof-sketch without formally writing out it in detail.

[median glade]

A lot of books effectively require you to rederive the material, with maybe 50% of it being proved for you

I like the idea of explicitly acknowledging this, and writing a book around it

providing sufficient detail and guidance to actually derive everything

[sweet wing]

honestly for a lot of things im too lazy to read the proof lol so i jus scan through and roughtly reproduce xd