serious-discussion

[neat lintel]

USC is really good though I thought

[empty stratus]

I only attended my first conference last month.

In my research, I ended up inventing a new area of analysis.

One that was overlooked by experts in non-archimedean analysis for being too "uninteresting".

[torn willow]

What is it called

[empty stratus]

I call it (p,q)-adic analysis.

[dense belfry]

CV have you ever considered that you read way too much into the anti establishment stuff

[empty stratus]

??

[dense belfry]

Lol

[empty stratus]

What is the "anti-establishment stuff" of which you speak?

[dense belfry]

I mean "the establishment thinks this is not worth studying"

[neat lintel]

What the heck

[empty stratus]

Uh, no.

[neat lintel]

[empty stratus]

The founder of the field thought as much.

And I've got Khrennikov on record saying that no one is studying it.

[neat lintel]

Who’s Khrennikov?

[dense belfry]

Sure I agree that the statement you made is true

But I think the sentiment you are taking away from it is very I guess revolutionary

[empty stratus]

Andrei Khrennikov, one of the more noteworthy scholars in non-archimedean analysis.

[empty stratus]

No, not revolutionary.

Just new.

[stark charm]

Have pride

[dense belfry]

A lot of how you talk feels very revolutionary in sentiment I guess

[empty stratus]

I need to sell it, Emma.

😉

[dense belfry]

Lol

Why

[stark charm]

Having confidence in your own creation should be something to be prideful of Emma

[dense belfry]

That's not my point

[empty stratus]

Because people think Collatz isn't worth studying?

Because they think it's a lost cause?

Because they think it's not interesting?

Because they think there's no greater theory?

[neat lintel]

So you had to invent new math to solve a problem, seems familiar…

[stark charm]

Yeah happens often in math

[dense belfry]

I think academics kind of don't like this sort of thing tbh

It's a big turn off

[empty stratus]

Because they think everyone who studies it is a crank?

[dense belfry]

Like maybe it works for young people

[empty stratus]

??

[dense belfry]

But this is literally the sort of attitude that can get you labeled as a crank

[stark charm]

Yeah I am confused at what behavior specifically?

Is it because they called it new?

[dense belfry]

I'm talking pretty broadly about CV's behavior

[stark charm]

or they said they invented it

[dense belfry]

Not about rn

For the most part

[neat lintel]

…

[stark charm]

Can you elaborate?

[empty stratus]

See, this is the bigotry I'm up against.

[dense belfry]

Anyway whatever

Lol

[empty stratus]

If I don't explain why my work is relevant or useful, people dismiss it as a waste of time.

[stark charm]

unhelpful tbh

[empty stratus]

If I DO explain it and try to motivate it and make it interesting, they think I'm calling for revolution.

[dense belfry]

I mean the way you explain it feels like that I think

[stark charm]

incomplete criticism + dismissive behavior can be interpreted as being blatantly disrespectful emma

[dense belfry]

What

I am critiquing long term behavior

[stark charm]

yeah they are theatrical somewhat

[empty stratus]

I'm sorry. I'm passionate about mathematics.

I like what I do.

I think it's really neat and really fun.

And I want to share that joy with others.

If you want to condemn me for that, go ahead.

[neat lintel]

I didn’t see a problem? What’s wrong Emma I don’t get it.

[stark charm]

I dont see any solutions being given though

[dense belfry]

[stark charm]

Its more like, I dont like how you act and I believe others would disapprove

[dense belfry]

This conversation doesn't exist in a vacuum colee and arrow

Smh

[azure nymph]

Colee you're being unnecessarily rude

[neat lintel]

Emma, considering your set theory is literally the most confusing abstract stuff I have ever heard in my life, you can’t really critique CV for researching/being passionate about the Collatz Conjecture

[stark charm]

proof?

[dense belfry]

That's not the criticism here

Lmao

[empty stratus]

What theatrics?

[dense belfry]

I have talked to CV about this before

[empty stratus]

I don't know. I just do me.

[dense belfry]

I shouldn't have mentioned this I guess

[stark charm]

yeah you shouldnt have

[empty stratus]

If you think certain statements of mine are melodramatic, please indicate them to me.

[neat lintel]

It makes his explanations more entertaining

[dense belfry]

I don't particularly want to get into this discussion

[neat lintel]

I like it

[empty stratus]

Because I have no idea what this was in reference to.

[dense belfry]

Lol

[stark charm]

its like telling someone you dont like how they communicate in general

[empty stratus]

I was just having a conversation with someone who was curious about my work.

[empty stratus]

This is literally my favorite thing in the world to do.

[neat lintel]

Bingo, I was the one who asked to begin with

[stark charm]

i can see what you mean by anti establishment though

[empty stratus]

Whether it is my mathematics or my writing, I want to share it with people.

[neat lintel]

And thank you for doing so, I learned a lot!

[empty stratus]

And I am not going to pass up or blow off an opportunity to do so.

[empty stratus]

My pleasure!

[neat lintel]

This really is making me more interested in my upcoming class I’m taking, now I’m kinda restless to learn more!

[wooden flax]

Which class?

[neat lintel]

Oh by the way CV, I’m trying to catch up on some more point set topology and Galois theory so that I’m ready for Gouvea

Like you recommended

[empty stratus]

Point-set topology and basic analysis (convergence of sequences, limits, Cauchyness etc.) is the most important stuff.

Anyhow, I'm used to Emma, nGroupoid and the others treating me like this.

I know they care, but they have an odd way of showing it at times.

[neat lintel]

Yeah I’ve been reading Tao and Abbott for that too

[stark charm]

idk maybe they have a point to make though

or they can just be general bullying

[empty stratus]

I feel it's usually this.

[stark charm]

it shouldn’t be your job to interpret that though

[empty stratus]

For example, in this conversation, not a single line of text I wrote was cited as evidence for their views.

[stark charm]

i think they want you to have some humility though

[stark charm]

the antiestablishment part

i can see it

because you state as if the majority of people are against what you are researching

[neat lintel]

He was answering a question that I asked

[empty stratus]

They are not against it.

Rather, no one is doing it.

It's considered uninteresting.

Read through the literature.

[stark charm]

that can be interpreted as not worthwhile

[empty stratus]

The (p,q)-adic case is a toy example, primarily.

[stark charm]

and thus against what you are doing

i dont see the problem with this even if it is false though

[dense belfry]

Things are generally considered unimportant until they are shown to be important

If you can show that this stuff is important that's great

[spare linden]

how many ways are there to factor?

[empty stratus]

I have been told that my non-archimedean analytical work is interesting.

[dense belfry]

But no one is obligated to pay attention to you

[empty stratus]

Ergo, my need to sell it a little.

[stark charm]

they seem to be well aware of this lol

[spare linden]

(in algebra)

[dense belfry]

And you should try to present your things in a way that is conducive to people paying attention to you

[empty stratus]

And I was. I was answering the questions Arrow was asking of me.

[dense belfry]

Your selling it like you are is actually part of the problem CV

[empty stratus]

Again: how so?

[stark charm]

completely factor?

[empty stratus]

Where did I go wrong, and how would you have done it instead?

[stark charm]

have you heard of unique factorization domains?

depending on your set of numbers you are working with there can be multiple ways

but with real numbers there is only one

[dense belfry]

I mean I can give you a bunch of stuff you should have done in the past if you want, but I doubt that will be helpful

[empty stratus]

You posted in response to my above conversation.

[neat lintel]

Emma like in the grand scheme of things I don’t see why this an issue

[dense belfry]

Anyway I think that pitching a revolutionary attitude with respect to collatz is a bad idea precisely because of the environment around it

[empty stratus]

if nothing in my above conversation merited criticism, then you were criticizing me for past behavior that was not germane to what I was doing.

[dense belfry]

If you want to be taken seriously

[stark charm]

yeah me neither to be honest

[dense belfry]

Lol

[empty stratus]

Again, indicate in the above conversation where I was being "revolutionary".

[stark charm]

i told you where

[empty stratus]

Or I'm going to take this as simple bullying.

[stark charm]

you can be perceived as such

[empty stratus]

I want a direct reply-to link.

[stark charm]

when you said collegues were uninterested

[neat lintel]

He was sharing new technology in the area, anyone with a pulse would be excited about that

[empty stratus]

Full quote.

[dense belfry]

You can parse this as bullying if you want

[spare linden]

wdym?

[dense belfry]

I don't particularly care

You may be right to some extent

[stark charm]

i dont think you shouldve brought it up then

[empty stratus]

And you see no problem with that?

[dense belfry]

I mean I think it's kind of a complicated situation I guess

With you

[empty stratus]

I would be aghast if I was told I was bullying someone. I don't want to be a bully.

[neat lintel]

I thought you were joking emma, a little rude?

[dense belfry]

[shrewd bobcat]

aight aboutta go into integral calculus which one's harder

differential or integral calculus

[empty stratus]

Emma, you came out just to attack me.

That's not nice.

[stark charm]

bruh

attack

[empty stratus]

Yes.

Attack.

[stark charm]

melodramatic

[dense belfry]

I mean if you read this convo

[empty stratus]

Accusing me of crankery, of fomenting revolution.

[dense belfry]

There's a pretty decent amount of melodrama

And falling on your sword

I never accused you of crankery

[neat lintel]

Emma a bunch of people talk about their research like CV

They aren’t out of the ordinary

[shrewd bobcat]

translate to peasant terms please i can't read

[stark charm]

thats what im saying

[empty stratus]

If I'm being melodramatic now, it's because you, once more, have upset me and (from my viewpoint) bullied me.

[stark charm]

bruh ngl this is why i dont talk to some math ppl

[empty stratus]

And I don't like that.

[neat lintel]

Heck, even I get excited about my research in microbiology and that’s about plants

[stark charm]

they talk uppity

[spare linden]

@stark charm ?

[torn willow]

CV came up with a novel approach for collatz that no one else uses

[empty stratus]

Ooh. Do tell!

[empty stratus]

Because it's novel.

[stark charm]

completely factor like reducing an expression to a multiplication of paranthesis

instead of having a summation term left over

[torn willow]

Oh mb that's redundant

[dense belfry]

I mentioned that some of the language you use isn't conductive to selling your ideas because of the context of collatz

[empty stratus]

And I really wish you wouldn't do this. I don't go out of my way to attack you personally.

[dense belfry]

I probably didn't need to say that sure

[wooden flax]

I don't see how someone can be a crank if they're work isn't disproved

[stark charm]

its more like its niche

[wooden flax]

like Mochizuki

[stark charm]

so people assume esoteric means crank

[neat lintel]

I do research on how certain plant species can be made into extracts that kill E. coli and a bunch of other microbial bad guys

[wooden flax]

or maybe Atiyah

[dense belfry]

I never said CV is a crank

In my replies

Smh

[shrewd bobcat]

aight looking at everyone's roles since your names are all different here. why are you guys all good at math

[wooden flax]

right but you're applying people like them are

[neat lintel]

Implied though?

[wooden flax]

implying*

[dense belfry]

No

[empty stratus]

But this is literally the sort of attitude that can get you labeled as a crank

I'm talking pretty broadly about CV's behavior

A lot of how you talk feels very revolutionary in sentiment I guess

CV have you ever considered that you read way too much into the anti establishment stuff

I mean "the establishment thinks this is not worth studying"

[dense belfry]

I literally didn't imply that

[stark charm]

wanting people to take someone seriously

[dense belfry]

I was talking about perception of researchers

[empty stratus]

How was I being polarizing?

[neat lintel]

Emma bruh

[spare linden]

none of that

[shrewd bobcat]

what the hell's going on

[stark charm]

should we work with examples

[dense belfry]

Literally collatz is a minefield

As CV said

[shrewd bobcat]

oh collatz that's something i know

only word i knew

[dense belfry]

And so you have to be careful if you don't want to get dismissed

[spare linden]

ok

[empty stratus]

It is an objective fact that the study of (p,q)-adic functions has been neglected in favor of the more fruitful and useful areas of complex-valued functions on the p-adics and functions from the p-adics to the p-adics.

[neat lintel]

Who cares though

[dense belfry]

This is what I was saying

[stark charm]

they might be socially unware

think of that

[dense belfry]

I mean

[stark charm]

like a good chunk of math people

[dense belfry]

I was informing them

[stark charm]

im assuming cv is autistic because of how they type

[dense belfry]

I don't understand why everyone has parsed this as attack

I am autistic too

Lol

[shrewd bobcat]

i'm drinking water rn

so tasty

[neat lintel]

nothing wrong with being autistic, i love my autistic homies

[stark charm]

it wasnt about you

[empty stratus]

Yes.

[neat lintel]

I think they know this, though, considering that this isn’t his first rodeo of dealing with the social repercussions of his research

[empty stratus]

And, for the record, my pronouns are he/him.

[stark charm]

i told you why

if you don’t particularly care

[empty stratus]

You came in to critique me when I was just having a casual conversation with an interested observer.

[stark charm]

and arent offering a solution it can be seen as rude

🏃‍♀️

[dense belfry]

I mean there is a solution

[deep mango]

Even though he is in this case, please don't assume that about people

[dense belfry]

Try to be more careful

With how you speak

That's it

[empty stratus]

I was having a conversation with an interested observer.

I was not trying to make a presentation to the AMS.

[neat lintel]

Emma this is only your perception, I was the one who asked

[empty stratus]

Christ.

[dense belfry]

Literally I wasn't the one who blew this up

[empty stratus]

YES YOU DID.

You could have said nothing.

[stark charm]

[cold needle]

ok you know what

can we stop

[dense belfry]

Yes I could have said nothing

[spare linden]

@stark charm ?

[empty stratus]

Thank you!

[dense belfry]

You're right

[cold needle]

this is for BOTH of you

[stark charm]

did you post the example?

[cold needle]

please stop

[stark charm]

we are takking about real polynomials right?

ig like taking x^2+2x+2

and factoring (x+1)^2 + 1

so when i say completely factor i mean there are no summations left

[torn willow]

Will there be a conjecture in the future that requires more effort than Fermat Last Theorem?

[stark charm]

no

they are all less effort

[spare linden]

all factoring in algebra

[stark charm]

the only ones that are more efforts are the ones i work towards

[stark charm]

no then

[cold needle]

kangaroo rat are you in highscool

[spare linden]

yes why?

[stark charm]

in all of highschool algebra everything is factorable

[cold needle]

ok colee's answer is probably too general for you

[torn willow]

x^2+1

[stark charm]

and the factoring is unqique

[torn willow]

Well That applies to any UFD in general

[cold needle]

cause highschoolers dont learn ring theory unless you go to some nice af school or ur like moth or sth

lmao

[stark charm]

who

are they

server people?

[cold needle]

a friend 🙂

yes

[stark charm]

bruh

i hate this life

too much inequality

[cold needle]

me too

its fine

dont compare to other people

[stark charm]

why not?

[cold needle]

i think if we are working hard that is enough

[stark charm]

i dont cope mr mod

[cold needle]

i cope

i huff the copuim

[stark charm]

u gotta do it sometimes

[spare linden]

can i DM you

[stark charm]

if you want a quick reponse you shouldnt

im about to watch anime

but go ahead if u want

[spare linden]

oh never mind then

[cyan goblet]

sniff oh yeah that’s the stuff sniff yeah oh yeah im gonna make it in this world sniff yeah as long as i try my hardest that’s all that matters sniff sniff ohhhh yeah im gonna make it

[neat lintel]

Haha, imagine being homeschooled and still knowing ring theory

[fair mural]

dang i didn’t even start group theory until a few weeks after i graduated high school

i’m a nobody now

[neat lintel]

Ring theory is nice

[cold needle]

i didnt do group theory until second year of undergrad 🙂

[fair mural]

ahead of metal 😎

[cold needle]

well i did my first year but it didnt count

[fair mural]

why doesn’t it count

[little vine]

Same

[cold needle]

it was mostly worthless i didnt learn anything of value

[fair mural]

if you learned it you learned it, i don’t care if it’s not documented on paper

oh

[little vine]

I learned it in college like a normie

[cold needle]

i think though that it doent rly matter when u learn because like

its not like ur learning this stuff ten years too late

[fair mural]

i know

[cold needle]

or whatever the right analogue of that feeling is

idk

[little vine]

All these anime highschoolers learning graduate mathematics in 11th grade. They're all 6'6" and ripped too

[cold needle]

hahah

[fair mural]

but it’s always impressive when people learn it so early

[little vine]

And are ace Gundam pilots or something

[cold needle]

idk im just having brainworms and coping before sleeping

[cyan goblet]

the only ring theory i learned was to define what a module was

then use that in linear algebra

all i know about quotient ring or something is like

Z mod 2 Z something something

[charred mortar]

Eh good enough

[azure nymph]

I didn't even learn pre-calc in high school

[neat lintel]

Yeah same, we did it in middle school in my country

They were pushing for calculus in high school

[azure nymph]

My schedule got messed up in high school so I was put in remedial math my 3rd year of high school meaning I had to do algebra 2 my senior year

[neat lintel]

What is remedial math

[azure nymph]

math for people who struggle with math

I got a 100 in the class it was basically pre-algebra and algebra 1

[neat lintel]

Are there separate courses for those subject

[azure nymph]

Which courses

[neat lintel]

algebra 1 and pre

[azure nymph]

Yes pre-algebra would be done in middle school and algebra 1 freshman year

[arctic grove]

im a negative body now

[fervent pebble]

L

[arctic grove]

[neat frost]

Hell yeah I’m ripped

[fervent pebble]

not 6'6" tho

[velvet dagger]

@arctic grove, @errant ridge, and @primal seal

Let's move here

[errant ridge]

yez

where?

[arctic grove]

yeah sure

[errant ridge]

oh

[brave hollow]

why the A&M hate

[errant ridge]

we are here

lol

[arctic grove]

atiyah

[velvet dagger]

But yeah I'm originally from Punjab but moved to Jabalpur 6 years ago

[arctic grove]

wait what

u are actually indian??

[errant ridge]

I like d&f (I only went though like the first 4 pages )

[velvet dagger]

Is this not known??

[errant ridge]

lol yea he said he was from cmi

[arctic grove]

i thought u were in US

stop confusing me dami!

[errant ridge]

or rather in cmi

[primal seal]

Man i fell for this once before when you pretended to be in hs

[arctic grove]

lmao

[velvet dagger]

Also @iron osprey and @devout nacelle

[brave hollow]

dami has some guy's bio open and is just describing their life

[primal seal]

😂

[velvet dagger]

Manan actually can testify for me here

[primal seal]

I still remember

[arctic grove]

so if u are from punjab

[velvet dagger]

I did troll about being a high schooler

[arctic grove]

write something in punjabi for me

[errant ridge]

yes do it

[iron osprey]

throw this in trash

i bought it too

[primal seal]

It’s already got mistakes in the intro material

[iron osprey]

i want to throw in trash

[errant ridge]

No I'm gonna finish the entire book

[iron osprey]

dont do that

[errant ridge]

even if it kills me

[primal seal]

Check their definition of gcd

[iron osprey]

please for the love of god

its literally unreadable

[velvet dagger]

Sata sri akala Shyshu

[iron osprey]

its worse than hatcher

[primal seal]

The passage on primes is mid worded

[neat lintel]

Never throw books in trash no matter how they're shit.
Just give them in some local library if u don't want it

[iron osprey]

no

[arctic grove]

Uhh
wrong spaces but that is correct...

[iron osprey]

throw books in the trash

[velvet dagger]

Yeah I'm not trying that hard rn

[iron osprey]

PDFs are free for copying

[arctic grove]

wtf

lmao

dami do be punjabi huh

[iron osprey]

inb4 dami is literally my professor

[arctic grove]

Oye paaji tennu kaisi gala karte ho ji

[errant ridge]

bruh you know punjabi?? i thought you only knew hindi and english

[velvet dagger]

To be fair I'm kinda trolling when I say I'm first year at CMI because I'm a grad student

[arctic grove]

Punjabi is kinda hindi

[forest jackal]

@velvet dagger Desi Nuts

[arctic grove]

i knew that

[neat lintel]

lmaooo

Desi nuts

[arctic grove]

LMFAO

desi nutz lmao

[velvet dagger]

Looooool

[errant ridge]

masters or phd?

[velvet dagger]

PhD

First year PhD

[errant ridge]

nice what topic

[velvet dagger]

So I wasn't technically wrong

[iron osprey]

wait

in what way do you mean first year

[velvet dagger]

Spectral theory

[errant ridge]

ohh nice

then

[iron osprey]

finishing or starting?

[errant ridge]

you must at least have heard of

"hearing the shape of a drum"

[velvet dagger]

Oh yeah that's a classic

[errant ridge]

that's really cool

[arctic grove]

??

[errant ridge]

i cant wait to learn that

[arctic grove]

whats that

thonkzoom

[errant ridge]

basically

you have a drum

[arctic grove]

i got that part

[errant ridge]

a 2d membrane

vibrating

[arctic grove]

Ooo

[errant ridge]

it's not circular like normal drums

it can be any shape

and you figure out the shape

by the sound it makes

but

mathematically

[velvet dagger]

Well you can't

[errant ridge]

[primal seal]

The different shapes allow different standing waves?

[arctic grove]

[velvet dagger]

There are isospectral manifolds which aren't isometric

[errant ridge]

yeah i think that's how u do it

[velvet dagger]

So you can't actually determine the shape fully by the sound

[arctic grove]

uhh

ok this is well beyond me

[primal seal]

Cmon man it’s too late for talking like that lol

[errant ridge]

noooooo

[arctic grove]

[velvet dagger]

I made that mistake once

[errant ridge]

same, which is why i cant wait to learn it

[velvet dagger]

Advisor was like

[neat lintel]

Spectral theory is a part of linear algebra right afaik?

[errant ridge]

that's where it starts

[velvet dagger]

Durr fiteh muh

[errant ridge]

durr fiteh muh?

[velvet dagger]

It's like calling you stupid

[errant ridge]

Lol he called you stupid for thinking you can determine the shaping of the drum just from the sound?

[velvet dagger]

I mean it's something I should've known lmfao

[errant ridge]

[iron osprey]

not just using neural nets...

smh

[dense belfry]

Oof

Dami that sucks

[errant ridge]

sloth what more info do you need?

to determine the shape

[arctic grove]

u need to know the shape to determine the shape

[iron osprey]

i was gonna say it

[velvet dagger]

I'm not actually sure. Tbh my angle on spectral theory is a bit different

[errant ridge]

which is?

[velvet dagger]

Also I'm completely larping about being from India lol

[arctic grove]

dami what exactly is spectral theory

[arctic grove]

i knew it

[errant ridge]

lmao what?

[arctic grove]

[primal seal]

😂😂😂😂

I’m done

[errant ridge]

where are you from then

[neat lintel]

Google translate sucks.

[primal seal]

Night y’all

[arctic grove]

hindi??

lmao

[arctic grove]

gn!

[velvet dagger]

@dense belfry yeah didn't actually happen in just trolling them really hard and used that as an excuse to throw in another Punjabi phrase I looked up

[brave hollow]

nobody got the dure fiteh muh lmao

[iron osprey]

https://tenor.com/view/goodbye-chat-gif-21291701

[errant ridge]

good night

[neat lintel]

Cya

[dense belfry]

Lmao

[alpine kindle]

hi shushu

[arctic grove]

hey ally

[errant ridge]

bye gristle

[velvet dagger]

Apparently it means may your mouth burn in hell

[arctic grove]

[dense belfry]

I wondered why you said you were first year grad

[errant ridge]

eating spicy stuff be like

[velvet dagger]

And it's a way to call someone a dumbass

[iron osprey]

that freaked me out

[velvet dagger]

Which is honestly s tier

[iron osprey]

made me start to tell myself i am a bit dumb

[arctic grove]

what is?

[errant ridge]

durr fiteh muh

[neat lintel]

Bro that was really harsh for u then

[velvet dagger]

Read from here

[dense belfry]

Oh I assumed Dami was playing a joke actually

But then I forgot

[errant ridge]

imma go eat lunch good bye everyone i wont be back for at least 7 centuries

[neat lintel]

Time is relative btw

Cya

[velvet dagger]

But yeah family is originally Moroccan

And I myself was there for high school

But otherwise lived in America

@iron osprey well in a way, I'm a third year PhD student but that's like masters + 1 year in Europe

[iron osprey]

do u mean starting or ending third year

[dense belfry]

I also just finished third year

[velvet dagger]

Ending

[iron osprey]

ah i see

im starting first year in US but

i only did undergrad 3 years

[velvet dagger]

With covid I feel like I'm ending first year because uh

[iron osprey]

:^)

[velvet dagger]

I haven't gotten shit done in so long

[dense belfry]

Huh what sort of things are you interested in?

[iron osprey]

who

[dense belfry]

You

[velvet dagger]

Emma knows what I do. Namely nothing :)

[dense belfry]

Aww

[arctic grove]

dami, what exactly is spectral theory

[velvet dagger]

It's like eigenvalues of stuff kinda

[forest jackal]

https://tenor.com/view/halloween-salem-ghost-boo-sabrina-gif-15297328

[iron osprey]

idk im just trying to learn some homological algebra & gauge theory right now. im vaguely interested in information geometry and dynamical systems

[velvet dagger]

Easiest explanation

[arctic grove]

its related to random matrix theroy?

[velvet dagger]

It can be but not necessarily

Spectrum of a linear operator in finite dimensions is the set of eigenvalues

[forest jackal]

a matrix or operator does not need to be random in order to have a spectrum that is interesting to study.

[velvet dagger]

Big important theorem is the spectral theorem

Which says that symmetric matrices have orthomormal eigenbases

[iron osprey]

spectral theorem has disturbing implications

[velvet dagger]

Equivalently they're orthogonally diagonalizable

One important example is the adjacency matrix of a graph

This leads to the subject of spectral graph theory

[iron osprey]

another one is the principal directions of a surface

[arctic grove]

[dense belfry]

What is information geometry?

[velvet dagger]

Like circular reasoning but more general

[iron osprey]

fisher information gives u a riemannian metric for stochastic manifolds

you get nice stuff from that

[dense belfry]

Oh I've heard of that before

One of my friends cares about that

[forest jackal]

https://tenor.com/view/circle-back-cat-circle-silly-tail-gif-5296834

[dense belfry]

At Stony Brook

[iron osprey]

hm

[velvet dagger]

But yeah on Riemannian manifold you have the Laplacian and you care about its eigenfunctions

[dense belfry]

What does fisher information tell you?

[iron osprey]

where to drive your boat

[dense belfry]

Lol

[velvet dagger]

I'm particularly interested in understanding spectral theory of the Laplacian on graphs and surfaces, esp from an arithmetic pov

And also in higher rank you have simplicial complexes called Bruhat-Tits buildings

[arctic grove]

so thats where the nt love comes from

[iron osprey]

@dense belfry

https://en.wikipedia.org/wiki/Fisher_information

thomas & cover have a nice intro book to info theory but

you can find fisher information in any stats text i think

[velvet dagger]

Higher rank symmetric spaces have a ring of invariant differential operators on top of just the Laplacian, and Bruhat-Tits buildings have "geometric operators" if they commute with the action of the overarching group

[iron osprey]

braces for impact

[velvet dagger]

And yeah there's a lot of links here with random walk, dynamics, arithmetic, representation theory

[dense belfry]

Looks pretty interesting

[velvet dagger]

Apparently quantum computing lol

Which is kinda wild

[viscid pecan]

I have been hearing random walks pop up a number of times now

[iron osprey]

qm stuff is all just infinite dim linalg looking at eigenvectors

so

[viscid pecan]

What exactly would you describe to be a random walk?

[velvet dagger]

I mean idk if I wanna define a general random walk but

Think of you're on a lattice Z^d

[viscid pecan]

Would that just be some kind of arbitrary displacement pattern?

[velvet dagger]

And at any point you have equal probability of going to any neighbor

Now just set the point off and see what happens

[viscid pecan]

Yea you have a lattice structure ahh

[velvet dagger]

You can also do random walk on graphs

[viscid pecan]

I can visualize it better when I think of molecular lattice structures lol

[velvet dagger]

Probably on manifolds tbh but I haven't thought too hard about what that would look like

[viscid pecan]

Wow I actually kind of understand this stuff. I guess I haven’t been wasting my time studying math 😂

[velvet dagger]

Probably a probability measure on the unit tangent bundle and then flow

[forest jackal]

Also the probabilities don't need to be equal, and your state space does not need to be discrete like this (eg brownian motion). Z^d is the ideal way to motivate it though, as there are already somewhat interesting results there.

[velvet dagger]

Or something

[viscid pecan]

Abstraction of sigma algebras

We can do anything with sigma algebras pretty much

[dense belfry]

What do you mean by that?

[velvet dagger]

The power doesn't come from the sigma algebras imo

[viscid pecan]

Well you can take topologies and make probability spaces out of them

[velvet dagger]

The point of a sigma algebra is just to organize what sets you're taking measures of

I guess the Borel hierarchy is kinda nifty from a descriptive set theory pov

[dense belfry]

I mean it's not just, it actually stores a lot of information

[viscid pecan]

Honestly the indicator function is used everywhere. You even see it in Munkres

[dense belfry]

Inside of it

[forest jackal]

One of my favourites for a first course in this kind of stuff is the question of what the probability is that a random walk starting at the origin in Z^d returns to the origin after some finite number of steps.

This probability is 1 for d=1,2, i.e. it happens almost surely.

[dense belfry]

The borel hierarchy

[forest jackal]

But for d >= 3 is is strictly less than 1.

[viscid pecan]

You mean borel field(s)

[dense belfry]

Oh lol

[velvet dagger]

But generically you think about Lebesgue measure on R^d

[dense belfry]

I didn't see dami's comment

[velvet dagger]

And there you don't really need to go farther than level 2 in the Borel hierarchy

[forest jackal]

So a drunkard wondering the streets of a gridlike city will almost surely find his way home from the bar, but a drunk bird that can only fly unit steps in axis directions will with positive probability stay lost forever.

[velvet dagger]

Since every measurable set is just G delta minus a null set

[viscid pecan]

Wdym Lebesgue measure here? Didn’t get that far in analysis yet

[dense belfry]

I think I have a neat Computability theoretic interpretation of that fact dami

Maybe

[velvet dagger]

Oh shit

[dense belfry]

Slash borel hierarchy theoretic

[velvet dagger]

It's the standard measure on R^d

[viscid pecan]

Oh ok

[velvet dagger]

Have you seen Caratheodory extension and/or Riesz representation theorem?

[viscid pecan]

I kinda understand what a metric space is

[velvet dagger]

Probably not

Oh

[dense belfry]

Okay so you can think of the level a borel set is in the hierarchy as a minimal length of a description of the set

Ie the complexity of a formula defining the set

[velvet dagger]

That's reasonable

[dense belfry]

Yeah there's more

[velvet dagger]

Oh I figured yeah I'm just saying so far I'm with you

[dense belfry]

Lol

Oof I can't really seem to nail this down in my head actually

Ah well

[velvet dagger]

Yeah I imagine it's pretty wild. My measure theory prof tried to show us a proof that the Borel hierarchy doesn't terminate in under omega_1 steps

It uh

Didn't go well lol

We're still not sure what the fuck universal sets are lmfao

[viscid pecan]

How long you been studying measure theory?

[velvet dagger]

I mean I had a class on it a very long time ago

[viscid pecan]

Oh

[velvet dagger]

Honestly my measure theory is probably very very lackluster

That class took a very specific angle on it

So there's a lot of standard problems I just haven't done

But I know how the theorems flow

[viscid pecan]

I am trying to pick up bits of measure theory without having gotten to the Lebesgue chapter in baby rudin yet

I’m trying to take my time to learn that level of math though as well

Maybe in a year I will get to the lebesgue stuff

[split glade]

Percolation

[velvet dagger]

Where are you in Rudin?

[viscid pecan]

I think I’m starting to learn quicker now

[dense belfry]

Oh I can tell you about that

[viscid pecan]

Chapter 2 but I been focusing on linear algebra right now

[velvet dagger]

I wouldn't really recommend the baby Rudin chapter on Lebesgue stuff

[dense belfry]

Probably

[velvet dagger]

Gotcha

[dense belfry]

Well I can give a Computability theoretic proof actually

[forest jackal]

from the analysis point of view there isn't that large a volume of content in basic measure theory, there are just a few key ideas/principles to master and then everything is very intuitive from there.

[viscid pecan]

Oh what do you recommend for measure theory stuff even with not much analysis background

[velvet dagger]

And that would be cool at some point Emma. Basically what we had done in particular was

[dense belfry]

Because open sets are Computable with an oracle

[fervent pebble]

what would you recommend?

[viscid pecan]

I think Casella and Berger is helpful but haven’t gotten very far in that book either cuz I want to go the math stat route as well

[peak tide]

stein and shakarchi's real analysis is a good intro imo

[velvet dagger]

We defined a universal set in the plane wrt a property to be one which satisfies it and for which every set in the line satisfying it is a horizontal slice

And then you wanna consider being universal wrt being G_{blah blah ordinal many things}

[dense belfry]

Okay so what is a universal set trying to do

[velvet dagger]

And somehow the diagonal messes shit up??????????

Emma if only we knew

[dense belfry]

So think of it like the halting problem

Okay

[viscid pecan]

How far in baby rudin should I go before getting to S&S

[velvet dagger]

Oh that was rhetorical

Oh shit let's go

[dense belfry]

So the halting problem is a universal set of a sort

[velvet dagger]

As for measure theory books I'm gonna soon write a long rant in book recs

[dense belfry]

Well maybe that's not the analogy I should use

Hmm

[viscid pecan]

Sweeet

[iron osprey]

axler has a great, easy book on this

[peak tide]

chapters 1-8

[iron osprey]

very nicely written, and i don't like anything else axler has written

[velvet dagger]

Honestly I don't trust Axler after his linear algebra book lol

[iron osprey]

same

but his measure theory 1 was great

[dense belfry]

Okay so what would the hierarchy collapsing mean

It means there is a top level in the hierarchy

[iron osprey]

better than tao and rudin to be sure

tao goes deeper though

[dense belfry]

Which means there is a set that represents the hierarchy

[iron osprey]

he just talks too much

[dense belfry]

So for example the halting problem represents the set of limit Computable sets

In the sense that the halting problem can compute limit Computable sets

And is limit Computable

[iron osprey]

bike lock arrived 🐲

[velvet dagger]

Limit computable meaning like, "infinite time"?

[dense belfry]

Meaning an infinite binary string A so that there is a Computable sequence of sequences of natural numbers so their limit is A

But also you can probably think of it as computation with finitely many mind changes

Like on a given input you output a string of numbers and the discrete limit of that string is going to be your output

[velvet dagger]

I see

[dense belfry]

I keep forgetting where I'm going with things

Lol

Should probably go to sleep

[velvet dagger]

Sounds good yeah, I'm pretty foggy myself lol

We should talk about this at some point though it's dope stuff

[dense belfry]

Oh actually nevermind I remember

How it works

[velvet dagger]

Lmfao

[dense belfry]

Lol

I think

Okay so this is kind of similar to something in Computability theory called the light face borel hierarchy

As opposed to the boldface borel hierarchy

So the regular borel hierarchy builds on itself by taking infinite conjunctions and disjunctions of lower levels

This is the boldface borel hierarchy

However the light face one needs to have extra computability conditions

So you only allow Computably enumerable unions and intersections of lower levels

And your hierarchy is indexed by Computable ordinals

Instead of by countable ordinals as in the regular borel hierarchy case

However you can kind of view the boldface borel hierarchy as being stratified by the light face one

So if you relativize to an oracle

So you basically give the construction of the light face borel hierarchy more power

Then you have that every borel set is eventually in one of these borel hierarchies

For some oracle

And then you can actually use the Turing jump to prove that it doesn't collapse

I mean I think basically the regular argument is using the borel equivalent of the Turing jump

So I'm being silly

But I thought about this a while ago and thought it was nice

I think I was pretty confusing

Probably

But maybe you can see some of the ideas

[velvet dagger]

Hmm, I'd prob need to know a bit more underlying background to understand this (also at a non-3AM time lmfao) but this all does sound kinda cool. I remember one analysis prof who used to be at Chicago started in logic

And said that descriptive set theory is the "computability theory of analysis"

[dense belfry]

Yes it is

[velvet dagger]

So it's interesting to get some idea of what that actually means lol

[dense belfry]

But yeah there are so many of these results connecting continuity and Computability

And there are good reasons why these results exist

[deep mango]

I had a freshman -15

[ancient flame]

oof

[deep mango]

It was fine

[eager reef]

What’s freshman+number

[deep mango]

Berkeley is a hilly campus and I walked so so much

[cyan goblet]

i hope i don’t have freshman -anything

[ancient flame]

im like 120-130 lbs

[cyan goblet]

weight gain

[deep mango]

weight gained during first year of uni

in pounds

not kgs

[deep mango]

wtf

[ancient flame]

lol

[eager reef]

Oh I have +22 then but I did it on purpose

[cyan goblet]

im 155

[neat frost]

Wow

[cyan goblet]

but still relatively skinny

[eager reef]

I eat in a surplus and work out

[ancient flame]

I need to work out

[eager reef]

So a lot of that weight gained is muscle/water weight

[neat frost]

Why work out when you could also not?

[eager reef]

Because of creatine as well

[cyan goblet]

this tbh

[eager reef]

To deadlift/squat and bench a lot of weight

[cyan goblet]

i still work out but i think about not working out and just sleeping a lot

speaking of which i’m in bed rn

[neat frost]

I don’t work out and I don’t sleep

[eager reef]

Well working out and not sleeping doesn’t work anyway

[neat frost]

Meh

[cyan goblet]

im permasleep

[eager reef]

Sleep is essential for recovery and muscle gain

[ancient flame]

💤

[neat frost]

Idk all this “take good care of your body” shit makes it seem like your body hella weak. My body does just fine with little maintenance.

[ancient flame]

ur just built different

[cyan goblet]

man i wish i were like you

[eager reef]

Depends on how you define a body doing fine

[cyan goblet]

my body is like

[neat frost]

Hell yeah you do

[cyan goblet]

fit but i still look skinny

[errant ridge]

I'm like 180 lol

[neat frost]

I’m not dead yet

[cyan goblet]

it’s a curse having broad shoulders

[eager reef]

Embrace it

Get dorito body

[cyan goblet]

yeah that’s why i’m working out

[odd narwhal]

You need to ingest calorie rich food

[eager reef]

🤝

[cyan goblet]

but for now it makes my somewhat normal arms look skinny

[eager reef]

Eat enough and eat calorie dense food

[neat frost]

Love your new name Gmod btw

[eager reef]

Enough protein as well

That’s how you gain

Roughly speaking

A lot of it happens in the kitchen

[cyan goblet]

probably better chances to do that in college tbh

at home i just eat whatever is put in front of my face

not much option

[eager reef]

Yeah that’s true

Already working out gives a good Basis tho

[cyan goblet]

yeah i do ppl with one day of rest

[eager reef]

Oh nice

[cyan goblet]

but only dumbbells cos i don’t feel like going to gym

[eager reef]

I quit ppl

But it’s a great split

[errant ridge]

ppl?

[eager reef]

Push pull legs

[cyan goblet]

i like it

[eager reef]

Yeah it’s good

It just doesn’t fit me perfectly

So I costumised it

But by a lot so it’s basically a new split

[cyan goblet]

ah kk

[open aspen]

did #algebraic-geometry get a name change??

double alg

alg on both ends

conjugation of geo-comm by alg

[surreal sapphire]

yes

[sleek wing]

ok with comm-alg being lumped in with alg-geo I really think abstract-alg should go to early uni lmfao

[surreal sapphire]

do you honestly?

abstract algebra is weird because its such a wide range of topics

i dont know if an abstract-algebra and advanced-abstract-algebra split is really necessary

also comm-alg was part of the algebraic geometry channel before the rename

[open aspen]

abs-alg is certainly not early university

assuming we take university to mean the 4 year program

granted, we don't exactly have a late university

so maybe early university should mean 4 years and advances is post-bacc?

in which case, there are abs-alg courses for both undergrad and grad. Its a large subject like Loch said

[sleek wing]

we learn groups in first year so yeah, it is early uni

the problem is group theory can either be like

"cosets, homomorphisms etc."

or like, wacky word problem, representation theory, etc. stuff

[open aspen]

Idk what university you go to, but not a single undergraduate freshman is learning what a group is anywhere I've been

[sleek wing]

ok cool

everyone I know learns group theory first year

[open aspen]

But yeah, this

Undergrad Freshman learning Jordan Rep Theorem

[sleek wing]

hell under a certain exam board we sometimes learn about groups in hs

[deep mango]

wew be like "noncommutative algebra doesn't exist"

[sleek wing]

it doesn't though

[deep mango]

rep theorist moment

[open aspen]

Based and non coexeter pilled

If you learn group theory in first year of undergrad wtf you doing for 4 years

[sleek wing]

our undergrad is 3 years

[open aspen]

That changes things, but still

Must have lots of electives

[sleek wing]

no not really

far too few at my uni imo it pissed me off

[surreal sapphire]

at like european universities you learn abstract algebra in first year

its normal

[open aspen]

Ain't that wild

[surreal sapphire]

and the channel gets a mixture of "show xy is a group" and more advanced questions

[sleek wing]

it's wild that you don't

[surreal sapphire]

i think the latter are way more common recently

[open aspen]

Our first year's are learning calc 2 (in the math programs)

[surreal sapphire]

so i dont think there is an issue

[open aspen]

In general, most freshman here take college algebra semester 1

[sleek wing]

the issue is I can't help those people loch

unless it's character theory

[surreal sapphire]

i will start work on the rep-theory containment channel for you right now

[open aspen]

This is why God made threads

[arctic grove]

[arctic grove]

the unis i plan to go to do teach some group theory early on
to everyone, no matter if u are a math major or now

[neat frost]

Good morning shyshy!

[arctic grove]

Good morning slurp!

[open aspen]

Well this just seems absurd. Why should an art major know what a normal subgroup is

[arctic grove]

there are no art majors lol

these are all science unis

[open aspen]

Oh, okay that makes more sense then

[arctic grove]

so People who wanna do Phys, chem, bio, maths, earth sciences and stuff will have to study everything for like 3 or 4 sems (and everything includes One course in each subject and a couple of courses in humanities and engineering stuff)

out of 8/10 sem program (10 in most cases, sometimes 8)

[wooden flax]

whats covered in it though

like up to the fundamental theorem of galois theory?

(including)

[arctic grove]

[surreal sapphire]

probably no, thats in a separate class midway through

[arctic grove]

i doubt that would be first year

[surreal sapphire]

i learned that in my 3rd or 4th semester, which is pretty standard at least in germany

[azure nymph]

Your first year math majors are taking Calc 2?

Actually I guess that's not too crazy my school just moved to doing pre-calc first

[neat lintel]

That's unusual, usually they take that in a proper field/Galois theory course

[wooden flax]

right

[neat lintel]

galois theory is fun though

[stark charm]

idk what fundemental theorem if galois theory

unless u mean galois correspondence

[neat lintel]

It states that there is a bijection between the diagram of the subfields of the fixed field of a field extension and the diagram of the subgroups of the galois group of said field extension

Basically the two lattices are the same, but are flipped upside down with respect to order/degree

[stark charm]

ig those are lattices

[vast surge]

The galois correspondence, then? But I don't think it's a lattice

[neat lintel]

If you chart it out it is a lattice

[stark charm]

i think they are talking about the diagram

[neat lintel]

like a diagram

[stark charm]

lattice is another object

but technically speaking galois extensions form lattices I think?

[neat lintel]

sorry fixed the wording

[vast surge]

You get a diagram, but again, I don't think it's a lattice.

[neat lintel]

yeah I fixed it from lattice to diagram

sorry

[stark charm]

dont galois extensions need to be seperable and regular or something

i dont remember specific terms

but its like the elements are linearly independent

[neat lintel]

yep

[stark charm]

so not splitting polynomials

[neat lintel]

it is seperable

[stark charm]

i think those are lattices algebraically speaking

[wild lantern]

I thought it was a lattice of subgroups? Like the order relation here is the "is a subgroup relation"?

[vast surge]

I thought lattices had to be embeddable in R^n

[neat lintel]

Let $K/F$ be a field extension. If $|\text{Aut}(K/F)|=[K:F]$ then $\text{Aut}(K/F)$ is galois

[stark charm]

any vector space yea

like ive heard lattice over field

[wild lantern]

Mmm, are we talking about diff kinds of lattices?

[fathom swallow]

Arr0w_04

[stark charm]

yeah the notion is similar though

[wild lantern]

Because order theoretic lattices are a thing.

[stark charm]

maybe there is idea of lattice over rings

[neat lintel]

yeah again I didn't mean a lattice I meant a diagram

[stark charm]

i dont know if thats what we are talking about

[vast surge]

I was thinking, like, how $\mathbb{Z}[i]$ is a lattice in $\mathbb{C}$

[neat lintel]

like the diagram of the subfields and subgroups

[stark charm]

but i dont know what those are

[fathom swallow]

Abelian Grapes

[vast surge]

Which doesn't have anything to do with order

[wild lantern]

Like, hasse diagrams and junk.

[neat lintel]

that is what I was implying but I didn't want any confusion.

[stark charm]

yea

[neat lintel]

its a minor point

[vast surge]

Maybe it's one of those words with two meanings

[stark charm]

so i think galois extensions are lattices

[neat lintel]

it is but it doesnt matter

just use diagram

in this case its fine

[wild lantern]

https://en.m.wikipedia.org/wiki/Lattice_of_subgroups

[neat lintel]

So the point Colee is that those two diagrams (lattices) are the same, just flipped with regards to ordering.

[stark charm]

oh

[vast surge]

Galois extensions are lattices, yes, but the diagram you get by drawing subfields and the galois correspondence isn't, I thought. (At least, not the way I'm used to the word)

[stark charm]

lattice wrt inclusion makes sense

[vast surge]

Whoops I was thinking rings of integers of galois extensions my bad

[neat lintel]

they are, but using the word diagram vs lattice is irrelevant in regards to the statement of the theorem

[wild lantern]

Yah it's an order theory thing

[stark charm]

oh then yeah

[vast surge]

Yeah it's one of those words with different meanings I think

[stark charm]

i guess it is a correspondence between lattices

[wild lantern]

And you depict them (and partial orders more generally) with hasse diagrams iirc.

[stark charm]

but relation invertibg

[neat lintel]

So does that make sense colee?

[stark charm]

yea

[neat lintel]

ok

galois theory is super neat.

[stark charm]

i know that form between field extensions and groups

but galois correspondence is more general

[vast surge]

I was thinking of this:

https://en.wikipedia.org/wiki/Lattice_(group)

[stark charm]

its the same thing

[neat lintel]

Basically it studies these things called automorphism groups, specifically galois groups, which are groups that are sets of automorphisms that have special properties

its nice

[stark charm]

there is a general form of lattices where you can embed them over any vectorspace not necessarily finite dim

[vast surge]

It is?

[stark charm]

yeah

[neat lintel]

Like you can prove that C (the complex numbers) is algebraically closed, and that there is no equation to find the roots of a polynomial of degree 5 or higher

[stark charm]

not the order theory one though

[vast surge]

That's what I thought you meant. That what I sent was the same as the order theory one.

[stark charm]

yeah solvability is really useful

[neat lintel]

it is! There are some other small things that help out in other areas, but those are the two main results you get from a course in galois theory.

[errant ridge]

with differential galois theory you can prove whether a integral has a closed form solution or not (I think)

I'm not sure

[stark charm]

yea

[errant ridge]

I don't know diff galois theory

[wild lantern]

That's cool lol

[errant ridge]

I'd love to learn it though

[vast surge]

Yeah, you use the picard-vessoit group of the differential equation

[errant ridge]

:O

[wild lantern]

I really wish we got to do more galois theory here

[neat lintel]

The point is that automorphism groups behave really nicely

[errant ridge]

in your uni?

[stark charm]

yeah

[neat lintel]

and it kind of relates all of abstract algebra (groups rings and fields) together into a final chapter

[stark charm]

they are probably most important idea in algebra

[wild lantern]

We got through the fundamental theorem in fraleigh like right as our semester ended

[stark charm]

endmorphisms in general are pretty important

[vast surge]

But you need differential rings and differential fields, which are rings (or fields) with a differential as well, which is a unary operation $D:R\to R$ so that $D(uv)=uD(v)+D(u)v$ for $u,v\in R$

[fathom swallow]

Abelian Grapes

[neat lintel]

so usually an AA course would touch on some intro galois theory topics

[vast surge]

(if R is your ring)

[stark charm]

african american course?

[vast surge]

Abstract Algebra