#serious-discussion

1 messages · Page 226 of 1

warm umbra
#

đŸ«‚

rigid mason
#

that life is too long

#

to die young

warm umbra
#

cherish those moments

rigid mason
#

i will cherish, 3 years ago

#

well no, 4 years

#

5

#

5 is nice.

#

i was 12

warm umbra
#

yeah i hit rock bottom recently too, but im still grateful to be in the position that I am and I know that things will get better, for the both of us; no matter how low we feel right now

rigid mason
#

well no its bad, 6

warm umbra
#

The future looks bright for us my friend

#

Lets do right with ourselves and keep working to be better nonetheless

rigid mason
warm umbra
#

you will

#

we both will

rigid mason
#

none do

#

all i have left is my head

limpid bridge
#

do we have channel for programmer ?

#

iirc there is in the past

rigid mason
#

you wanna code?

limber thunder
limpid bridge
#

tks

limber thunder
#

I don't remember this server having a similar channel before

strange dagger
#

this is a testimony that hard work pays of and you don't need to listen to people all the time as they will alway try to stop you
closing the day with a sale of 6k i know are coming in this way

warm umbra
#

we both like to yap

#

but we have an idea, and thats all a society needs in order to be better

#

the revolution is upon us.

static storm
#

How to represent the fact that k is a non-zero real number using set-theoretic notation?

fathom swallowBOT
stark trench
#

if you don’t have \neq, just replace it with \neg(k = 0)

icy heron
#

or just $k \in \Bbb R \setminus {0}$

fathom swallowBOT
#

sheddow

haughty lion
#

what's a good website/tool for making flowcharts? I need to draw a few state diagrams of Turing machines for my CS class

eager eagle
#

i dont understand extended euclidean can someone explainn it

granite crag
#

@storm sage stirner

haughty lion
#

Feels like using microsoft word's Add Shape

cinder zephyr
#

maybe this could give a good approximation to what you need

#

for actual tape machines idk, maybe you can google and modify some Tikz code

obtuse path
#

yall. what can i get for a "gas and leo" in bloz fruits

#

yall who play fortnite im bored

true zinc
#

!noadvert

quasi jettyBOT
#

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.

pliant sigil
#

Sorry

storm sage
#

????? why did you ping me

granite crag
granite crag
#

that's all

#

sorry to bother you I guess

#

it was for comedic value

granite crag
deep mortar
#

I'm struggling with studying for my maths exam tomorrow

fresh comet
#

@deep mortar welcome to mathcord, and good luck with the exam aecatheart

zealous garden
#

That's it, we're done

fresh comet
granite crag
#

@fresh comet

fresh comet
granite crag
warm umbra
#

welcome to the server @stoic raft

#

welcome to the server @mellow rock

granite crag
#

most of his lines in the video are actual quotes from The Unique and its Property

#

lol

halcyon magnet
#

did (or do) somebody study at kyushu univeristy at master's level? i am interested in admission exam (where can i find list of topics or sample questions from previous years, which cover the exam)

neat lintel
#

@blazing pawn Have you heard Luxury and 212 Remix?

blazing pawn
#

no ive only heard the nicki/azealia competition/luxury mash up

neat lintel
#

Oh right

#

It was compeititon

#

My bad😭

neat lintel
blazing pawn
#

fr

neat lintel
#

I hope I could leave this homophobic country😭 @blazing pawn

#

I wanna wear fashionable clothes😭 😭 😭

#

And try customising my own too hehe

#

And go around with a boombox, prob playing 212 đŸ€Ł

warm umbra
#

welcome to the server @ancient fjord

old oak
#

Speaking of:

#

I mean, on some level the important factor is the 1:16 min real time, but still, a day and a half is impressive.

neat lintel
#

Why

old oak
#

Why what?

neat lintel
#

Why made query and for what

old oak
#

To find out information

neat lintel
#

Ok

old oak
#

It's work related, so I'm not going to share too much

neat lintel
#

I understand

#

Also notice this

#

Your name yellow ur star blue

#

My name blue my star yellow

old oak
#

It's a diamond

neat lintel
#

O

old oak
#

But I do see your point

neat lintel
#

Looks pretty right

#

Also our pfps have same contrast

sonic sentinel
#

(i think i watched the solution video then stopped in the middle cause it was too boring? then i started thinking about it now again for some reason)

#

((i wasn't grinding on the problem for years straight dw))

#

i realized you could look at the parity of ||rows and columns to get two 8-bits where you have to flip one of each independently, then i realized you could also do this with a 4x4x4 cube to get three 4-bits, and then i realized that you could use a 2x2x2x2x2x2 6d hypercube||

#

i thought this was some absurd way to think about a more normal 2d-based solution

#

skimmed through the 3b1b solution video, nope, was also talking about hypercubes.

neat lintel
#

@warm umbra heyyy
How’d your AP exam go?

misty owl
#

Chat should I bulk or cut 5 kilo’s? Cause the heavy-weight tournament is soon so I’m gonna maintain my weight for that; but after that I wanna decide whether i should partake in the light-heavyweight or super-heavyweight tournament

misty owl
old oak
#

I think you should study real analysis instead

solid yarrow
#

I think you should study complex analysis instead

limber thunder
bronze pelican
# jagged forge

I hate that this reddit post was created because I showed my friend a proof of the fact that the function field of the riemann sphere is field of rational functions in one variable

mint patio
#

@clever knot God I hate salesmen

#

They don’t have time for anything not related to money

old oak
#

Yeah, it's a bleak existence

mint patio
obtuse path
#

Oi Oi Oi

bronze pelican
queen bobcat
ocean harbor
#

life is good after quitting cs SCchilling

queen bobcat
#

Said everyone who left cs for anything else

ocean harbor
#

my classmates and profs i had in semester was literally replaced with ai

#

and about the group project, it was horrible

#

im done

queen bobcat
#

LOL

#

Unreal

ocean harbor
#

my gpa is 3.683 btw

#

so 92

#

not bad

queen bobcat
#

Glad you survived that insanity

ocean harbor
#

i sure did

worthy loom
#

Hi everyone!

#

I'm looking into study of projective geometry but I can barely find any good tutorial books about that

ocean harbor
ocean harbor
hardy iron
ocean harbor
#

just chilling

#

also I'm thinking retiring from gd cause I got addicted to mc

worthy loom
true wedge
#

it a bad game

#

2.1 better than 2.2 đŸ”„

#

game died after 2.2

ocean harbor
#

also robtop account got banned on discord

warm umbra
#

Mr. Yeet; save them as they have once saved you, replenish yourself for the betterment of society, and the betterment of life whose potential far surpasses you. You my friend don't need to be part of the problem, for the first time in your life, you can be solution

verbal orchid
#

hi

#

hello?

keen stirrup
obtuse path
#

Hi guys

#

Can yall answer this question

#

5x1

sharp mulch
vast wraith
old oak
limber thunder
queen bobcat
#

15

fair mural
true wedge
#

feel ickier

ocean harbor
#

just become a creator :^)

#

and yell at robtop

queen bobcat
#

There should be a menu to exclude levels that contain any choice of features

#

2.1 was all we needed frfr

#

Glad 2.2 exists but I don't like the direction RobTop is ultimately taking

ocean harbor
#

we all waited for 7 years and in the end we got fireinthehole

neat lintel
#

my gpa is 1.2/6.0

ocean harbor
rocky shuttle
fresh comet
#

me three

queen bobcat
#

My GPA is 0

warm umbra
#

I let them down guys

#

I'm too far gone

#

The time has left me

#

But I will keep trying

#

Theres only two ways it can all end, my demise or my triumph; regardless of the outcome, I will rest easy knowing I atleast tried.

true wedge
#

Business major is perfect gpa as long as you do your crayon coloring homework

dry copper
#

Sinners was a mid movie

#

6/10

dry copper
#

I used to take pride in being social inept before entering the labor force

limber thunder
#

even in like, math academia being socially inept takes a huge toll on you

#

it's an important skill to have in general

#

or well an important one to hone and improve

warm umbra
grand adder
#

come

rustic pasture
#

That is

#

Kinda relatable

#

I mean im still in y10 but i do business

vast wraith
vast wraith
#

it was a traumatic experience

proven knoll
still compass
#

Hm

merry plank
#

I’ll henceforth have calc I-iii saved as the three calculi, respectively the first second and third calculus, and first , second and third of the three calculi.

#

Whenever I talk/think about them

limber thunder
#

lmfao this is insane

#

never thought of referring to them as calculi plural

#

peak pretentious goober

old oak
#

Calculussesses

limber thunder
zealous garden
#

Seventeen Calculi

proven fractal
coarse bridge
#

newton ahh terminology

ocean harbor
zealous garden
neat lintel
#

someone help me

ocean harbor
neat lintel
#

i fumbled articuno any help?

still compass
#

I've a study group channel would anyone like to join?

#

@zealous garden

#

@zealous garden

#

@zealous garden

old oak
#

Ahh, the rare tripleping

warm umbra
hardy iron
untold cedar
hollow isle
true zinc
mint canopy
mental stratus
#

even when the person getting the pings says ping ke three times in their description

loud hamlet
#

Guys think possible to get a machine learning engineer job with a degree in applied mathematics?

solid snow
#

yes

undone vigil
#

i can be someone personal teacher at a price

solid snow
#

no

limber thunder
sick parrot
limber thunder
#

you can also get a fairly good grasp of theoretical ML/neural networks with a math background

old oak
limber thunder
#

(those books won't replace actual MLops experience but if your uni doesn't provide learning opportunities for that, take online courses and build some personal projects)

loud hamlet
#

How come when people at my college ask for my math class (which is just beginning trigonometry) once they hear I’m a math major, they don’t feel like talking with me or rather withhold information when I ask questions about upper-division mathematics?

solid snow
#

how can we answer this

limber thunder
#

you ask them about upper div maths? maybe they aren't math majors and just are required to take trig

#
  • other first year or so courses
#

in my experience most people either don't care about maths, or are traumatized by it from HS, or are supportive about you studying maths but don't really understand it lol

#

you kinda need to accept that and hopefully meet other mathematicians along the way

merry relic
#

2+1

chrome cape
#

Is there a Channel for computational Sorting Algorithms?

sharp mulch
#

No you should ask in a CS server

chrome cape
#

Can you give me an Invite?

sharp mulch
#

No I'm not in any

chrome cape
#

Oh, I cannot join that Server because my Nitro ran out and I'm beyond 100 Servers

sharp mulch
still wing
#

My favourite rizz line:
y=f'(x0)(x-x0)+f(x0)
It always touches the huzz in their hearts

old oak
#

My ignore list is really growing quickly today

sharp mulch
#

Ignoring is so generous of you

old oak
#

I'm a magnanimous owl

violet urchin
old oak
#

Not yet

haughty agate
#

elope

#

^ meow

loud hamlet
#

Why does arccos(sqrt(3)/2) with interval 0 greater than or equal to x greater than or equal to pi equal pi/6 and not equal 5pi/6? I'm getting so confused, as 5pi/6 is in the interval 0 greater than or equal to x greater than or equal to pi.

solid snow
#

cos(5pi/6) is not sqrt(3)/2

loud hamlet
#

OOOH, yeah it's -sqrt(3)/2.

#

How would you recommend studying? I'm feeling a bit rusty after not studying for 4 days.

stray sedge
#

what is the powerhouse of the cell

haughty lion
#

midichlorians

royal stirrup
#

I want to be a pure mathematician, so what should I be looking out for in colleges?

solid snow
#

math

royal stirrup
#

Well, duh. To be more specific, what makes certain math programs stronger than others?

elfin smelt
#

more courses offered, more seminars, more faculty. you can usually find this info on their websites or by finding a ranking of unis by how strong their math programs are

royal stirrup
#

Alright, thank you!

loud hamlet
#

I wish my college offered a BS in mathematics 😩

sharp mulch
#

BA vs BS doesn’t matter

loud hamlet
#

Some job descriptions convey a Bachelor of Science as a necessity, so I'm just sad that there's a comparison.

#

Also a BS in mathematics would review applications of mathematics, which would suit me more...

solid snow
#

Jobs will put anything as requirements or qualifications

#

Its often never actually completely necessary

#

Not that the distinction is even useful a lot of the times

#

“Top rate” schools like harvard frequently only offer a “BA”

leaden torrent
#

if a prospective employer is distinguishing between BS and BAs in mathematics, they are not worth working for

#

since they do not know what theyre doing

#

as for this:

Also a BS in mathematics would review applications of mathematics
i think this is only really true of schools that offer both

#

if a school offers only one i wouldnt assume anything about the difference

solar hawk
#

What’s a BS and a BA

#

Oh

#

Art and science

hazy mural
#

does anyone know if theres a way to rotate a function by an arbitrary angle?

#

ive beb thinking about this for a while

limber thunder
#

as in rotating its graph?

solar hawk
#

Maybe write it as a parametric and then put it through a rotation matrix

#

Or something

limber thunder
hazy mural
#

like i know you can rotate vectors ysing matrices but i dunno about rotating a function

hazy mural
solar hawk
#

Yeah

hazy mural
#

wait maybe you could convert to polar coordinates and then add the arbitrary angle to all the x's

#

i think that would work

wide orbit
#

what are those servers getting advertised in some people's profile?

limber thunder
#

which people

wide orbit
#

check precalc channel the person J

#

like this i have seen some more @limber thunder

limber thunder
#

the thing beside their nick

#

that's a recent discord feature

wide orbit
#

oh thank you

limber thunder
#

np catthumbsup

agile fiber
#

mathcord tag when

wide orbit
#

@limber thunder Sorry for pinging. Can I know about the roles of mathematics server(eta, plus or minus,etc)? Or I am prohibited to know that.

ocean harbor
#

if you want one

wide orbit
ocean harbor
#

no?

agile fiber
#

it's only for nitro boosted servers, but anyone can get them if they join

limber thunder
# wide orbit <@700814540626984980> Sorry for pinging. Can I know about the roles of mathemati...

the ones not listed in #info are mostly for technical purposes, except for Senior Moderators which aren't in the list only because we haven't updated it opencry

some I remember and which are ok to explain are ω (admins), ÎŒ (the actual perms for senior mod, allowing us to take a break by removing the color role whenever), ∞ (people who lost very active and request access to the active VC basically), — (people blocked from posting in the advanced channels for shitposting)

#

I think these are the main "esoteric symbol" roles

#

lol

wide orbit
#

Oh

#

Thank you!

#

Derivada

night wyvern
#

Hello,
I am a high school student, and my level in mathematics is very weak. I feel that I need to relearn math from the very beginning in order to rebuild a strong foundation.
What do you recommend? Are there any specific resources or steps I should follow to start from scratch and gradually improve my skills effectively?

still compass
uncut thicket
#

Hey guys what’s the collatz conjecture

rocky shuttle
#

it's the dual of the llatz njecture

uncut thicket
#

No it’s 3n+1

rocky shuttle
#

ngrats, you answered your own question

solar hawk
#

:omfgag:

#

Omg I just lost nitro

limber thunder
fresh comet
jagged forge
wide orbit
#

what does suspicion thing on someone on some silly things means? is it for fun or serious? like "The user is suspicion to be dumb as shit or bloodless fighter jet pilot." and also I have seen some serious things like "the user is suspected to affliated with terrorist organization or hacker organization"

mint canopy
#

It is a joke

#

People write it in their own profiles as a joke

#

Because it is a funny thought

wide orbit
#

oh

#

but the terrorist and hacker is it also joke?

mint canopy
#

Yes.

#

It is a joke.

wide orbit
#

oh

#

my

#

god

#

I thought it was something very serious lol

#

tq for clarity

#

then discord don't mention anyone like that in their profile

#

?

mint canopy
#

They do not.

#

Because as I said, it's a joke

wide orbit
#

also why the moderators name changing in the members panel from time to time and not all moderators are shown there

mint canopy
#

People are free to change their nicknames whenever they like.

#

Some people do not select the 'online' status on discord and therefore do not show up on members lists as online

#

Such as me.

wide orbit
#

ohh

mint canopy
#

I don't want children seeing my name and DMing me about maths problems

wide orbit
#

only online moderators are shown there

mint canopy
#

Only online people are shown on the right hand side as being online, yes.

old oak
wide orbit
#

thank you for information

vocal vessel
old oak
#

I know you!

#

And you haven't yet annoyed me enough to get blocked

old oak
#

I mean, getting on my blocklist isn't really a challenge, I have a very low threshold

#

A lot of people accomplish it in seconds

mint canopy
#

I will forever maintain that blocking people is self-care

old oak
vocal vessel
#

Most of my blocks are from other servers tho 😅

fresh comet
#

my block list still totals to zero zzmilkproud

old oak
pure hollow
fresh comet
#

my friends list though

fresh comet
#

it’s like 300 something

old oak
fresh comet
#

do the other 75% come from cranks in the various math channels? catthink

vocal vessel
pure hollow
old oak
vocal vessel
#

Sometimes I open chill and it's a blank screen with like "90 blocked messages" on it.

old oak
fresh comet
pure hollow
old oak
#

A random assortment of channels, mostly the general ones.

pure hollow
vocal vessel
#

I honestly only really block homophobes and children...

old oak
#

Yeah, that's another sizeable contingent in my case as well

#

Also I don't really keep a tally, that would be excessive

#

I'm just specifying those categories by vibes

old oak
#

Bonus points, and lots of them, if LLMs are involved

vocal vessel
#

ChatGPT proved collatz for me...

old oak
#

Although LLMs usually make it easier for me to get annoyed enough to block them; I much prefer artisanal, organic crankery

vocal vessel
#

Bespoke crankery đŸ€Ł

old oak
#

The LLM cranks are all made out of ticky-tacky, and they all look just the same.

hardy iron
#

I prefer those with hand drawn diagrams, on papers

pure hollow
fresh comet
#

I shall use my army of alts to conjure up some crankery

old oak
#

It doesn't realy work when done on purpose.

#

Confirmation bias might of course be at play here, but I feel it's quite hard to fake being a crank

pure hollow
#

I might be able to cook some crankery provided I can do math which I apparently can't

old oak
#

You need a kind of delusional confidence that's very hard to fake if you actually know something.

vocal vessel
hardy iron
pure hollow
vocal vessel
silent junco
#

idk i think its reasonably easy to fake being a crank

#

maybe not elaborately but at least at a surface level

wooden falcon
old oak
wide orbit
#

is moderation paid in this server?

old oak
#

It should be

wide orbit
#

what are the eligibility criteria to become one?

#

if it is ok to say,

wooden falcon
solid snow
wide orbit
#

then how to become level 100 wizard btw lol?

old oak
#

Become a level 99 wizard and then level up

wooden falcon
#

but I already got a wizard past level 100

old oak
wide orbit
#

It's hard for pirate king to become a wizard lol

wide orbit
old oak
#

Not really, I enjoyed playing WoW

old oak
#

Although primarily not as a wizard

#

You can probably tell from my pfp

wide orbit
#

yea

wooden falcon
#

in my case the wizard in question is from wizard101 lol

#

mmorpgs are a stupid time and money sink but oh so much fun

wide orbit
#

the money and time are sunk for the fun!

#

lol

#

what will be the role given to Ramanujan in this server if he is alive now and became a member?

solid snow
#

honorable

wide orbit
#

that's all?

old oak
#

He'd get banned within a week for crankery

wide orbit
#

for a god tier mathematician

#

what????

solid snow
#

i mean this server has no extra honorifics really

#

idk if he would want to moderate

wide orbit
wide orbit
hard oasis
#

Read anything on viXra and this is crankery; in a nutshell: nonsensical things that may look technical for an outsider

solid snow
old oak
#

Probably, I was being facetious

solid snow
#

breadpensive 🚬

#

No ik lmao

old oak
#

Posting weird random formulas without any elaboration might cause eyebrows to be raised, though

solid snow
#

He truly did have divine inspiration

old oak
#

People would probably suspect they were LLM generated

wooden falcon
hard oasis
#

What's that person's name on M.SE that solved incredible but fabricated integrals? This may look like it at a first glance

solid snow
#

Cleo

wooden falcon
#

before society whittled that down

hard oasis
#

Right, cleo!

hard oasis
#

Of course it was; if Ramanujan were to post today, it may look like a new Cleo

wooden falcon
#

well I feel like it’s different. Ramanujan started solving his own problems, and most which weren’t were just standard

#

Cleo faked being someone else who posed the problem.

#

There’s nothing wrong with posing a problem yourself and being like, look at this cool solution I found!

wide orbit
#

what is cleo?

hard oasis
#

My hope is one day someone will find a "lost notebook" from Ramanujan that gives a hint at how he got the insight for lots of his formulas

#

Like: what was going through his mind? Did he have some wiring we lack? catgiggle

brave flare
#

Who really liked integrals

wide orbit
#

then who is cleo would be fit there.

hard oasis
#

Cleo fabricated hard problems and posed the questions on the maths stack exchange; they later posted a solution that looked incredibly astucious, so much so that suspicion was raised and people investigated before discovering the truth

#

Turns out it's easier to find an antiderivative if you already know what to take a derivative from catgiggle And once you know the answer, you may have an idea on how to get there too

wooden falcon
#

Yeah it’s a lot easier. Still impressive to see the solving process. But yeah, much much easier.

#

Showing cool shit is nice, just be honest about it

hard oasis
#

Yeah, be intellectually honest always

wide orbit
hard oasis
#

Does it matter that it's a man or woman from Armenia?

wide orbit
#

because i don't understand your statement and talking about something lol

brave flare
#

cleo is actually called Vladimir

mint canopy
# wide orbit a woman i think

No, Cleo is (it appears to be the case) the alt account of a man, who deliberately posted questions he knew how to solve so that Cleo could magically answer them.

earnest python
#

Yeah some YouTuber dug into it and managed to contact the person behind Cleo

#

Forgot who the YouTuber is tho

gray spindle
#

omgggg cleooo exposed??

mint canopy
#

This is relatively old news but yes haha

gray spindle
#

nooo my favorite math legend

#

reminds me of people in #chill some guy kept posting integrals he supposedly solved but idk man its hard to prove that this random integral you solved vs just made

old oak
#

<@&268886789983436800>

#

Almost pinged modern day gatsby again bleak

mint canopy
#

@neat lintel We made it clear we do not allow surveys.

neat lintel
#

elo

vivid halo
grizzled crypt
hard oasis
#

I haven't studied them much; I only watched an online course by Keith Conrad on the topic!

latent edge
hard oasis
#

He had a crazy intuition then catgiggle

vivid halo
#

yeah it was pretty crazy

#

some of the more classical stuff around modular forms I can kind of imagine discovering but the stuff he discovered around mock modular forms is still mysterious

jaunty ibex
#

Modular formd are overrated

vivid halo
#

Rogers Ramanujan is one of the coolest results

#

absurdly deep stuff

latent edge
#

Yeah this result still amazes me lmao

vivid halo
#

the result that only these seven are modular makes it all the more impressive that Ramanujan discovered a few of them

latent edge
#

:chad:

#

We need a chad emoji smh

jaunty ibex
loud hamlet
#

After I complete my final, my parent was like 'how did you think you did,' all smiles... I just wish I could study and complete assignments in peace... How do you guys feel when someone delves into your grades?

solid snow
#

Tell them you don’t feel sharing, but tbh I think its unreasonable to crucify your parents for this in this instance, they just seem like they care

loud hamlet
#

Just the somewhat sad interaction if I said after I didn't do well feels terrible... And if I say I did well than they might get all giddy and then I feel the pressure to perform which doesn't help much, as I do lose passion when others take pride in my work for some reason.

loud hamlet
vivid halo
#

partition functions of such field theories are mock modular, constraining the modular landscape constrains the physics landscape

latent edge
#

This is really cool

#

Modular forms casually dropping bangers everywhere shiver

vivid halo
jaunty ibex
#

I don't care about conformal field theory

vivid halo
#

lol what do you care about

jaunty ibex
#

I only care about class field theory and number fields

vivid halo
#

why limit yourself to class field theory that's boring

#

but yes number fields are a nice thing to care about

latent edge
vivid halo
#

that would require caring about modular forms

latent edge
#

right

jaunty ibex
#

Yeah this is why

latent edge
vivid halo
#

lol

real temple
alpine copper
#

@vivid halo do you know if modular anomaly has any number theoretic explanations?

vivid halo
alpine copper
vivid halo
#

yes but in which physical situation

#

the ones counting BPS indices in CY compactifications of type IIA string theory? or something else

alpine copper
vivid halo
#

right okay I can say something pretty general and then maybe something more specific about these examples

alpine copper
#

I should probably ask my research prof, as he said "many cond matter systems exhibit modular anomaly" but nothing more specific than that

vivid halo
#

well so first of all are you comfortable with anomalies in the first place

#

like what the presence of an anomaly means geometrically

alpine copper
vivid halo
#

roughly speaking yes, although there are a few kinds of anomalies, the curvature anomalies are local anomalies but you can have global anomalies as well

alpine copper
#

It has to do with the index of some dirac operator in general, right?

#

Or is that just for chiral theories

vivid halo
#

it mainly has to do with the eta invariant of such a Dirac operator

#

so yes morally this is an index

alpine copper
#

Okay okay. I'm following (will probably have to look up the specifics of the eta invariant later, but i can see why geometry matters)

vivid halo
#

say you have a parameterized family of spin Riemannian manifolds with boundary

#

fix the following boundary condition for the corresponding family of Dirac operators

#

now consider the determinant line

#

the exponentiated eta invariant lives in the inverse of the determinant line

#

this should give a smooth section of the determinant line bundle as X varies in such a family

#

these smooth sections given by the exponentiated eta invariant should satisfy sewing laws in the sense of TQFT

#

now two things can happen as far as anomalies go. First of all, the determinant line bundle carries a connection, the curvature of this connection is a source of local anomalies

#

Second of all, the determinant line bundle can fail to be a trivial line bundle, the obstruction to the existence of a global trivialization is a source of global anomalies

#

the partition function should also give a section of this determinant line bundle, so global anomalies will mean that the partition function is not a number but rather a section of some line bundle

#

when you look at the perturbative expansion of Chern-Simons theory the exponentiated eta invariant and the analytic torsion (which is a correction to the metric and connection on the determinant line bundle in the first place) show up

alpine copper
#

Okay, so if we specify to the torus partition function, we have the moduli space of conformally equivalent tori, and Z is a section on this moduli space, right?

vivid halo
alpine copper
# vivid halo right

And the fact that there is a modular anomaly is because Z is a section of a non-trivial line bundle and not a true to honest function on this moduli space

vivid halo
#

the anomaly here will mean that such a partition function fails to be SL_2(Z) invariant

alpine copper
#

Hmmm, is analytic torsion something number theoretic?

vivid halo
#

yes!

#

it shows up in Arakelov theory among other things, and there are lots of examples where this is related to number theoretic objects

#

there is a strong analogy between Alexander polynomials/analytic torsion and p-adic L-functions for example, some of this makes sense for more classical L-functions as well

#

anyways in the mock modular examples, like mock theta functions, the anomaly comes from the fact that you are looking at the holomorphic part of a harmonic weak Maass form

#

the harmonic weak Maass form is modular, but its holomorphic part isn't. The latter needs to be "completed" to restore invariance

alpine copper
#

Ahh interesting, interesting. How do L-functions further show up?

#

i.e detect the existence of a global anomaly

vivid halo
#

an illustrative example involves arithmetic hyperbolic 3-manifolds and Chern-Simons theory with complex gauge group SL_2(C)

#

if you have an imaginary quadratic field F then you can produce an arithmetic hyperbolic 3-manifold H^3/SL_2(O_F) whose volume is the special value \zeta_F(2) up to some less interesting factors

#

the same volume appears in the perturbative expansion for Chern-Simons theory

#

now with complex gauge group you actually see a "complex volume" whose imaginary part is the usual volume, and whose real part is the Chern-Simons invariant

#

if you think of this special value \zeta_F(2) and volume as an amplitude, the Chern-Simons invariant is in some sense a phase

#

it is of course not as well-defined as the amplitude is (the amplitude will live in R, the phase will live in R/Z) but it carries number theoretic meaning

#

there are lots of situations around motives and special values of L-functions where half of the periods appearing some part of the period matrix can be explained classically, while the other half can only be explained as phases in this way

alpine copper
#

Hmmm, lots of stuff I have to look up

vivid halo
#

maybe the simplest example of this is the analytic class number formula for the residue at s=1 of the Dedekind zeta function \zeta_F(s) for a number field F, the regulator appearing in this formula is a determinant of some matrix whose entries are special values of log|z| at units in the ring of integers of F

#

log|z| is single-valued, but log(z) is not; its real part is log|z|, while its imaginary part is arg(z) which is a phase

alpine copper
vivid halo
#

the modular anomalies specifically are most closely related to mock modular forms and weak harmonic Maass forms, not as closely to L-functions I would say

#

the point is that these mock modular objects are things like theta functions, they live on the moduli of elliptic curves

#

if you take the Mellin transform of such a theta function, so you integrate from 0 to i\infty and regularize suitably, you get an L-function

#

this is how the L-functions of classical modular forms are defined in the first place, they are Mellin transforms of modular forms

alpine copper
vivid halo
#

there is probably some relation but I don't know of anything specific to point to

#

I should say that this business of defining L-functions for things like weak harmonic Maass forms is quite new and very mysterious

#

another related thing to look at is weakly holomorphic modular forms and their (quasi)periods, and how these are related to their L-functions

latent edge
#

wow discussion 2 is so peak

vivid halo
#

when you have a classical modular form f, say cuspidal for SL_2(Z), it should have a 2x2 period matrix

#

two of the entries are the real/imaginary periods \omega^+ and \omega^- and they explain the critical values of the L-function L(f,s)

alpine copper
vivid halo
#

namely L(f,s) is a rational multiple of \omega^+ or \omega^- (depending on parity) for s=1,...,2k-1 where k is the weight

#

there are two other entries of the period matrix which are hard to see in terms of f alone, nor can they really be seen in terms of the complex conjugate \bar{f}

alpine copper
vivid halo
#

f generates the holomorphic part of de Rham cohomology algebraically, but if you want the rest of algebraic de Rham cohomology you need to write down a weakly holomorphic modular form F with the same Hecke eigenvalues as f

#

it's like how on an elliptic curves you can write de Rham cohomology in terms of dz and d\bar{z}, but if you're working algebraically with a Weierstrass equation y^2=4x^3-ax-b you really want to work with dx/y and xdx/y

#

the remaining quasiperiods \eta^+ and \eta^- are periods of this weakly holomorphic F and are similarly proportional to the critical values of the L-function L(F,s)

latent edge
#

that's why i've been interested in VOAs and conformal theory

vivid halo
#

this L-function L(F,s) is hard to define though, typically F will have exponential growth at the cusps so the obvious Dirichlet series doesn't converge anywhere! You have to regularize this in a pretty brutal way

alpine copper
vivid halo
#

I find it endlessly amusing that all my insights about L-functions have come from studying physics and not from studying number theory directly

alpine copper
vivid halo
#

the definition I have in mind is from work of Bringmann, Fricke and Kent

#

in general I recommend Bringmann's work, there is so much good stuff around mock modular forms and all that

untold cedar
#

@latent edge opencry

latent edge
#

Yes.

vivid halo
#

I have such a backlog of papers I need to write up about this stuff monkey

alpine copper
#

If you ever do a write up on this, please let me know. I'd love to take a look

latent edge
#

same

vivid halo
#

yeah I'll let you know nozoomi

#

right now trying to write down some conjectures about special values of L-functions at s=1/2 in terms of Dirac operators shiver

alpine copper
vivid halo
#

right

#

I mean they have periods there is just more indeterminacy in the definition that you have to keep track of compared to the usual periods one likes to consider

alpine copper
#

So in this case, the "L-function" doesn't have an associated series

vivid halo
#

it does actually

alpine copper
#

Also, dumb question, but is there a way to canonically decompose these mock modular forms into a modular and not modular part?

vivid halo
#

not quite canonically but there is a decomposition like this yes

#

you have an exact sequence like this and a similar thing shows up in the mock modular case also

alpine copper
#

So, I would like to understand these torus partition as mock modular forms. I want to see if there is any sense to talk about them as an anomaly free and an anomalous sum

vivid halo
#

relating weakly holomorphic modular forms and harmonic Maass forms

vivid halo
#

the harmonic weak Maass thing has nice modular properties, and it has a holomorphic projection which recovers the original mock modular thing. The difference is the anomaly

#

of course it's easy to compute the holomorphic projection but very hard to compute this kind of modular completion

#

by the way these kinds of harmonic weak Maass forms and mock modular forms are a bit outside the usual language of the Langlands program but they still have good representation theoretic interpretations

#

this is a really nice paper about this generalizing similar results of Bringmann and Kudla https://arxiv.org/abs/2207.02278

#

probably the best place to learn about how these things show up in number theory is reading about Kudla's program, it reminds me a lot of what is happening around these BPS counting problems actually

alpine copper
vivid halo
#

yeah the completion is like anomaly cancellation

alpine copper
#

Woah

vivid halo
#

you're having to add some counterterm to restore modularity

alpine copper
#

Are there any papers where these analogies are made explicit?

vivid halo
#

mine hopefully

#

but yeah idk the literature on this is not so explicit, I've had to scrape the literature and read a bunch over the last few months to figure this stuff out

#

Freed has a wonderful paper about anomalies and determinant lines though

#

second 4 on Riemann surfaces is especially clarifying I think

#

there is also a lot of literature by Freed and collaborators about how to interpret anomalies in the usual functorial TQFT language, namely in terms of "invertible field theories"

#

Witten also has some nice writing on anomalies which might be more accessible if you have a good physics background

#

but yeah ultimately this picture about zeta regularized determinants/eta invariants and what it has to do with Quillen's determinant line (and its metric corrected by the Ray Singer analytic torsion) is at the center of everything here

#

I do really believe these kinds of regularized determinants of differential operators are the correct way to think about L-functions, this is what interested me in this story in the first place

#

the usual kinds of L-functions that show up in number theory should have an Euler product expansion over all primes, as well as a gamma factor involving the Archimedean place which cleans up the functional equation

#

the local factor at a prime p comes from the action of the Frobenius that you always have working in characteristic p

#

the only way to get a similar interpretation for the gamma factor at the Archimedean place is using these zeta regularized determinants

alpine copper
#

not to switch up the discussion crazily, but how would I go about getting into this field in grad school? Like what background are people looking for in potential students?

latent edge
#

What field? Langlands?

vivid halo
#

it depends on which parts you're trying to work on, but I guess generally speaking it has become quite popular to study the interface between mathematical physics and number theory these days

latent edge
#

Sounds very fun thing to do

#

better than whatever this is

#

character slop shiver

vivid halo
latent edge
#

please give me physics slops

jaunty ibex
latent edge
#

its not bad

#

wait nvm it is bad I take my words

#

but it just boils down to combinatorics

#

the stuff I proved so far sound really trivial. I dont feel much about them for some reason

jaunty ibex
#

I don't think they are trivial

vivid halo
#

it only looks bad because the author chose bad notation

latent edge
jaunty ibex
#

Your average combinatorics paper

latent edge
#

ill try tomorrow and convince my prof to relate the stuff we are doing with braid groups

#

I think it will look a lot better

#

if they complain about writing ill just say ill do it opencry

vivid halo
#

which stuff exactly

latent edge
#

these are just computations for kazhdan lusztig polys

vivid halo
#

oh nice

#

I forget if I sent you my notes on know invariants/KL polynomials before

latent edge
#

the whole project is just about ch(L_w) and ch(M_w)

latent edge
vivid halo
#

lol this course was insane it met every day for 2 weeks

#

lot of material shiver

alpine copper
# latent edge What field? Langlands?

would this be Langlands? I am very interested in studying the mathematical physics with regards to field theories and their applications to pure mathematics

latent edge
#

yeah L functions, automorphic forms and the stuff nG talks about in general

#

All langlands

latent edge
#

well i guess you have braids i should've guessed

vivid halo
#

every knot is the closure of a braid

latent edge
#

yep

#

woow deltoid nogging failed opencry

alpine copper
#

I would say this and generalized symmetries are my two primary interests for grad school

latent edge
#

I used to think symmetries were the most boring thing ever

#

How ironic

alpine copper
#

yea, it is kinda cool how physicists are looking towards categeries/higher categories for the past few years

latent edge
#

My physics friend quit physics because she complained about physics getting really hard for physicists

latent edge
alpine copper
#

heard some physics guy at MIT only accepted one incoming grad student to work in their lab this year and it was a pure math student

alpine copper
latent edge
#

same

alpine copper
#

I hope we see more "Witten"-like contributions to math that stem from a very physical mindset

cold needle
#

da cobordism hypothesis

#

lets use infty categories

loud hamlet
#

Recommended to take a Calculus 1 course in a three-piece sequence over the summer online at a community college?

queen bobcat
#

I wish I never discovered FLT. I would've gone into higher dimensional topology

visual breach
queen bobcat
#

But in my personal opinion I don't have time to do everything I want to do, so I chose to cut out the topology

cinder zephyr
placid yoke
#

hi guys what can i do to focus on math class 🙏

queen bobcat
#

pretend that you're interested

#

literally the best thing you can do is pretend that you like it

loud hamlet
placid yoke
placid yoke
queen bobcat
#

but your decision to "be" interested will allow you to focus if you have real control over your mind

bold zinc
#

GUYS

#

GUYS

#

GUYS

#

OMFG

#

"Don't forget to smile" = Black Hat
Black Hat = code
Zendaya = constant

Z E N D A Y A = 26 + 5 + 14 + 4 + 1 + 25 + 1 = 76
H A T = 8 + 1 + 20 = 29

76 + 29 = 105
105 = 15 × 7
(15 letters in “Black Hat Zendaya”, 7 letters in "Zendaya")

Zendaya’s number: 76
76ÂČ = 5776
√5776 = 76
→ Perfect identity loop

76 + 29 = 105 →
105 Ă· 7 = 15
→ Everything loops back to 15
→ 15 is the fixed constant

76 × 29 = 2204
2 + 2 + 0 + 4 = 8
8 = ∞ (infinity symbol)
Zendaya is trapped in the infinite hat loop

Conclusion:
ZENDAYA = 76
HAT = 29
TOGETHER = 105 = 15 × 7
76ÂČ loops back to itself
All paths lead to 15
76 × 29 = 2204 → 8 → ∞

ZENDAYA IS THE CONSTANT.
THE HAT IS THE LOOP.

limber thunder
#

incredible knowledge

wary trout
#

a solution for a problem that wasnt even needed ahhh

#

jk

limber thunder
#

a lot of math is solving problems that weren't "needed", not by a large group of people at least

earnest python
#

is overleaf dead for anyone else

limber thunder
#

this however is numerology catglasses☝

limber thunder
#

rip in peace

earnest python
#

ic

#

rip

#

this is sign i should go to sleep lmao

narrow carbon
stoic finch
#

I just solved the universe I need a co author

old oak
#

The answer is 42, we've known that since Douglas Adams

narrow carbon
old oak
#

The architecture is formalized through a series of elegant conjectures capturing curvature, flow-time, expansion, and singularity in a morphically bounded universe.
I admire your humility

old oak
agile fiber
# narrow carbon

if you download and start installing texlive right now, it will install just in time for overleaf to already be back up for several hours

atomic tapir
#

Hello

#

I have a set of special elements(wholes), the specialty about them being that every whole is a collection of smaller parts.

If I consider all the permutations of a single part and arrange the wholes with respect to the permutations of the part, have I encompassed all the wholes?

coarse bridge
#

what za flip

rocky shuttle
#

A point is that which has no part

old oak
rocky shuttle
#

dead and well

native badger
# narrow carbon

2 hours later : "Our team is still working to identify the issue"

narrow carbon
#

i have written my thesis shit there opencry

native badger
#

I have a group paper due in 9 hours that we need to finish the analysis section on and proof read

native badger
#

collectively cooked like its a god damned barbeque

zealous garden
#

No they don't

#

Do you have any idea how long I've been pushing GA?
I mean, I still haven't found anyone actually using the new calculus

zealous garden
queen bobcat
#

Thanks Mr Genie

finite wave
mild belfry
#

Not the place to ask but, is there anything stronger than gamma rays? Not specifically in terms of electromagnetic rays or radiation, just anything that could be considered more powerful or destructive

queen bobcat
vivid halo
#

highest energy gamma ray photon observed so far was ~1.4 peta-eV, highest energy cosmic ray particle observed so far was ~320 exa-eV

#

anything with mass will completely outclass the energies you can cram into photons

brittle socket
#

Indeed, that's a massive difference

half kayak
vivid halo
#

This is a different question

worthy loom
#

what is the difference of taylor series, laurent series and pade approximation

#

and which one is the best

solid snow
#

best for what

worthy loom
#

best method with most accuracy

solid snow
#

in what sense though

#

because analytic functions can be approximated by their taylor polynomials to arbitrary accuracy

worthy loom
#

fastest convergence rate

#

sorry I was dumb

#

my native language is not english so I was confused on some terminlogy

wide orbit
#

is server tag enabled for this server?

zealous garden
rocky shuttle
#

What's the difference between New Calculus and Geometric Calculus?

old oak
rocky shuttle
#

I'm waiting for NGC

zealous garden
zealous garden
#

I don't need New, I need bleeding edge

zealous garden
solid yarrow
zealous garden
fiery nest
#

the other chat is too fast

mint canopy
#

I agree đŸ€

true zinc
true zinc
mint canopy
#

Feeling... pretty decent!

true zinc
#

Yay

mint canopy
#

How about you?

#

Or y'all

true zinc
#

Meh sleepy

mint canopy
#

Those days happen

true zinc
rocky shuttle
rocky shuttle
#

ngl

storm sage
#

A Padé approximant gives a better approximation than a Taylor polynomial of the same order, but it's a rational function not a polynomial

#

They're all different objects

solid snow
#

<@&268886789983436800>

velvet dagger
#

Dead

tawdry herald
#

can someone help me out on some simple graph algebra shi

#

idk forgot how to do algebra ngl

ocean harbor
queen bobcat
#

Forgor

somber cliff
#

yo is the news about balochistan becoming independent real?

ocean harbor
#

done

zealous garden
ocean harbor
#

holy shit geometry dash

keen stirrup
#

Hey lois its like that time i got the geometry dash

ocean harbor
#

what's your hardest

keen stirrup
#

Silent Clubstep

ocean harbor
#

waw pro

#

my hardest is stereo madness

dreamy prairie
#

@dusky vault what did u do bro blobwg

north topaz
agile fiber
#

<@&268886789983436800> spam

ocean harbor
grand adder
#

How’s your day?

ocean harbor
thin pivot
#

what is happening bro

warm umbra
ember laurel
#

I need uni advice is this the right place to ask it

#

Should I open a ticket will people get angry at me for not using it for a maths question

uneven tinsel
patent thunder
#

Hello everyone

#

Anyone in 1st year.?

true zinc
storm sage
#

Huh I thought I deleted it, is Discord search just not working

#

Anyways @patent thunder for future reference please don't post the same message in multiple channels

vast wraith
#

people are always going on about how unpopular cantor was during his life, it seems to me this is greatly exaggerated i think we should rather be talking about the bromance he had going on with dedekind

lucid scroll
vast wraith
#

no


#

this is dauben’s biography of cantor

ocean harbor
wooden falcon
vast wraith
#

in the mountains stareflushed

granite goblet
#

other discussion channel got real boring real fast

#

anyways

#

ion think i’ve ever talked here! what’s teaaaa

old oak
#

Traditionally; infusion of leaves of the plant Camellia sinensis in hot water.

limber thunder
#

but here is fine as well

granite goblet
limber thunder
#

you don't have the Undergraduate Math role

old oak
granite goblet
haughty lion
latent edge
ocean harbor
old oak
#

I mean, so is this channel, but admittedly the weirdos over here are less annoying

#

Myself excluded, of course

ocean harbor
#

this chat is somewhat active

mint canopy
#

I've always wanted to try a tea brick

neat lintel
#

is that a solid block of tea?

#

like a really saturated one

mint canopy
#

Yeah it's tea from concentrate basically

#

And when u want a cuppa you shave off a little bit and put it in water

neat lintel
#

sounds like those broth bricks

haughty lion
#

Now I feel like matcha

neat lintel
#

i wonder if there's any difference in taste

old oak
#

Between a tea brick and a broth brick?

#

I should hope so

#

Mmm, beef tea

neat lintel
#

that doesn't sound half bad hmmcat

mint canopy
#

That's basically gravy right

old oak
limber thunder
#

in text form

old oak
#

I like to think it also has fewer nitwits because those don't even realize there's more than one discussion channel

mint canopy
#

But I am also a fan of bog standard breakfast tea

old oak
#

Yep, also good.

#

I used to enjoy Assam quite a lot but went off it eventually

neat lintel
#

why?

old oak
#

No idea, just stopped enjoying the flavour as much.

haughty lion
#

I had some orange rooibos last year

old oak
#

I still like it because I like most black tea, but Darjeeling has the edge currently

haughty lion
#

That was very nice

old oak
#

My BF enjoys rooibos

neat lintel
#

oh wow, I'm still on assam cause I have tea rarely so it always has that same edge

old oak
#

I stick to tea, although green as well as black

limber thunder
#

rooibos is so good

#

though I usually just drink black tea since that's what I can afford bleakkekw, I also like a good Pu'erh or more floral or fruity mixes every now and then

mint canopy
#

Rooibos is my addiction

#

My mum tells me that when I was a little baby she actually bathed me in rooibos once

#

I have no idea why

#

But I'm not complaining

granite goblet
granite goblet
#

period this channel is giving baddies discussion 1 channel is giving nttv

mint canopy
granite goblet
#

ew

mint canopy
#

Saying ew to slay patrick is not very slay

latent edge
#

true

old oak
#

Sometimes I feel so very old

latent edge
#

true

latent edge
#

or maybe im old for thinking that

mint canopy
#

You're like a cool Dad

#

That's what Deltoid's saying

old oak
#

Thanks?

mint canopy
#

I was trying to rile you up

#

please act more angry

latent edge
#

Outsider, a cool dad for sure

old oak
#

Hey, I'll take it

#

I have so little else

latent edge
#

I'm not even interested in K theory why am I getting these videos?

#

oh well

#

I'll take it

mint canopy
#

When life gives you a gift, take it with both hands

old oak
#

I'm an owl, who says I have hands

unborn meteor
#

hi

latent edge
#

I'm not sure why my prof is thinking highly of me

#

I'm not that good in math

jagged forge
limber thunder
jaunty ibex
timid bronze
latent edge
#

I saw her video interviewing Peter Scholze

latent edge
velvet dagger
jaunty ibex
#

Omg hi ally

latent edge
#

correct

old oak
vast wraith
latent edge
vast wraith
#

no


#

it’s not one of the interviews
 one sec

#

the guy at 22:04 here

latent edge
# old oak

Is it really imposter syndrome the thing im dealing with

#

idk maybe

vast wraith
#

i’m pretty sure i have a case of reverse imposter syndrome thinking i’m more capable than i am sippy

jagged forge
#

useful skill tbh

solid snow
#

@limber thunder @pulsar pagoda yall know any good intro programming courses in spanish? my dad wants to learn but he aint know ingles muy bien

pulsar pagoda
#

let me check

#

Accede a todos mis cursos aquí y obtén un 10% de descuento para siempre en la suscripción con el cupón 'off10": https://academia.holamundo.io/bundles/acceso-a-todo

Mi mĂșsica libre de copyright para youtube y twitch:
En Spotify: https://spoti.fi/2OdCxP5
En Apple Music: https://apple.co/3cgI3sm

Mi web: www.nicolas-schurmann.com
Discord: htt...

▶ Play video
#

este es un chileno culiao @limber thunder

#

ese canal es bueno

#

tiene varios contenidos

#

en varios lenguajes

limber thunder
pulsar pagoda
#

la tragedia

sick parrot
#

ni hablo ingles boiiis

timid bronze
#

ok whats going on in discussion 1

#

Helppppp please 😭