#serious-discussion
1 messages · Page 226 of 1
cherish those moments
OH I WONT
i will cherish, 3 years ago
well no, 4 years
5
5 is nice.
i was 12
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
well no its bad, 6
it will get better
one day.
The future looks bright for us my friend
Lets do right with ourselves and keep working to be better nonetheless
will i survive till then, thats the question
they all want to survive
none do
all i have left is my head
we have the https://discord.com/channels/268882317391429632/1213610885277421588 thread where you can discuss code and tech
tks
I don't remember this server having a similar channel before
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
i think we will grow to be good friends
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.
How to represent the fact that k is a non-zero real number using set-theoretic notation?
$k \in \bR \land k \neq 0$
magma
if you donât have \neq, just replace it with \neg(k = 0)
or just $k \in \Bbb R \setminus {0}$
sheddow
what's a good website/tool for making flowcharts? I need to draw a few state diagrams of Turing machines for my CS class
i dont understand extended euclidean can someone explainn it
if u don't want latex/typst, then try https://draw.io
@storm sage 
Am I doing something wrong or is it very clumsy to work with
Feels like using microsoft word's Add Shape
you need turing machines or like DFAs / NFAs?
for DFAs / NFAs this exists: https://madebyevan.com/fsm/
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
yall. what can i get for a "gas and leo" in bloz fruits
yall who play fortnite im bored
!noadvert
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.
Sorry
huh?
????? why did you ping me
cause stirner
that's all
sorry to bother you I guess
it was for comedic value
have you seen this video https://www.youtube.com/watch?v=XcPHG-ro3VA
We're screwed.
Support Non-Compete:
https://www.patreon.com/noncompete
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I thought you would find the emote funny đ
I'm struggling with studying for my maths exam tomorrow
@deep mortar welcome to mathcord, and good luck with the exam 
How come you pinged them?
That's it, we're done

@fresh comet


funny portrayal of max stirner
most of his lines in the video are actual quotes from The Unique and its Property
lol
Good luck
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)
@blazing pawn Have you heard Luxury and 212 Remix?
no ive only heard the nicki/azealia competition/luxury mash up
This is literally a big bop tho
fr
I hope I could leave this homophobic countryđ @blazing pawn
I wanna wear fashionable clothesđ đ đ
And try customising my own too hehe
And go around with a boombox, prob playing 212 đ€Ł
welcome to the server @ancient fjord
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.
Why
Why what?
Why made query and for what
To find out information
It's work related, so I'm not going to share too much
I understand
Also notice this
Your name yellow ur star blue
My name blue my star yellow
It's a diamond
O
But I do see your point
i finally solved the 3b1b chessboard coins thingy problem after some years of seeing the problem but not the solution
(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.
@warm umbra heyyy
Howâd your AP exam go?
Chat should I bulk or cut 5 kiloâs? Cause the heavy-weight tournament is soon so Iâm gonna maintain my weight for that; but after that I wanna decide whether i should partake in the light-heavyweight or super-heavyweight tournament
Mine went great
I think you should study real analysis instead
certified hood classic
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
@clever knot God I hate salesmen
They donât have time for anything not related to money
Yeah, it's a bleak existence
How do you compute the function field of a given domain?
Pretty easy
Oi Oi Oi
What do you mean?
The conclusion of this post is so funny
life is good after quitting cs 
Said everyone who left cs for anything else
I have my reasons 
my classmates and profs i had in semester was literally replaced with ai
and about the group project, it was horrible
im done
Glad you survived that insanity
i sure did
Oh
Hi everyone!
I'm looking into study of projective geometry but I can barely find any good tutorial books about that
how's it going?
sounds like you want book recommendations
Not bad, wbu?
đ
quit gd
it a bad game
2.1 better than 2.2 đ„
game died after 2.2
you mean the game has gotten laggy and new top #1 is coming soon
also robtop account got banned on discord
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
no not the lava drinker
This is peak
hello
me trying to get out of bed only to be spooked by life
The answer is ||a really lazy and unoriginal trolling attempt||
=1x5
15
then just donât play new levels⊠lol
I mean the game overall
feel ickier
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
we all waited for 7 years and in the end we got 
my gpa is 1.2/6.0
are you a business major
me too
me three
My GPA is 0
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.
Not possible
Business major is perfect gpa as long as you do your crayon coloring homework
To be fair, they have farrrrr better social skills than the math majors
I used to take pride in being social inept before entering the labor force
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
take this back right now
come
đđđ
That is
Kinda relatable
I mean im still in y10 but i do business
it happened to me #serious-discussion message
it was a traumatic experience
it is actual school though
lmfao
Hm
Iâll 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
lmfao this is insane
never thought of referring to them as calculi plural
peak pretentious goober
Calculussesses
Seventeen Calculi
Speaking french?
newton ahh terminology
bonjour
What kind of Endomorphisms are you
someone help me
#âhow-to-get-help if math
i fumbled articuno any help?
I've a study group channel would anyone like to join?
@zealous garden
@zealous garden
@zealous garden
Ahh, the rare tripleping
ay chill out
We are the wraithlords, feed us!
Because she actually does hang around in physcord
<@&268886789983436800> spam ping
Just one ping is enough. Got it?
even when the person getting the pings says ping ke three times in their description
Guys think possible to get a machine learning engineer job with a degree in applied mathematics?
yes
i can be someone personal teacher at a price
no
yes absolutely, plenty of people go from applied math into corporate ML or data jobs, if you're still working toward your degree make sure you take courses related to data analysis, inferential statistics and opportunities where you can work on code implementations e.g. in electives or internships
no you have to do it for free
you can also get a fairly good grasp of theoretical ML/neural networks with a math background
an introductory, and free book is https://mml-book.github.io, another more advanced (think grad level/state-of-the-art monograph) one is https://www.cambridge.org/core/books/mathematical-aspects-of-deep-learning/8D9B41D1E9BB8CA515E93412EECC2A7E
Alright, how much will you pay me?
(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)
How come when people at my college ask for my math class (which is just beginning trigonometry) once they hear Iâm a math major, they donât feel like talking with me or rather withhold information when I ask questions about upper-division mathematics?
how can we answer this
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
2+1
Is there a Channel for computational Sorting Algorithms?
No you should ask in a CS server
Can you give me an Invite?
Oh, I cannot join that Server because my Nitro ran out and I'm beyond 100 Servers

My favourite rizz line:
y=f'(x0)(x-x0)+f(x0)
It always touches the huzz in their hearts
My ignore list is really growing quickly today
Ignoring is so generous of you
I'm a magnanimous owl
Am I in that ignore list?
Not yet
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.
cos(5pi/6) is not sqrt(3)/2
OOOH, yeah it's -sqrt(3)/2.
How would you recommend studying? I'm feeling a bit rusty after not studying for 4 days.
what is the powerhouse of the cell
midichlorians
I want to be a pure mathematician, so what should I be looking out for in colleges?
math
math
Well, duh. To be more specific, what makes certain math programs stronger than others?
if their maths is stronger
if they uh teach more too
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
Alright, thank you!
BA in mathematics?
I wish my college offered a BS in mathematics đŠ
BA vs BS doesnât matter
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...
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
âTop rateâ schools like harvard frequently only offer a âBAâ
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
Whatâs the difference?
Whatâs a BS and a BA
Oh
Art and science
does anyone know if theres a way to rotate a function by an arbitrary angle?
ive beb thinking about this for a while
as in rotating its graph?
Maybe write it as a parametric and then put it through a rotation matrix
Or something
I'd also think of smth like this
like i know you can rotate vectors ysing matrices but i dunno about rotating a function
yeah like rotating the graph
Yeah
wait maybe you could convert to polar coordinates and then add the arbitrary angle to all the x's
i think that would work
what are those servers getting advertised in some people's profile?
which people
oh you mean like guild tags
the thing beside their nick
that's a recent discord feature
I haven't read about this feature at all but https://support.discord.com/hc/en-us/articles/31444248479639-Server-Tags
Represent your server with Server Tags - 4-character identifiers that members can display proudly on their profiles, anywhere.
What this article covers:
What are Server Tags?
How to Use Server Bo...
oh thank you
np 
mathcord tag when
@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.
if you want one
Isn't that only for Nitro boosters?
no?
it's only for nitro boosted servers, but anyone can get them if they join
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 
some I remember and which are ok to explain are Ï (admins), ÎŒ (the actual perms for senior mod, allowing us to take a break by removing the color role whenever), â (people who lost very active and request access to the active VC basically), â (people blocked from posting in the advanced channels for shitposting)
I think these are the main "esoteric symbol" roles
lol
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?
He said __ping me ping me ping me Ă3 times so I pinged him 3 times đ§
Hey guys whatâs the collatz conjecture
it's the dual of the llatz njecture
No itâs 3n+1
ngrats, you answered your own question

L
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"
It is a joke
People write it in their own profiles as a joke
Because it is a funny thought
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
?
also why the moderators name changing in the members panel from time to time and not all moderators are shown there
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.
ohh
I don't want children seeing my name and DMing me about maths problems
only online moderators are shown there
Only online people are shown on the right hand side as being online, yes.
I just block people immediately when they DM me if I don't know them
thank you for information
Don't block me đ
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
I will forever maintain that blocking people is self-care
Can we compare?
Well yeah, but you spend a lot of time in #discussion , so you have unfair advantage
Most of my blocks are from other servers tho đ
my block list still totals to zero 
You might be literally a saint
this might change drastically if you were to be there
my friends list though
same here
itâs like 300 something
That's what I mean, probably about 25% of my blocks come from #discussion , and I go there like once a week
do the other 75% come from cranks in the various math channels? 
You pass my vibe check.
Advice. Avoid #chill
wow you really hate discussy that's fair enough 
Nah, I rarely block cranks, they entertain me; exceptions if they go aggressive or just repetitive.
Sometimes I open chill and it's a blank screen with like "90 blocked messages" on it.
I don't hate discussy, I just hate a lot of the discussiers
where do the blocks come from then? 
that's fair enough
A random assortment of channels, mostly the general ones.
Another sizeable contingent is the people who try to turn #calculus into a worse #discussion
what is the metric for cranks here?
I honestly only really block homophobes and children...
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
People who claim to have solved a long-standing conjecture/developed some other general breakthrough/uncovered a flaw in the foundation of mathematics.
Bonus points, and lots of them, if LLMs are involved
ChatGPT proved collatz for me...
Although LLMs usually make it easier for me to get annoyed enough to block them; I much prefer artisanal, organic crankery
Bespoke crankery đ€Ł
The LLM cranks are all made out of ticky-tacky, and they all look just the same.
I prefer those with hand drawn diagrams, on papers
I much prefer artisanal, organic crankery
this is beautiful...
I shall use my army of alts to conjure up some crankery
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
I might be able to cook some crankery provided I can do math which I apparently can't
You need a kind of delusional confidence that's very hard to fake if you actually know something.
I always assumed you couldn't.
I have an idea but itâs against the discord ToS
the correct assumption for the math part yeah
Message reported to discord
idk i think its reasonably easy to fake being a crank
maybe not elaborately but at least at a surface level
Sir sir. I have figured out how to decide any proposition in ZFC. Godelâs theorems are false! I just need a halting oracle.
Rare to see one's point proven so immediately: #serious-discussion message
is moderation paid in this server?
It should be
I donât think itâs hard. But I have enough self respect and respect for others to not make an earnest attempt and make it clear that itâs a shitpost.
Level 100 Wizard
then how to become level 100 wizard btw lol?
Become a level 99 wizard and then level up
but I already got a wizard past level 100
omg
I used to but then they did the level squish in WoW 
It's hard for pirate king to become a wizard lol
is it related to any sad past?
Not really, I enjoyed playing WoW
damn
yea
in my case the wizard in question is from wizard101 lol
mmorpgs are a stupid time and money sink but oh so much fun
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?
honorable
that's all?
He'd get banned within a week for crankery
he won't... I suppose
what's crankery?
Read anything on viXra and this is crankery; in a nutshell: nonsensical things that may look technical for an outsider
i like to imagine this server would recognize his genius like hardy did
Probably, I was being facetious
Posting weird random formulas without any elaboration might cause eyebrows to be raised, though
He truly did have divine inspiration
People would probably suspect they were LLM generated
well to an extent. But people have done weirder things. Like Iâm really autistic and I love posting random shit that I just learned or figured out
What's that person's name on M.SE that solved incredible but fabricated integrals? This may look like it at a first glance
Cleo
before society whittled that down
Right, cleo!
it was staged it seems
Of course it was; if Ramanujan were to post today, it may look like a new Cleo
well I feel like itâs different. Ramanujan started solving his own problems, and most which werenât were just standard
Cleo faked being someone else who posed the problem.
Thereâs nothing wrong with posing a problem yourself and being like, look at this cool solution I found!
what is cleo?
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? 
then who is cleo would be fit there.
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
And once you know the answer, you may have an idea on how to get there too
Yeah itâs 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
Yeah, be intellectually honest always
a woman i think
Does it matter that it's a man or woman from Armenia?
because i don't understand your statement and talking about something lol
right sorry it was an uzbek man not an armenian
cleo is actually called Vladimir
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.
Yeah some YouTuber dug into it and managed to contact the person behind Cleo
Forgot who the YouTuber is tho
omgggg cleooo exposed??
This is relatively old news but yes haha
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
@neat lintel We made it clear we do not allow surveys.
elo
he simply intuited the world of modular forms
I don't think it would matter much a priori, but since the profile description explicitly decides to emphasize it by starting with My real name is Cleo, I'm female. it becomes interesting
I haven't studied them much; I only watched an online course by Keith Conrad on the topic!
Chad
He had a crazy intuition then 
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
Modular formd are overrated
lol very false
Rogers Ramanujan is one of the coolest results
absurdly deep stuff
Yeah this result still amazes me lmao
the result that only these seven are modular makes it all the more impressive that Ramanujan discovered a few of them
I mean undeniably Ramanujan was an impressive figure but why is this result deep? It just looks like a curious question to ask about
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?
Tell them you donât feel sharing, but tbh I think its unreasonable to crucify your parents for this in this instance, they just seem like they care
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.
Thank you for responding! I appreciate your feedback.
it is secretly a theorem about classifying conformal field theories
partition functions of such field theories are mock modular, constraining the modular landscape constrains the physics landscape
I did not know of this
This is really cool
Modular forms casually dropping bangers everywhere 
yeah this is basically the story behind what Zagier and others have been studying around Nahm sums and quantum modularity
I don't care about conformal field theory
I only care about class field theory and number fields
why limit yourself to class field theory that's boring
but yes number fields are a nice thing to care about
Why not class field theory in more general cases (Langlands)
that would require caring about modular forms
right
Yeah this is why

lol

@vivid halo do you know if modular anomaly has any number theoretic explanations?
which modular anomaly specifically?
The one corresponding to the torus partition function not exhibiting modular invariance
yes but in which physical situation
the ones counting BPS indices in CY compactifications of type IIA string theory? or something else
Any one of these examples would be useful (if they answer the question)
right okay I can say something pretty general and then maybe something more specific about these examples
I should probably ask my research prof, as he said "many cond matter systems exhibit modular anomaly" but nothing more specific than that
well so first of all are you comfortable with anomalies in the first place
like what the presence of an anomaly means geometrically
In the case of conformal anomaly it has to do with curvature + central charge, right?
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
It has to do with the index of some dirac operator in general, right?
Or is that just for chiral theories
it mainly has to do with the eta invariant of such a Dirac operator
so yes morally this is an index
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)
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
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?
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
the anomaly here will mean that such a partition function fails to be SL_2(Z) invariant
Hmmm, is analytic torsion something number theoretic?
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
Ahh interesting, interesting. How do L-functions further show up?
i.e detect the existence of a global anomaly
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
Hmmm, lots of stuff I have to look up
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
My professor wanted to explore the structures behind how modular anomalies shows up, and I vaguely remember seeing this being related to L-functions, but i didn't know enough to piece it together
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
Do the special values of the L-function tell you anything about the modular anomaly?
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
wow discussion 2 is so peak
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)
This is useful, so thanks. Def a got a decent amt ahead of me
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}
I find it cool how number theorists and physicists can be interested in the same objects
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)
yep I found out the same thing as well
that's why i've been interested in VOAs and conformal theory

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
And my group isnt even high energy, they are cond matter theory đ
I find it endlessly amusing that all my insights about L-functions have come from studying physics and not from studying number theory directly
What would be the first things to look for (maybe naively so)?
Pure insanity
this thesis has probably the cleanest explanation of how to define these things and the regularization procedure involved https://theses.hal.science/tel-02965542/document
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
@latent edge 
Yes.
Thanks again
I have such a backlog of papers I need to write up about this stuff 
If you ever do a write up on this, please let me know. I'd love to take a look
same
yeah I'll let you know 
right now trying to write down some conjectures about special values of L-functions at s=1/2 in terms of Dirac operators 
These mock modular forms don't have well defined periods, right?
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
So in this case, the "L-function" doesn't have an associated series
Also, dumb question, but is there a way to canonically decompose these mock modular forms into a modular and not modular part?
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
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
relating weakly holomorphic modular forms and harmonic Maass forms
right, what you are doing is trying to complete the mock modular thing to a harmonic weak Mass thing
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
We give a classification of the Harish-Chandra modules generated by the pullback to~$\SL{2}(\RR)$ of \emph{poly}harmonic MaaĂ forms for congruence subgroups of~$\SL{2}(\ZZ)$ with exponential growth allowed at the cusps. This extends results of Bringmann--Kudla in the harmonic case. While in the harmonic setting there are nine cases, our classif...
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
Is this at all related to anomaly cancelation when defining an edge theory to a bulk one?
yeah the completion is like anomaly cancellation
Woah
you're having to add some counterterm to restore modularity
Are there any papers where these analogies are made explicit?
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
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?
What field? Langlands?
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
lol you underestimate how much slop is in physics papers
please give me physics slops
This sounds nightmarish
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
I don't think they are trivial
it only looks bad because the author chose bad notation
the notation is just bad in general
Your average combinatorics paper
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 
which stuff exactly
these are just computations for kazhdan lusztig polys
the whole project is just about ch(L_w) and ch(M_w)
that is just based now wtf
would this be Langlands? I am very interested in studying the mathematical physics with regards to field theories and their applications to pure mathematics
yeah L functions, automorphic forms and the stuff nG talks about in general
All langlands
didnt know you can use the polynomials for knots
well i guess you have braids i should've guessed

every knot is the closure of a braid
ah gotcha
I would say this and generalized symmetries are my two primary interests for grad school
That's very cool
I used to think symmetries were the most boring thing ever
How ironic

yea, it is kinda cool how physicists are looking towards categeries/higher categories for the past few years
My physics friend quit physics because she complained about physics getting really hard for physicists
I was very surprised and kinda more satisfied that I had to study a bit of physics to get a better understanding of these stuff
I feel like this reminds me of some quote about "the math that physicists have to deal with is too difficult for the physicists"
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
I am also very satisfied by the growing intimacy in these areas between pure math and physics
same
I hope we see more "Witten"-like contributions to math that stem from a very physical mindset
Recommended to take a Calculus 1 course in a three-piece sequence over the summer online at a community college?
I wish I never discovered FLT. I would've gone into higher dimensional topology
This is obvious tho
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
I think you mean excise the topology 
hi guys what can i do to focus on math class đ
pretend that you're interested
literally the best thing you can do is pretend that you like it
Then the enjoyment materializes?
I force myself to do something i hate? That's pretty difficult for me..
Is it useful?
you're not going to actually enjoy it
but your decision to "be" interested will allow you to focus if you have real control over your mind
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 Ă 7
(15 letters in âBlack Hat Zendayaâ, 7 letters in "Zendaya")
Zendayaâs number: 76
76ÂČ = 5776
â5776 = 76
â Perfect identity loop
76 + 29 = 105 â
105 Ă· 7 = 15
â Everything loops back to 15
â 15 is the fixed constant
76 Ă 29 = 2204
2 + 2 + 0 + 4 = 8
8 = â (infinity symbol)
Zendaya is trapped in the infinite hat loop
Conclusion:
ZENDAYA = 76
HAT = 29
TOGETHER = 105 = 15 Ă 7
76ÂČ loops back to itself
All paths lead to 15
76 Ă 29 = 2204 â 8 â â
ZENDAYA IS THE CONSTANT.
THE HAT IS THE LOOP.
incredible knowledge
a lot of math is solving problems that weren't "needed", not by a large group of people at least
is overleaf dead for anyone else
this however is numerology
âïž
maybe they are updating it
I just solved the universe I need a co author
The answer is 42, we've known that since Douglas Adams
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
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
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?
what za flip
A point is that which has no part
Hey Euclid, how have you been?
dead and well
2 hours later : "Our team is still working to identify the issue"
damn
i have written my thesis shit there 
I have a group paper due in 9 hours that we need to finish the analysis section on and proof read
damn
collectively cooked like its a god damned barbeque
still have time
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
I disagree
Thanks Mr Genie
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

gamma rays can vary quite a bit in energy, and are hardly the most energetic things out there
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
Indeed, that's a massive difference
Yes a nuclear bomb
Ooh, what new calculus?
Since super massive black holes have some of the most masses in the universe, do they have the most energy?
This is a different question
what is the difference of taylor series, laurent series and pade approximation
and which one is the best
best for what
best method with most accuracy
in what sense though
because analytic functions can be approximated by their taylor polynomials to arbitrary accuracy
fastest convergence rate
sorry I was dumb
my native language is not english so I was confused on some terminlogy
is server tag enabled for this server?
You don't know about the New Calculus crank? I think his name is John Gabriel
What's the difference between New Calculus and Geometric Calculus?
One is new, the other is geometric
I'm waiting for NGC
Geometric Calculus only uses slurs against matrices
Im waiting for Surreal Numbers to make it to the fundamental theorem of calculus so we can get Surreal Geometric Calculus
I don't need New, I need bleeding edge
Which means we just need someone insane enough to figure out how to handle integration over the entire Surreal Number "Line"
Still waiting for the zana dlc for analysis :3
New Geometric Evangelion
the other chat is too fast
I agree đ€
The other chat is just painful most days
How're you today
Feeling... pretty decent!
Yay
Meh sleepy
Those days happen
now it's gone to just "Bad"
zana dlc? 
A Laurent series is like a Taylor series but for a function with a singularity.
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
<@&268886789983436800>
Dead
can someone help me out on some simple graph algebra shi
idk forgot how to do algebra ngl
Forgor
yo is the news about balochistan becoming independent real?
done
Hmmmm
Nonstandard Geometric Lie (theory)
holy shit geometry dash
Hey lois its like that time i got the geometry dash
what's your hardest
Silent Clubstep
@dusky vault what did u do bro 
at least you completed it hey
<@&268886789983436800> spam
yes :D
Howâs your day?
day just started hbu
what is happening bro
dont worry i got the hooligan
My days about to end, it's 12:20am here
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

<@&268886789983436800> user spamming this in all channels
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
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

is this the book called men of mathematics
you can talk about it in here or #advanced-lounge
and they took vacations together đ
other discussion channel got real boring real fast
anyways
ion think iâve ever talked here! whatâs teaaaa
Traditionally; infusion of leaves of the plant Camellia sinensis in hot water.
soooo quirky
probably, since those are for math questions specifically
like ken said above you should have access to #advanced-lounge which among other things is fit for questions about uni/academic life
but here is fine as well
why donât i have access
you don't have the Undergraduate Math role
That is how I am often described, yes
đ„șđ„ș
I would rather describe owls as quilly
discussion 1 is horrible
discussion 1 is where you meet weirdos
I mean, so is this channel, but admittedly the weirdos over here are less annoying
Myself excluded, of course
this chat is somewhat active
I've always wanted to try a tea brick
Yeah it's tea from concentrate basically
And when u want a cuppa you shave off a little bit and put it in water
sounds like those broth bricks
Now I feel like matcha
i wonder if there's any difference in taste
that doesn't sound half bad 
I'm more of a Darjeeling person
this channel is just slower
in comparison Discussy the First feels like https://www.youtube.com/watch?v=AsdJFNaiXzs
banger multiplayer. would play again
in text form
I like to think it also has fewer nitwits because those don't even realize there's more than one discussion channel
Darjeeling is great
But I am also a fan of bog standard breakfast tea
why?
No idea, just stopped enjoying the flavour as much.
I had some orange rooibos last year
I still like it because I like most black tea, but Darjeeling has the edge currently
That was very nice
My BF enjoys rooibos
oh wow, I'm still on assam cause I have tea rarely so it always has that same edge
I stick to tea, although green as well as black
rooibos is so good
though I usually just drink black tea since that's what I can afford
, I also like a good Pu'erh or more floral or fruity mixes every now and then
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
and is
period this channel is giving baddies discussion 1 channel is giving nttv

true
Sometimes I feel so very old
true
tbf if you haven't mentioned stuff I would've still thought you were around 20's
or maybe im old for thinking that

Thanks?
Outsider, a cool dad for sure
I'm not even interested in K theory why am I getting these videos?
oh well
I'll take it
When life gives you a gift, take it with both hands
I'm an owl, who says I have hands
hi
she usually uploads vids about math academic life in general so the channel kind of reaches out to a broader audience
Bro says this and casually works with automorphic forms
@velvet dagger
That makes sense
I saw her video interviewing Peter Scholze
it's because I love automorphic forms so I dont mind how hard they are to understand
Fantastic
Omg hi ally
Deltoid is automorphic on H
correct
i was so surprised when my alg geo prof showed up in one of her videos 
plot twist: it was peter scholze
noâŠ
itâs not one of the interviews⊠one sec
I've asked my colleagues, algebraic geometers, to share with general audience their favourite examples of the beauty of math! See what happened :)
Cast:
Gabriela Guzman: https://sites.google.com/view/gguzman/about?authuser=0
Louis Hainaut: https://www.su.se/english/profiles/loha1119-1.444917
Siddharth Mathur: https://sites.google.com/view/sidma...
the guy at 22:04 here
iâm pretty sure i have a case of reverse imposter syndrome thinking iâm more capable than i am 
useful skill tbh
@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
let me check
Accede a todos mis cursos aquà 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...
este es un chileno culiao @limber thunder
ese canal es bueno
tiene varios contenidos
en varios lenguajes

la tragedia
ni hablo ingles boiiis

đŹ


