The h Bar

0celo7

00:10

@bolbteppa reed and simon vol 1 is undoubtedly useful for most non algebraic people

ACuriousMind

00:27

@skullpatrol Yugoslavian?

I don't remember any "Yugoslavian" PDE guy

0celo7

@ACuriousMind yugibb or yuggib or whatever

ACuriousMind

...why would you think yuggib was Yugoslavian?

0celo7

the name

ACuriousMind

...it's the reverse of "Big Guy" :P

0celo7

holy fuck

that explains a lot

he's big and yugoslavian

ACuriousMind

00:31

Yes. Sure :P

0celo7

@ACuriousMind I have an unusually friendly prof this semester

she made me feel like a dick for not saying hello properly

ACuriousMind

"How do you recognize an extroverted mathematician?" - "They stare at your shoes, not their own"

0celo7

the antisocial nod or half-smile isn't good enough

amazon is omniscient

I wonder if google and amazon share data

@BalarkaSen at the end of class the russian lady asked one of the students to come to her office

she kept asking him if he had questions during the lecture, he said no, and she said she didn't believe him

wonder what happened

ACuriousMind

He probably looked confused...

0celo7

@ACuriousMind he always looks confused

@ACuriousMind he literally said he had no questions, and then she went on a speech about it being an "open class" and saying we should ask questions

on the other hand, she always asks me questions when I look at my phone or do something else

ACuriousMind

00:41

Well, if someone looks at me confused, I'm going to assume he has some questions but is for some reason afraid to ask them in front of the class

@0celo7 Oh sure, that's an attempt to get you to stop looking at your phone :P

0celo7

@ACuriousMind I realize that

but I conduct important business with my phone

emailing my advisor, calling balarka a fucking topologist, etc.

memes

Balarka Sen

this Russian lady is weird

I'd send her to gulag

0celo7

she comes to class 5 minutes late and goes 10 minutes over

@BalarkaSen that's not nice

ACuriousMind

@BalarkaSen ಠ_ಠ

0celo7

@ACuriousMind are we allowed to send people to prison camps on SE

Balarka Sen

00:45

@0celo7 Solzhenitsyn disagrees with you

gulag is a v e r y n i c e place according to him

0celo7

he wrote a book saying the opposite

Balarka Sen

oh damn you're not illiterate

there goes my communist agenda

0celo7

I don't actually want that sentence attributed to me

@BalarkaSen I asked her about the regularity of something and she answered "don't worry about it, smooth enough"

the Russian sense of rigor is confusing

ACuriousMind

@0celo7 Ah, a physicist!

0celo7

@ACuriousMind definitely not

I gave her shit about not telling us what $L^2([0,T];\mathscr S)$ is supposed to be

so she just changed it to "smooth enough"

Balarka Sen

00:50

rekt

0celo7

meaning $C^0([0,T];\mathscr S)$

Balarka Sen

Supa hot fire ohhhhhhh!!!!

►

0celo7

the spaces used in hyperbolic PDE are cancer

Balarka Sen

I can believe that

0celo7

there's a book on vector valued measure theory I could read if I cared enough

one can allegedly do integration with values in any locally convex TVS

Balarka Sen

00:55

new racist video by pewdiepie

0celo7

is this one actually racist for once

Balarka Sen

no lol

but its about Indians

0celo7

I would say something but I might get banned

Balarka Sen

hahah

0celo7

link?

Balarka Sen

00:56

just go to his channel. first one uploaded

0celo7

hahaaaaaaaaaaaaaaaaaaaaaa

i luv bobs

@BalarkaSen are these indians trolling

has to be, right?

Balarka Sen

I can only hope

0celo7

well you're around these people

Balarka Sen

yes, thence the fear that it's prolly false hope

0celo7

@BalarkaSen these people will one day control your country's nukes

Balarka Sen

01:03

they already are...

this video gets better as it progresses

0celo7

@BalarkaSen some of these are fakes, or at least the pictures have been reused for multiple memes

"straighter than the pole your mom dances on" ok that's p. good

Balarka Sen

right?

0celo7

blood or milk

:D

Balarka Sen

so good

the economics dude tho

0celo7

he's doing it for the waman

ACuriousMind

01:13

Do I want to know what this is about?

Balarka Sen

Sure, it's basically the #1 youtuber reading out some r/indianpeoplefacebook stuff aloud

0celo7

wonder what multilinear harmonic analysis is

amazon seems to think I need a book on it

Balarka Sen

My copy of Milnor arrived a few days ago

Hopefully I'll get time to read it

0celo7

@BalarkaSen does the top of it look shitty

the top edge?

Balarka Sen

nope

ACuriousMind

01:15

@BalarkaSen That sounds wild.

Balarka Sen

@ACuriousMind It's funny to me, but I can't understand if it's unfunny for non-Indian people (in the same way the ugandan knuckles meme is unfunny to me, perhaps)

Fawad

> The mean time between collisions is temperature dependent

0celo7

mine has this damn black stripe across the top i.gyazo.com/695bc2362f9f0e945c8c5d94bb214add.jpg

Fawad

How?

Balarka Sen

That is strange @0celo7

ACuriousMind

01:18

@BalarkaSen Oh, I find some of the stuff funny alright, I'm just not sure why I'd prefer a video reading them out to me instead of just browsing it :P

0celo7

you find indian memes funny?

what about the one where balarka goes a month without bathing

2

Fawad

Seems everyone watched pewds new video

ACuriousMind

@0celo7 That was a meme?

Balarka Sen

@ACuriousMind It's just some handpicked ones

0celo7

in the discord h bar it is

Balarka Sen

01:19

i thought that was dead

did you guys revive it again

0celo7

two of us did

it's worse than ever

Balarka Sen

jesus

0celo7

it's basically just linear algebra and memes

ACuriousMind

@BalarkaSen Eh.

0celo7

and PUBG of course

@BalarkaSen actually I take it back

you never saw the NSFW h bar

Balarka Sen

01:20

yeah i didnt

Fawad

Help me finding equation for time between collision in gases

> The mean time between collisions is temperature dependent

0celo7

@loocsieulb look at discord

loocsieulb

looked

0celo7

@loocsieulb I am reviving the discord server

trying to come up with a clever name

Fawad

@JohnRennie help me when you come.

ACuriousMind

01:28

Well, I realize y'all are just gonna think I'm a big spoilsport again, but just let me say that e.g. the content of that video is not exactly the stuff we'd like to see discussed here - it has a rather real potential to turn off newcomers. Don't make this into a 'bobs and vegana' chat.

0celo7

lol

Balarka Sen

@ACuriousMind That's why I didn't want to link it here

loocsieulb

content of what video

Balarka Sen

scroll up

ACuriousMind

@BalarkaSen Thanks for that, but there were still quotes and the discussion took a considerable amount of screen space - just better don't bring it up in the first place. This is really rather mild but I don't know how to say it without sounding so terribly earnest.

Balarka Sen

01:32

Fair enough

0celo7

ACM is so strict

Balarka Sen

Let's talk about ACM memes instead

0celo7

acm is a meme too

ACuriousMind

@0celo7 That's possibly the most ambiguous compliment I have ever received :P

0celo7

you take that as a compliment?

not saying it wasn't meant as one

I guess it is ambiguous, but what is an ambiguous compliment?

I'm confused

ACuriousMind

01:36

I was giving you the benefit of the doubt...

loocsieulb

is acm born in '95?

0celo7

he's 24

ACuriousMind

@loocsieulb No, I'm older

0celo7

@ACuriousMind in all seriousness, most mathematicians I know are very nice and sociable people

loocsieulb

i was gonna say tfw ur birthdate is the same as your shift

0celo7

01:38

I know one who is not social and it's kind of awkward because he does like looking at shoes

loocsieulb

acm memes shrug

0celo7

but is very friendly

loocsieulb

'95 ---> nine-ty five ---> nine to five ---> 9 - 5

Balarka Sen

I am neither a nice nor a sociable people

loocsieulb

= acm

0celo7

01:38

@BalarkaSen you don't wash

Balarka Sen

Yes

Proudly so

ACuriousMind

@0celo7 Consider that there's a selection bias in that you tend to not get to know people who are not sociable

Balarka Sen

cavemen didn't wash themselves

ACuriousMind

(That goes for everyone, not just mathematicians :P )

Balarka Sen

capitalism has taught us how to bathe

loocsieulb

01:40

i wash my hair every 5 days

0celo7

can one die from an eye roll?

loocsieulb

gonna make it 7 once i dye it blue

0celo7

can the eyes get stuck?

@ACuriousMind well I consider them to be more friendly than the engineering professors

and certainly not as stuck up as the physicists

Balarka Sen

@loocsieulb way too much water

0celo7

@ACuriousMind that might also just be department culture

Balarka Sen

01:42

kids in Atlantis could survive drinking that much water

shame on you

0celo7

the engineering departments seem pretty toxic

loocsieulb

@BalarkaSen i don't let it go down the drain my dude i savour it and then use it for drinking later in the day

ACuriousMind

@0celo7 that's certainly a large part of it

0celo7

"some people distrust logic, regarding it as a tool of oppression"

you're damn right axiom of choice is oppression

ACuriousMind

All hail Banach-Tarski

Balarka Sen

01:46

axiom of choice is strange

but ill take it

0celo7

axiom of choice has to be real

but well ordering is false

therefore ZFC is inconsistent

ACuriousMind

...and no one can tell about Zorn's lemma :)

0celo7

but we use it anyway like a bunch of fools

I can't even remember the statement of zorn except for when I have a partial order I wave my hands, say Zorn, and get some shit

ACuriousMind

If every chain in a partial order has an upper bound, then there is a maximal element

Balarka Sen

if every totally ordered subset has a maximal element the poset has a maximal element

F

ACuriousMind

01:48

Not hard to remember, but hard to get a feeling for

0celo7

I was joking

yeesh

ACuriousMind

Never joke about Zorn

bolbteppa

Zorn = if a functional is bounded on a subspace, it's bounded on the whole space runs

ACuriousMind

I still find it oddly appropriate that Zorn means "rage" in German

bolbteppa

I have rage for Hahn-Banach right now

Balarka Sen

01:50

Zorn has a lot of applications

0celo7

zorn is used in geometric measure theory, functional analysis, and PDE

damn thing is impossible to avoid

Balarka Sen

in commutative algebra too

0celo7

no one cares about that

Balarka Sen

ears droop

0celo7

PDE seminar is during my philosophy class

what the heck

"Fractional Laplacian Schrodinger equations"

Balarka Sen

01:54

"In this sense, we see how Zorn's lemma can be seen as a powerful tool, especially in the sense of unified mathematics[clarification needed]."

0celo7

@BalarkaSen sorry it just seems like commutative algebra has no worthwhile applications

Balarka Sen

Damn right you need to clarify that you pretentious bag of crap

0celo7

and studying it for itself seems silly

Balarka Sen

commutative algebra is an essential tool in algebraic geometry

meaningless algebra but impossible to avoid

0celo7

polynomials are so 1700

Balarka Sen

01:55

no one cares about polynomials

they care about Grothendieck topoi

0celo7

meme

Balarka Sen

the are #realmath

0celo7

I have no feeling for how advanced that stuff is tbh

it looks like random shit

Balarka Sen

A category C is a Grothendieck topoi if there is a small category D and an inclusion C ↪ Presh(D) that admits a finite-limit-preserving left adjoint.

bolbteppa

You can't really read too much algebraic geometry without commutative algebra which is absolutely horrible

Balarka Sen

01:59

It's not too terrible if you have background in classical algebraic geometry and some topological things

I interpret most of commutative algebra in terms of pictures

bolbteppa

I'd like to be able to do that

Balarka Sen

The ones I cannot I declare as worthless

0celo7

See, to an algebraist that might be like what a sobolev space is to me

I just have no idea

Balarka Sen

until they prove their worth

@0celo7 You know what a Grothendieck topology is

0celo7

I do?

Balarka Sen

02:01

It's not even a topology

It's a category with some properties lmao

bolbteppa

I can't even remember what a flat module is, but apparently this is just basic linear algebra if you believe Bourbaki

Balarka Sen

aren't those the modules s.t. tensor product is an exact functor with them?

preserves exact sequences

0celo7

why should I care about any of this crap

Balarka Sen

i only ever cared about projective modules which are flat

bolbteppa

I just keep asking why why why why in algebra about everything and the turtles shells get bigger on the way down and the answers less childish and I give up, but find answers slowly over time

Balarka Sen

02:03

@0celo7 If $X$ is compact Hausdorff vector bundles on $X$ are in 1-1 correspondence with projective $C(X)$-modules

Is that reason enough?

bolbteppa

Bourbaki sets this up as part of analyzing Hom(E;F) over exact sequences, why you want to do this is another question

Balarka Sen

the key is to stop reading bourbaki

bolbteppa

Projective modules is the brother of a flat module in some sense and more of these problems

Balarka Sen

That's the Serre Swan theorem btw

I should have added "finitely generated" before projective

bolbteppa

An A-module is projective if for every exact sequence $F' \to F \to F''$ of A-linear mappings the sequence $Hom(P;F') \to Hom(P;F) \to Hom(P;F'')$ is exact, I mean my god what is this

Balarka Sen

02:06

um yeah fuck that definition

that has no content to it

a better definition is the classical lifting definition tbh'

bolbteppa

Hmm

Balarka Sen

M is projective if for every surjective module morphism f : N --> N' any map M --> N' lifts to a map M --> N

0celo7

@BalarkaSen nope

Balarka Sen

Still not super illuminating, but at least something

bolbteppa

How can the domain determine whether some linear map into some $N'$ also maps into some other $N$

Lets see why they even want to map $\mathrm{Hom}(E;F)$ to some $\mathrm{Hom}(E';F')$

Balarka Sen

02:10

@0celo7 a module is like a vector bundle with varying fiber, a projective module is a vector bundle with constant rank fiber i.e. a normal person's vector bundle

thats all

i am sure the definition i gave is equivalent to the one you wrote

@bolb

bolbteppa

Yeah there are like 3 ways to view these things iirc

Balarka Sen

ok its way too late

i need sleep

bye all

bolbteppa

Hmm, so lets say you have linear maps $u : E ' \to E$, $v : F \to F'$ over $A$-modules $E,E',F,F'$, then a map $f$ in the set $\mathrm{Hom}(E;F)$ of linear mappings from $E$ to $F$ can be associated with $v \circ f \circ u \in \mathrm{Hom}(E';F')$ setting up the mapping $\mathrm{Hom}(E;F) \to \mathrm{Hom}(E';F')$. I guess some of this is just 'change of variables' or something expanded into concepts

0celo7

05:03

@Semiclassical could be interesting but the price is insulting global.oup.com/academic/product/…

Semiclassical

05:48

jeeze

table of contents here: gbv.de/dms/ilmenau/toc/244497915.PDF

Can't say it really excites me.

0celo7

06:13

@Semiclassical it’s very analytic for sure

The average physicist would take N to infinity and be happy

Semiclassical

ehhh

They'd be happy to not worry about how one justifies the limit, at any rate

But one of the calculations I worked on was where, for finite N, the leading behavior was $E_N=N\overline{E}+E_0+\text{other stuff}$

where the last bit vanishes as $N\to\infty$. But while the first term was easy to compute and the second had some interesting stuff, it was the behavior of the remainder term which was our main interest

So it's hardly out of the realm of possibility for a physicist to be interested in finite-size effects like that.

Bernardo Meurer

06:44

@BalarkaSen Almost deleted my entire music library

Accidentally

Balarka Sen

oof

Bernardo Meurer

Yeah

My knowledge of Linux never came so in hand

I literally read the raw filesystem, piped to a decompressor, a file checker, a stream verifier and a recompressor

I felt like God for a moment

Captain Bohemian

@BalarkaSen haven't you gone to bed? I saw you said you was going to sleep.

Balarka Sen

I woke up a few minutes ago

Bernardo Meurer

@CaptainBohemian He always responds to me

Our love is strong like that

@BalarkaSen I got this album from the lagoon santa

And it's fuckign amazing

Like I can't even

It's so damn good

And it's rare too, the motherfucker isn't on Spotify even

Balarka Sen

06:50

lol

Bernardo Meurer

I'm not even joking, the album is amazing

It's him in a quartet

Quarteto Novo

Quarteto Novo was a group formed in São Paulo, Brazil in 1966 which released one landmark instrumental album and launched the careers of some of the band's members. The eponymous 1967 album has been influential in jazz and pop music. Originally named Trio Novo, the group consisted of Theo de Barros (bass and guitar); Heraldo do Monte (Viola caipira and guitar) and Airto Moreira (percussion). The group was created to accompany singer/songwriter Geraldo Vandré in concert and on recordings. With the arrival of flutist Hermeto Pascoal, the group was renamed Quarteto Novo. In 1967 the group recorded...

ACuriousMind

07:52

@BalarkaSen the slogan I always heard was: projective is as free as we can hope for

Balarka Sen

@ACuriousMind Right, basically a free module is the trivial vector bundle.

That projective modules are factors of free module under direct sum is saying that every vector bundle is stably trivial

ACuriousMind

Maybe? I'm not sure I get the bundle analogy

To me a bundle is something "locally trivial" (a product) but I don't see that in the module

Secret

0

Q: Topic challenge: alien geometry

I propose an alien-geometry topic challenge. Its often hard to tweak the mathematics of a world (for example, you can't really make 2+2=5 in a reasonable way), but one way you can is by tweaking the geometry. This can lead to many interesting implications, including chemical, biological, and eve...

not weird enough

Balarka Sen

Aha, the analogy is that if M is a projective R-module, M_p is a free R_p-module where R_p is the localization of R at the prime ideal p, @ACuriousMind

Or at least I think that's true

Yup, googled it. Finitely generated projective modules over local rings are free

ACuriousMind

Oh right

I like the analogy now :D

Balarka Sen

07:58

heheh

I think there's an explicit dictionary. Serre-Swan theorem says if $X$ is a compact Hausdorff space the category of vector bundles over $X$ and the category of f.g. projective $C(X)$-modules are isomorphic

Algebraists have always made a living out of abstractizing geometry, and so did Quillen and Suslin: The proved every f.g. projective module over polynomial algebras is free. This is analogous to saying every vector bundle over $\Bbb R^n$ is trivial

(That's Quillen's Fields medal work)

bolbteppa

08:26

Six hours in, and maybe a very basic understanding of where projective and injective modules really come from, maybe...

Algebra is awful but when you get even a basic thing it's worth it

John Doe

@Mithrandir24601 Hi how are things going your side?

@ACuriousMind Let me know if you have had a chance to check out the post. Sorry to bother.

Slereah

08:48

John Dvorak

131 2 7

estimation order-of-magnitude visible-light vision

His profile includes a quote of himself

Balarka Sen

Lmao

Truly a legend

Mithrandir24601

@JohnDoe ni hao! Very good :) Thanks

John Doe

@Mithrandir24601 Are you still involved in quantum measurement theory research?

Mithrandir24601

@JohnDoe not exactly, no - I'm doing something not entirely unrelated, but it's not measurements

(along the lines of PT-symmetry and open systems)

John Doe

@Mithrandir24601 Oh okay and how's the PhD going?

Mithrandir24601

08:55

@JohnDoe quite a lot of work and nothing ever works or happens as I'd like it to :P but still very enjoyable :)

John Doe

@Mithrandir24601 Are you famaliar with Kraus operators and the completeness condition required to be a Kraus operator?

Mithrandir24601

@JohnDoe yeah

John Doe

@Mithrandir24601 I want to define Kraus operators which has a normal distribution. So it projects with a normal type distribution on a finite number of states. I defined it as in this post. If you have a chance please see if you agree that it defines a valid Kraus operator for the system.

Mithrandir24601

@JohnDoe At first glance, it looks like a PVM, in which case, it would be a valid set of Kraus operators

John Doe

09:18

@Mithrandir24601 Thanks for checking. The actual problem I have is that there are only a finite number of states $\{ |x \rangle \}_{x}$ yet the index $C$ is continuous and unbounded, so for some $C$ (the mean), the peak of $Pr(x|C)$ will be well outside the range of any $|x \rangle$. Do you see what I mean? This might not be a problem, I'm not sure.

Mithrandir24601

09:42

@JohnDoe I think you're thinking of this the wrong way round - each $\lvert x\rangle$ doesn't have any sort of range - it's a projection stating that 'I have measured the system and I believe it was measured to be in the state $\lvert x\rangle$' - uncertainties can only be found from this by multiple measurements

(you have obviously generalised the 'discrete' Kraus operators to 'continuous' Kraus operators, but I'll assume that's fine :P)

John Doe

@Mithrandir24601 Yeah 'range' is probaby the wrong word to use informally for mathematical discussions. And yes to the discrete Kraus operators to continuous Kraus operators as well. Have you experience in experimentally using these general quantum measurements in any way?

Mithrandir24601

@JohnDoe yeah - I've looked at them to model things like gate dependent noise, derive the Lindblad formalism and am currently looking at them in the context of PT-symmetry...

I mean, you've got an infinite number of Kraus operators is essentially what you're saying...

John Doe

@Mithrandir24601 Yes an uncountably infinite amount, that's part of what I want to confirm is okay.

Mithrandir24601

"so for some C (the mean)" - this is where the issue appears to come in - C is actually the thing that's varying, while there's a discrete set of x's that are constant

John Doe

@Mithrandir24601 Yes that's right. The index $C$ of my measurement operators corresponds to the mean $C$ of the normal distributions. So $C$ varies, giving different measurement operators.

Mithrandir24601

09:55

@JohnDoe Mathematically, I don't really see the problem (assuming you're got something continuous etc.), physically though I think you're making this complicated - is there a reason that you can't just say that $\lvert x\rangle\langle x\rvert$ are the Kraus operators?

i.e. $K_x = \lvert x\rangle\langle x\rvert$

John Doe

@Mithrandir24601 For what I am doing I want the type of spread of $|x \rangle$ that you get from a normal distribution.

Mithrandir24601

@JohnDoe Can you use a measurement pointer?

John Doe

@Mithrandir24601 Yeah the theory I am studying uses probe states, which I assume are the same thing as pointer states.

@Mithrandir24601 Are you famaliar with the book. I think I discussed some stuff with you in this book a long time ago. But anyway he uses probe states to describe general quantum measurements.

@Mithrandir24601 I'm busy reading this paper. Maybe you will find it interesting as well.

Kane

10:20

can someone tell me why more coils in a wire leads to higher induced voltage?

does having more coils allow a higher current that increases the voltage?

Anonymous

2

A: Transformers - Why more coils in second coil causes more voltage

Expanding on Jan Dvorak's comment: When you change the magnetic field inside a loop, an emf (electromotive force) will be generated. Now if you have two loops, each of these will experience the same e.m.f. When you put them in series, you have a coil with two loops, or two coils with one loop. N...

Hamilton

0

Q: Stern-Gerlach and spin-1 measurement

An unpolarized beam of spin-1 particles goes through a SG apparatus with magnetic field in direction $$\hat{\mathbf{n}}=\frac{1}{\sqrt2}\left(\hat{\mathbf{x}} + \hat{\mathbf{z}} \right).$$ We then select the emerging beam such that $$\mathbf{S}\cdot\hat{\mathbf{n}}\equiv S_n=0.$$ If we make anoth...

quantum-mechanics homework-and-exercises angular-momentum

Can you take a look?

I wanna know why my question is downvoted.

oh I said question, it ought have been answer.

John Rennie

10:37

@Hamilton Not my downvote, but that looks like a homework problem and we don't answer homework problems. I'd guess the downvoter thought you should not have answered.

Hamilton

@JohnRennie Oh sorry, I thought that they found my answer wrong.

I will be more careful next time.

Kane

@Blue thanks for that

@Blue would i be correct in saying that as we put more loops in the coil, then a given magnetic field line will travel through more coils, and each coil adds some total voltage in line with faradays law?

Anonymous

@Kane Yeah, sort of.

John Rennie

@Hamilton your answer may be wrong too :-) I only glanced at the question so I can't comment.

Kane

@Blue would it be more accurate to say that as coils are added, their respective magnetic fields are adding to give a stronger magnetic field which leads to a higher induced voltage?

Anonymous

10:53

@Kane All the loops have the same flux passing through them. So I'm not sure how you conclude magnetic fields are added

Kane

@Blue I just assume something has to be additive here. It seems multiple coils -> multiple induced voltage increase. From what I've learnt, V = IR, so an increase in V should come from an increased I (given R). But apparently in this case I doesn't change (not sure what happens to R).

Trying to understand why V increases here and it seems to be really difficult to find a simple explanation

Transcript for