Mathematics - 2022-05-09

Ted Shifrin

00:19

Now that @leslie has sullied it, I retract the rhetorical tool.

Obliv

What allows math to exist?

Akiva Weinberger

Ted Shifrin

Whatever allows you to exist.

Akiva Weinberger

Finally figured out how to do it with intervals

(The thingy from before)

On the left I have three intervals and on the right I have two, and the sum of their indicator functions is the same

(Make them shrink as they head to the right so that they are compact)

(and so that the summands on the right become only one line)

Ted Shifrin

I have no idea what you’re doing, DogAteMy.

Akiva Weinberger

00:33

That's OK

Obliv

00:43

@TedShifrin Can math/philosophy explain everything we experience though?

Akiva Weinberger

Obliv

Yeah this is more in the realm of metaphysics/philosophy I'm just gonna scurry away.

anak

01:03

@Obliv The answer is no.

leslie townes

no it isn't

anak

GET OUT OF HERE LESLIE

leslie townes

ok, but no is not the answer

anak

Tell me, leslie, what is the answer?

leslie townes

yes is the answer. no is the question

anak

01:06

yes

dc3rd

no

leslie townes

yes

dc3rd

$$no^{e^{2}}$$

Ted Shifrin

puts everyone on ignore

leslie townes

ted: yes

Akiva Weinberger

01:12

This is somewhat difficult to draw

Imagine the diagram shrinks to a point as it goes to the right, so that the two red curves in the top join up to a single curve, and the same for the two white curves

Then on the top we have $Y_1$ and $Y_2$ (the red and white curves)

and on the bottom we have $X_1$, $X_2$, and $X_3$ (the disconnected red segment, the rest of the red curve, and the white curve)

and the sum of the indicator functions of the $Y$ equal that of the $X$

and they're all homeomorphic to an interval

Akiva Weinberger

01:28

Alternate version^

anak

01:44

@TedShifrin I am trying to understand why the dual of Lie algebra of vector fields on S^1 is isomorphic to the quadratic differentials of the form $u\,d\theta\otimes d\theta$. This might not be unique to the circle, but do you have any ideas?

Maybe the quadratic differential part isn't supposed to be special...

Ted Shifrin

What’s $u$? How is that a Lie algebra?

anak

C^\infty. It's from an old Kirillov paper that I am reading.

Ted Shifrin

No clue.

Ajay

English exam in an hour.

leslie townes

ajay: huh? what did you say?

:)

anak

01:53

Ajay

I have my english final exam in 1 hour.

Ted Shifrin

Why the dual of vector fields isn’t just $1$-forms? Both bundles are trivial. Shrug.

leslie townes

ajay: what style of exam is it? what are they testing?

anak

Well that's why I am wondering if it's not just 1-forms and quadratic forms are isomorphic, too.

Ajay

This kind of stuff drive.google.com/drive/folders/…

anak

01:55

Like that it's just an isomorphism that's being brought up because it suits the needs later, rather than being something super insightful alone.

Ted Shifrin

This is too much structure for me at this hour.

anak

Can you read Russian, by the way, Ted?

Ted Shifrin

Yes, but long forgotten.

leslie townes

ajay: huh, seems like a weird mix of basic comprehension and persuasive writing.

Ajay

Its descriptive writing and persuasive writing.

Describe what you see, feel and hear in a very crowded street.

As I wandered leisurely down the street, swarms of bodies swirled around me. Stepping out of their reserved shells, exuberant adults and teenagers dressed in exquisitely crafted and snug kimonos humoured each other with high-pitched stories from work and school. Loitering young men rapidly attacked their phone screen as if determined to slay the ultimate villain at the final level in a video game. Next to the pier, young and old couples shared sphere-like lollipops while huddled together. They laughed vibrantly and unashamedly …

Ted Shifrin

01:56

I am never persuasive.

leslie townes

reminds me a little bit of portions of the LSAT [exam taken in the USA to qualify for law school].

Ajay

An example I wrote

leslie townes

you will ace it.

Ajay

i'm so stressed as this whole paper is impressionistic, it depends on the marker if they want to give you the marks.

@leslietownes I Hope

leslie townes

the trend in the US is to abolish reliance on big exams but i'm personally a fan of them. it's how i got into college and beyond. if it comes down to something more holistic, they'll find out who i am.

Ted Shifrin

02:00

Yup, crap.

Ajay

I like some exams, just because I can "celebrate my learning".

And because they have set mark schemes

leslie townes

ted: we went to the duck pond and saw not one but two forms of baby geese, and baby ducks. dinner (on me) is sushi. my daughter will yell about sashimi as usual before eating more than her fair share.

i have no idea how i would have changed careers without the LSAT and people relying on it.

Ted Shifrin

so munchkin knows the difference between sushi and sashimi? She wants to cut down on carbs?

leslie townes

yes, she's very particular.

anak

02:17

Oh, Kirillov is just using the coadjoint representation to construct the literal smooth dual.

linear_combinatori_probabi

hola, chat

anak

hola amigo

Akiva Weinberger

03:02

Is it Day of the Mother or Day of the Mothers

Apparently in Spanish both Día de la Madre and Día de las Madres are used

and in English we have arguments over where to put the apostrophe

leslie townes

03:18

the person who founded it wanted it in the singular.

i dunno. my name ends with s and i've been struggling with apostrophes all my life.

put 'em where you want 'em.

Ted Shifrin

Theyr’e where they do’nt bel’ong.

Akiva Weinberger

03:53

@leslietownes No commen't

leslie townes

pbhhbt

Xander Henderson

@TedShifrin Ow... that hurts my head.

Ted Shifrin

04:21

Go’o’d!

Rithaniel

04:34

Ah, yes, my favorite contraction: Go over there -> Go o'er dere -> Go'o de -> Go'o'd

Ted Shifrin

04:50

LOL

Koro

05:21

I had skipped this question also in my yesterday's exam math.stackexchange.com/questions/4446340/…

:(

William John

Hi how can I access trash?

porridgemathematics

05:40

hi, im trying to understand this paragraph from Jost: Riemannian geometry and geometric analysis , imgur.com/a/Pzqz83H , page 134 of the latest edition, im familiar with the definition of sobolev spaces of vector valued functions on open subsets of $\mathbb{R}^d$, but not sure what he means by $H^{k,r}(U)$ when $U$ is an open subset of a manifold , im also unsure why he claims that $\phi_{2} \circ \phi_{1}^{-1}$ has bounded derivative on the support of $s$ in $U_1 \cap U_2$

he seems to be claiming that this support is compact in $U_1 \cap U_2$, but i dont see why this has to be the case

in his appendix he has a bunch of results for sobolev spaces on open subsets of euclidean space, but nowhere in the book does he actually define these spaces on open subsets of manifolds, although these spaces are referred to

Ajay

My exam has finished!

It was much easier than my first paper!

user400188

06:03

Personally I have only ever found it to be a joy.

Any of the not so joyful stuff that can come with it tends to not be mathematics.

Koro

Can anyone please take a look at this? math.stackexchange.com/questions/4446340/…

One thought: Let $\ker \pi:=K$.

$G/K\cong H$

So $H\times G/H\cong G/K\times G/H$

Define $f: G\to G/K\times G/H $ as $f(g)=(gK, gH)$.

I aim to show this $f$ to be isomorphic but the problem at hand is that $f$ might not be onto (?) as I think that if $a\ne b$ are in G then $(aK, bH)$ is not in range f.

Even if f is onto, then ker f=$K\cap H$ ,which may not be identity so this seems wrong.

William John

I am confused about theorem 1.11.

In Rudin.

Why is $\alpha\in L$?

What concludes $\alpha\in L$?

porridgemathematics

06:21

hmm, I suspect jost was speaking modulo partitions of unity and some other nonsense

dc3rd

06:31

@WilliamJohn draw a picture and I guarantee you will see why that is the case.

Akiva Weinberger

06:57

I'll put my apostrophes where I wan't

*whe're

Wave

Is it true that if I have a uniform variable of the unit square [0,1]^2 that then the characteristic function is the product of the characteristic function in each coordinate? So I mean that $\Phi_(X,Y)(u,v)=\Phi_X(u)\cdot \Phi_Y(v)$?

William John

@dc3rd Doesn't work.

user400188

How do you specify that a compliment of a set, is taken from another set?

e.g. I have a set $A$ which is a subset of $B$, which in turn is a subset of $C$. I want to talk about $B-A$ as the compliment of $A$, but I am unsure how to refer to $B$ as the set the remaining members are taken from, (as opposed to $C$).

Wave

07:44

my question from above is now clear I could prove it!

Akiva Weinberger

08:05

Desmos comes to the rescue for my graphic design needs

The same pattern (with multiplicity!) from two lines and four lines, respectively

Pretty

Both together

Akiva Weinberger