12:04 AM
Measure Lebesgue $[0,1]$ is equal to zero.

wat

@PawełKusz Because 0=1?

I'm a bit confused by a hint on a homework problem. Given an embedding $f: T^2 \to S^3$ and a closed 2-form on $S^3$, I want to show that $\int_{T^2} f^* \omega = 0$ and the hint is to homotope $f$ to a constant map and then use Stoke's theorem. But if we homotope $f$ to a constant map then the image of $f$ is just a single point in $S^3$ and I'm not sure how to apply Stoke's theorem to that setup
I don't see the boundary of anything anywhere

If a manifold has no boundary, the integral of anything over its boundary is $0$

12:17 AM
Thats what I though, but then why do I have the condition that the 2-form must be closed?

Good question... :thonk:

Somehow this has to become the integral of $d \omega$ over $S^3$ or some part of $S^3$ so the thing I homotope to should be the boundary of that corresponding thing.
Maybe I can think of the point as being the boundary of some $S^1 - \{p\}$ sitting in $S^3$

Maybe? This is quite strange honestly

12:44 AM
Oh I think I need that the form is closed because if $f \sim g$ then $f^*$ and $g^*$ are equal as maps.... on the appropriate DeRham Cohomology which only include closed forms

OH RIGHT
Yeah homotoping stuff requires closedness

1:17 AM
Octonions are like quaternion but instead with 3 imaginary parts they have 7 imaginary parts?

And they are not associative

@EnderLook the space of purely imaginary octonions is 7-dimensional
so, you specify the imaginary part of an octonion by using 7 real parameters

2 hours later…
2:58 AM
Hot take: MS Paint > MS Word > LaTeX
@Eric can confirm

i agree

Staying around for Thanksgiving?

yup
also may potentially doing a reading course with professor ngo next quarter

Wait really? That'd be sick, what on?

some kind of number theory
otherwise potentially might do something with amie or eskin

3:15 AM
I see. Chances are if I do a reading course with anyone, it'd be Nori

he's cool

Otherwise meaning, you're deciding? Or that Ngo might be too busy next quarter or something?

oh like a friend approached me to do a joint one w me
and these are the people who he has approached already

Ah, I see

How can I think about computing an integral like $\int_{M} g^* \omega$ where $g:M \to N$ is a constant map?

3:17 AM
Oh I guess there's also a chance I'll try to do a reading course with Marianna
Like a few people are doing descriptive set theory and I might hop in
Though thing is, it's between that, something with Nori, or civ
Probably not ready to do anything with Nori yet, Marianna would be an open option that's fun, civ is the responsible thing
That or I wouldn't do algorithms, I dunno

if i do a reading course im not registering for it
im taking it conjunction w 4 other things

Oh yeah I could just drop in on the descriptive set theory folk

ik some of my HA crew did an informal schlag-quest last year

Also turns out Nori's doing AG next quarter
Lol your group seemed to be quite close to Schlag
We've got a few people working with Soug, like he's teaching literacy in PDE but since enough (3-4) of us were thinking of a reading course with him, he was like yeah do literacy and I'll just focus on you guys

wait there's an AG class next quarter?

3:27 AM

ahhhhh right grad ag is winter i forgot

Yup

we are also considering reaching out to benson to do some low dim top or MCG

Oh that could be fun

3:54 AM
Algebraic Geometry: A Geometric Approach

@user104729 Euclidean Geometry: A Geometric Approach

Approaching Geometry: A Geometric Approach
5

You know there are finitely many sub-fields of mathematics studied up to this point in histroy
So we could just build a bot that appends ': A geometric Approach' to every one of them and then never have to do that work again

@KevinDriscoll but where's the fun in that?

hi chat

4:05 AM
hullo

Geometric Approaches: A Geometric Approach

Yo

I guess that's not so different than what Leaky had, though

@Semiclassical hi

hollu

4:15 AM
Approaching Algebra: An Algebraic Approach
Approaching Number Theoy: A Number Theoretic Approach

Approaching Logic: A Tautological Approach

Approaching SemiClassical Physics: A SemiClassical Approach

i see what you did there

Approaching Baymax : Baymaxian approach

4:24 AM
Approaching -1/12: A Natural Number Approach

Oh no

Approaching Limits: A Limited Approach

Approaching Daminark: A Thonking Approach
3

Approaching the Limits of the Joke: An Exhaustive Approach

Approaching Insanity: Approached

4:28 AM
@LeakyNun You know what I'll take it

Approaching Approach: An approach0.xyz Approach

Approaching The Unapproachable: An Impossible Approach

Approaching the Disconnected: An Obstructed Approach

Approaching The Center of a Blackhole: An approach from which there is no return

4:38 AM
Approaching Light Speed: An Electromagnetic Approach

Approaching mathematics: A metamathematics approach
Approaching Ted: The Origin of Geometric Approaches

Approaching People: A Polite Approach

4:53 AM
Omae wa mou shindeiru: A NANI? approach
@Balarka

Approaching The Unknown: A Discovery Approach

Oh Ted's gonna have a time when he sees this

Imitation is a form of flattery
Approaching Flattery: An Imitation Approach

And if it is not the correct chat forum. Please give me link of proper one

5:45 AM
It seems that recently the activity in functional analysis chatroom is bigger than before. And there is no shortage of users who ask questions there. It would be nice to get more users with good knowledge of functional analysis who could help with the question which remained unanswered.
Of course, there are many other chat rooms which could have more activity that they currently have: List of chatrooms
@Sadhu Maybe posting the question here in chat in the format which includes the title might increase the chances that somebody have a look.
If the title is included, users in chat can have at least a basic idea what the question is about without having to click the link. And if they see that it's a topic they are interested in, they might have a look.
In this case you might also try to make the title more descriptive. The phrase "following expression" does not say much about the question, maybe something like "modular computation with Fibonacci numbers and factorials" would be better.
Or you could simply include the expression $(\frac{\sum_{i=N}^M F_i\cdot i!}{K}) \mod p$ in the title.

Also, click on the "help" link in the bottom right corner :-)

6:32 AM

hi chat

I have problem with one pdf on my ipad
it keeps crashing on only 1 book
the rest works fine
do you know if it can be fixed?

I did that :/
Its heirstein book
17.2 mb
it is smaller than the others for some reason
that could be it but not sure

6:37 AM