Someone fucking help me.

[OrganicEuphoria !C5Eg6mdVac No.4604331]

Fuck symplectic manifolds.
6 hours,
24 sheets of paper,
and 200mg of Vyvanse later...

I still have am not fully comprehending the fucked up solutions I'm formulating here.

If someone could please help me out here, point me in the right direction, anything, it'll be greatly appreciated.

Pic related.

[OrganicEuphoria !C5Eg6mdVac No.4604351]

I'm thinking it seemingly reduces to linear algebra problem, however that seem trivial and too simple. I don't fucking know.

[Anonymous No.4604366]

Nobody is going to do this entire thing for you. How did you start? Post some of your reasoning.

[OrganicEuphoria !C5Eg6mdVac No.4604373]

>>4604366
That would take me way too long, as most of what I've formulated isn't organized and looks like a page of incoherent scribbles.

I don't want anyone to just do this for me, as that would lessen my comprehension of the material, which isn't what I'm looking for. I'm just asking for a GENERALIZED summary or direction to get me going in the correct direction.

[Anonymous No.4604389]

For a) check for harmonic forms and see if they decompose then use the index theorem

For b) decompose the tangent space and try to show that there is a harmonic form in the Hermitian metric

[OrganicEuphoria !C5Eg6mdVac No.4604414]

>>4604389
I've been doing that for part A, I'll try again.
And for B, I'll give that a shot, thanks.

[Anonymous No.4604427]

fucking dumbfuck. get out. this is babby math. I seriously hope you're not wanting to be a mathematician.

[OrganicEuphoria !C5Eg6mdVac No.4604445]

>>4604427
I do not, thank god.
If this is babby math I don't want to see the big boy math you must do.

[Anonymous No.4604458]

Out of interest, how much lecture time does it take to get to this type of maths?

[Anonymous No.4604462]

>>4604458
addition: I'm assuming a knowledge of linear algebra and basic diff geo stuff

[Anonymous No.4604474]

>>4604445
Which course for people, who don't want to be mathematicans covers Kähler manifolds, index theorems and whatnot??

[OrganicEuphoria !C5Eg6mdVac No.4604475]

>>4604458
After you get the fundamentals down, not all too much time. I'm still an undergrad, but this particular class is a second-semester graduate course (although I'm not the only undergraduate attending), on the geometry of manifolds. I've seen some of this stuff at other Unis being potentially covered in 4th year undergrad math.

[OrganicEuphoria !C5Eg6mdVac No.4604483]

>>4604474
Eh, someone who enjoys learning, and implementing their knowledge in mathematics to other facets of science? I don't know man, a math degree just never fully appealed to me, I guess.

[Anonymous No.4604508]

>>4604483
but 300k starting!
:)

In any case, the problem looks quite interesting and nice. As far as the math goes, this really on the sharp edge of topics I understand. I always wanted to learn Riemannian geometry (or more broadly, Cartan geometries) from a side which emphasises the monodromy and holonomy concepts more, but sadly that takes some time and required to really do excesed like that.
:(

[OrganicEuphoria !C5Eg6mdVac No.4604548]

>>4604508
Yeah, once you get up the the higher maths (and for me personally, the abstract geometries) things start to get real interesting. That's ultimately the only rational justification I have for learn (or attempting too) learn this shit, as some of this won't be beneficial to me in any way.

Whatever, math is still fucking awesome.

[OrganicEuphoria !C5Eg6mdVac No.4604561]

>>4604508
Yeah, once you get up the the higher maths (and for me personally, the abstract geometries) things start to get real interesting. That's ultimately the only rational justification I have for learning, or attempting to learn this shit, as some of this (read: the majority) won't be beneficial to me in any way.

Whatever, math is still fucking awesome.

[OrganicEuphoria !C5Eg6mdVac No.4604650]

I think I have finally found the answer!
I'm about to type in up into its finalized version, would any of you care to see it?

I'll probably post it anyways for some sick and twisted self-gratification!

Thanks /sci/

[Anonymous No.4604730]

>>4604650
sure, post it.

Also, I don't think learning that you'll not use it. If not directly, you still got more understanding which helps understanding other things.

[OrganicEuphoria !C5Eg6mdVac No.4604775]

Here we go.
If someone tells me this is wrong I'll seriously give up and cry myself to sleep.

[OrganicEuphoria !C5Eg6mdVac No.4604779]

>>4604775
Also, what kind of fucking professor wants our answers written in Microsoft fuckin' Word? The equation editor absolutely blows.

[Anonymous No.4604781]

>>4604775
It's wrong.

[Anonymous No.4604788]

>>4604775
this stuff looks amazing...

i am currently in precalc

how long until i get to stuff like this?

calc 1, calc 2, calc 3, differential equations and linear algebra

would this be linear algebra?

sorry for bad english

[OrganicEuphoria !C5Eg6mdVac No.4604798]

>>4604781
Why's that. I smell a troll.

[Anonymous No.4604801]

>>4604788
upper level undergrad here who's taken all that and this stuff still looks incomprehensible. It's probably graduate level

[OrganicEuphoria !C5Eg6mdVac No.4604802]

>>4604788
You've got a long way to go, but stay motivated!
You'll get there.

[Anonymous No.4604806]

>>4604801
>>4604802
haha something to look forward to

[OrganicEuphoria !C5Eg6mdVac No.4604808]

>>4604801
I'm still an undergrad as well; this is, indeed, a graduate level geometry of manifolds class, although there are quite a few undergrads taking it with me.

[OrganicEuphoria !C5Eg6mdVac No.4604831]

>>4604775
Anyone confirm or deny this?
I'm about to just submit it and hope for the best.

[Anonymous No.4605030]

>>4604831


I think there is about a 1 in 1 million chance anyone on here has any clue whether it is right or wrong. I'm a theoretical physics major starting my grad studies who has done manifolds before and it would take me a week with textbooks sitting in front of me to put a dent into that thing.

[Anonymous No.4605050]

>>4605030
Babby pretentious physicist doesn't realize 4 other people in the thread helped the guy

[Anonymous No.4606508]

>>4604775
that looks fine for b, although it's a bit dirty and doesn't really state what you're doing. i don't know why you're introducing <span class="math">|\partial s_{x}| > |\bar{\partial} s_{x}[/spoiler] without explaining such first. it's pretty elegant to use the mapping <span class="math">\nabla s_{x} : T_{x} M \to L_{x}[/spoiler], though. ...is <span class="math">x \in Z[/spoiler]?


your proof doesn't at all handle a. for that you need to deal with <span class="math">\nabla s(u)[/spoiler]. you could do this by proving the graph has transversality to its lagrangian subspace which would give you the smoothness you need (think of vectors in <span class="math">T_{x} M[/spoiler]. you can then find the tangent space with simple set intersections to this graph.

>>4604389
what? do you even know what a harmonic form is? this would do absolutely nothing, there's no application to morse/hodge theory in here...

[Anonymous No.4606516]

>>4604775
that looks fine for b, although it's a bit dirty and doesn't really state what you're doing. i don't know why you're introducing <span class="math">|\partial s_{x}| > |\bar{\partial} s_{x}|[/spoiler] without explaining such first. it's pretty elegant to use the mapping <span class="math">\nabla s_{x} : T_{x} M \to L_{x}[/spoiler], though. ...is <span class="math">x \in Z[/spoiler]?


your proof doesn't at all handle a. for that you need to deal with <span class="math">\nabla s(u)[/spoiler]. you could do this by proving the graph has transversality to its lagrangian subspace which would give you the smoothness you need (think of vectors in <span class="math">T_{x} M[/spoiler]). you can then find the tangent space with simple set intersections to this graph.

>>4604389
what? do you even know what a harmonic form is? this would do absolutely nothing, there's no application to morse/hodge theory in here...