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/sci/ - Science & Math

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2784433 No.2784433 [Reply] [Original]

Explain the Hodge conjecture in layman's terms.

Nightmare mode: Explain why anyone gives a shit.

>> No.2784449

Let X be a projective complex manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

>> No.2784457

>official problem statement
>In despair, efforts have been made to find substitutes for the Hodge conjecture.
>In despair

lol pure math

>> No.2784461

>>2784449

layman here; I understand the Hodge conjecture now and I can imagine multiple ways to apply it.

Thanks.

>> No.2784497

Mathematicians discovered how to approximate complex shapes by gluing together simpler shapes of increasing dimension. It turns out that this idea is so useful and powerful that mathematicians went ahead and generalized it in many ways. Unfortunately while the initial idea started out geometric, the generalizations weren't as much: they had to add pieces that didn't really have a geometric interpretation.


The Hodge conjecture asserts that for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually (rational linear) combinations of geometric pieces called algebraic cycles.

So we get the geometric interpretation of these pieces back if the Hodge conjecture is true, which has many nice consequences I'm sure.

>> No.2784585

>>2784497
Okay, well thanks for trying anyway. I suspect no one on /sci/ can do much better.

>> No.2784598

>>2784585
>>2784585
Stop acting like you have the final say.

That was a decent explanation. YOU'RE the reason why 4chan is meant for people >17.

>> No.2784616

>>2784585
It can't get any more simpler you high schooler

What the fuck do you want?
A picture book?
Do you want a picture book?
Do you want me to read it to you while you drink warm milk from a bottle and slowly drift off into a slumber?

>> No.2784637
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2784637

>>2784616

that'd be nice thanks

>> No.2784669

You mathfags can't explain shit.

That's why you can't get laid, I bet.

I don't need to understand probability to know you're virginity quotient= 1

>> No.2784673

>>2784637
It means that everything is made of atoms.

>> No.2784688

I'M ANONYMOUS
SON OF A BITCH OP
OP IS PIG
DO YOU WANT A PICTURE BOOK?
DO YOU WANT A WARM MILK?
OP IS PIG DISGUSTING
MOOT IS A MURDERER
FUCKING /SCI/

>> No.2784704

>>2784616
>>It can't get any more simpler you high schooler

not that it wasn't a pretty good explanation, but...

>>2784497
>>The Hodge conjecture asserts that for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually (rational linear) combinations of geometric pieces called algebraic cycles.
>>projective algebraic varieties
>>Hodge cycles
>>algebraic cycles

...yeah

>> No.2784708

>>2784497

that's nice so it's a bit like a 3d algebraic Taylor equation in that it allows you to assertion a shape by taking other shapes that sorta fit and just keep adding smaller and smaller shapes until the difference is zero?