Posts by ZevenKorian@mathstodon.xyz
(DIR) Post #A4pO5PgPWuVT7m3wx6 by ZevenKorian@mathstodon.xyz
2021-03-03T08:44:25Z
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you know reading my undergrad thesis again is a fucking ride because i realise I knew NOTHING about the math I was usinga lot of shit you could easily do for all n I just did for n=2 and said "the general case is the same" because I didn't want to deal with itmy master thesis is the same tho I remember proving an identity involving exterior products for n=1 and saying "the general case is v complicated"
(DIR) Post #A4pO5RvjAvwm5rFD6W by ZevenKorian@mathstodon.xyz
2021-03-03T08:45:33Z
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it's complicated if you have no clue what you're doing but it's literally realising you can use the binomial formula because you are for all intents and purposes multiplying 2-forms
(DIR) Post #A4w94ArH1YAbeOoY1A by ZevenKorian@mathstodon.xyz
2021-03-06T15:05:45Z
1 likes, 0 repeats
2021: I'm citing two youtube videos
(DIR) Post #A59rYjQC0NO2ZX0XDc by ZevenKorian@mathstodon.xyz
2021-03-12T08:05:53Z
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Good morning to everyone except to the power series expansion of the function sin(log(log(x)))It knows what it did.
(DIR) Post #A5PosgJnqEJt6i2WcS by ZevenKorian@mathstodon.xyz
2021-03-20T22:42:27Z
1 likes, 0 repeats
writing an article about bounds and trying your best not to say "it is bound to" because the pun is too predictable
(DIR) Post #A5phJBv56dtyN8Kxhg by ZevenKorian@mathstodon.xyz
2021-04-02T10:19:55Z
1 likes, 0 repeats
@NaiJi it's fridayfridayget down on friday
(DIR) Post #A5rkxodRGqImCx4Fua by ZevenKorian@mathstodon.xyz
2021-04-03T10:09:30Z
1 likes, 0 repeats
(DIR) Post #A6Af7fmg7pj7vnwejQ by ZevenKorian@mathstodon.xyz
2021-04-11T21:48:53Z
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things I finally understand after looking them up a billion times: p-adic numbersthings I keep looking up: moduli spaces, lattices
(DIR) Post #A6Af7gSrazTG2dgLU8 by ZevenKorian@mathstodon.xyz
2021-04-12T13:04:45Z
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OK, I was under the impression that a lattice was something more sophisticated, but apparently it's just an algebraic structure over a poset.
(DIR) Post #A6CHV85p1yjbo2THX6 by ZevenKorian@mathstodon.xyz
2021-04-13T07:41:35Z
1 likes, 0 repeats
@meeper looks like someone ran out of memory 😳
(DIR) Post #A6bnSFmNxIN50h3wW0 by ZevenKorian@mathstodon.xyz
2021-04-25T15:13:59Z
1 likes, 0 repeats
arxiv has an option to bookmark on reddit
(DIR) Post #A789hJWkic7l1m3Rpo by ZevenKorian@mathstodon.xyz
2021-05-11T05:52:45Z
1 likes, 0 repeats
Dynamical systems people be like: \(f(f(f(f(f(f(f(f(f(f(f(u)))))))))))\)
(DIR) Post #A7MnUGPrgt07zfbVb6 by ZevenKorian@mathstodon.xyz
2021-05-18T07:05:32Z
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Let \(\xi\) be a vector field along a smooth mapping \(f\colon N \to P\), and \(f_t\) be an integral curve of \(\xi\). If \(\omega\) is a differential form on \(P\), then \(f_t^*\omega\) is a differential form on \(N\) (or \(N\times\mathbb{C}\) if you want to keep the parameter as a variable). So far so good.
(DIR) Post #A7MnUGqo4iYHLED1ai by ZevenKorian@mathstodon.xyz
2021-05-18T07:07:18Z
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Thing is, we now have the Lie derivative of \(\omega\) along \(\xi\), which is defined as\[\left.\frac{d}{dt}\right|_{t=0}f^*_t\omega\] and is again a differential form. I've been thinking how derivating preserves the differential form structure.
(DIR) Post #A7MnUHISPufaiz96gq by ZevenKorian@mathstodon.xyz
2021-05-18T07:08:37Z
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I imagine it's because \(t\) only affects the coefficients of \(f^*_t\omega\) in a given basis for \(\Omega^k(N)\)?
(DIR) Post #A7MnUHgYyHx5vkQMGO by ZevenKorian@mathstodon.xyz
2021-05-18T07:23:32Z
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The reason why I'm tinkering about this is because of something called contact geometry. A contact manifold is a smooth manifold \(M^{2n+1}\) where you fix a subbundle \(\Delta\) of \(TM\) of dimension \(2n\). This subbundle is the "kernel" of a 1-form \(\alpha\) such that \(\alpha\wedge d\alpha\neq 0\); that equation is called the non-integrability condition.
(DIR) Post #A7MnUI6nOkw5F6hJ9U by ZevenKorian@mathstodon.xyz
2021-05-18T07:24:21Z
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Quote-unquote because I'm not sure if there's a well-defined thing such as the kernel of a 1-form, but I think you can easily imagine what I have in mind when I say that.
(DIR) Post #A7MnmUJujbfQKRViCm by ZevenKorian@mathstodon.xyz
2021-05-18T07:27:24Z
1 likes, 0 repeats
@absturztaube differential geometry is hard :blobcatlul:
(DIR) Post #A7MnyVSWKIDXKsGbYG by ZevenKorian@mathstodon.xyz
2021-05-18T07:29:31Z
1 likes, 0 repeats
@absturztaube :blobcatsnuggle:
(DIR) Post #ACkcTCI7gBP7OuDzqS by ZevenKorian@mathstodon.xyz
2021-10-25T16:33:28Z
1 likes, 0 repeats
@meeper it's supposed to be like a deconstruction kind of thing iirc, like madoka for magical girls