What is...Lie theory?
ฝัง
- เผยแพร่เมื่อ 24 ม.ค. 2025
- Goal.
I would like to tell you a bit about my favorite subfields of mathematics (in no particular order), highlighting key theorems, ideas or concepts and why I like them so much. This is a variation of “My favorite theorems” and I park the videos on that list as well.
This time.
What is...Lie theory? Or: Subfields of mathematics 26.
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
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TeX files for the presentation.
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Thumbnail.
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Main discussion.
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Background material.
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Computer talk.
doc.sagemath.o...
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Pictures used.
Picture from • What are...the groups ...
Picture from en.wikipedia.o...
Picture from • What is...the smooth p...
www.researchga...
Picture from arxiv.org/abs/...
TH-cam and co.
• What is Lie theory? He...
• Why study Lie theory? ...
• Lie theory for the rob...
#linearalgebra
#differentialequations
#mathematics
Yeah! It’s here! Yours videos at weekend are One of my favorite times of the week😊
Thanks, friend, I am happy to hear that you find them enjoyable ☺
You have an absolutely lovely way to explain the essentials of these topics.
Thanks, I am glad to hear that. I hope you enjoyed the video 😀
9:00 I've personally seen a guy (I think he was from the ENS Paris) effortlessly use the fraktur typeface, in chalk, on a blackboard. I was so in awe
Wth? I can't do that at all (my mathfrak looks like normal font used weirdly), I am seriously in shock 🙃
@@VisualMath He used the chalk a bit sideways to give different thickness to the lines 🤔
@@mrl9418 Brilliant 😮
This is much easier to understand than most other TH-cam math instructors
Thanks for watching, I am happy to hear that the video was helpful ☺
Beautiful and informative video. Thanks!
Welcome, friend ☺
Im very interested in the concept of groups associated with partial differential equations. Especially how those groups may evolve or deform a little bit as the parameters in the differential equations vary for example the heat diffusion coefficient in the heat equation. Have you heard of others studying this concept and have any pointers on how to study this? In artificial intelligence there is a crowd how approximate operators using neural networks and the deep O nets/fourier neural operators do use this concept of parameter variation as a tunable parameter in part of their training algorithm. However, I haven’t seen them study algebra or operator algebras tangential to doing operator approximations in that way. And that’s what I’d like to study and research in more detail.
Hmm, excellent yet difficult question. Somehow the natural topic of differential Galois theory never really took flight. I feel its because its actually difficult.
It turns out the the idea that originated in the study of differential equations got mostly carried on by algebraic geometers under the slogan of D-modules. See that mathoverflow post 201853 for a discussion and a few references. The post 175761 is also useful.
I likes the lecture notes of Tobias Dyckerhoff at Yale from 2008 (try to google “Tutorial on Differential Galois Theory I - Yale Math”) useful.
I hope that get you started 😀
(For some reasons TH-cam hides my comment if I put links into it - probably some spam filter thingy - so sorry for the brute force way to give references.)
Check out Lucia Di Vizio's work in differential Galois Theory.
Are you familiar with Olver's "Applications of Lie Groups to Differential Equations?"
See also Pommaret's Partial Differential Equations and Group Theory
Nice video and explanation! Subscribed!
Thanks for watching 😀
Lie theory is nice when applied to nt
Yes, its super applicable; thanks for pointing that out. I have not seen it much in number theory, but that is probably a bias on my end 😀