Vinberg lecture part 1.Vinberg's algorithm
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- Опубліковано 15 вер 2024
- This lecture is part of a series which gives an expanded version of the Vinberg lecture on "Vinberg's algorithm and Kac-Moody algebras". This video is part 1 and describes how Vinberg used his algorithm to calculate the reflection groups of some Lorentzian lattices.
Vinberg's paper can be found at
mathweb.tifr.r...
The original version of the lecture is here:
amathr.org/Bor...
For the other lectures see
• Vinberg lecture
I think we all can agree that this channel is the best place to learn higher level mathematics
Probably it is.
Definitely
I really like math major, Keenan crane, insights into mathematics, physics with Elliot, imaginary angle, surreal physics, pacovideolectures, sudgylacmoe
Hi Dr Borcherds, I'm a first year math PhD student. Have watched at least 50 hours worth of your videos now but don't usually comment. Just wanted to say thanks for all your online content. My classwork often burns me out but these lectures really put the flavor back in higher math. Very appreciated
Best math professor in the universe. Brilliant!
It's great to see the author(Vinberg) of your first serious math book in a lecture by Richard Bordchers
Thanks for making this lecture series!
It's actually a bit funny to me, like,
I was playing around with the mandela mode in a drawing program and that was very nice and fun;
and for some reason, hyperbolic space was on my mind; so I ended up thinking "hey, what if I did these mandela drawings but in *hyperbolic* space, because iirc those have loads of symmetry groups as well";
and later, I - for an unrelated reason - visited the channel again, and noticed "oh, Richard Borcherds has new lectures; let's goooo";
and the lectures are about symmetry groups on higher dimensional lattices and also lattices in hyperbolic spaces;
so that was awesome for me.
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I'm definitely not at the point yet where the math in Vinberg's paper makes perfect sense to me (I'm still on the first few pages, reading very slowly).
And I'll definitely need to rewatch this lecture and then maybe play around with the concepts a bit until it really all clicks into place; I have never played around with Coxeter/Dynkin diagrams, but it was really cool seeing the "you can see subgroups/subalgebras etc. just by hiding one of the nodes" etc.
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Also, at the part where you showed the way that n-dimensional hyperbolic space can be embedded into n,1-dimensional spacetime, and how the reflection planes can be thought of, several ideas in my head really clicked into place;
now I'm even thinking about, like, what if I could try to find a clever way to do hyperbolic reflection group stuff using like, spacetime geometric algebra; though, I will still need to explore that to see if that idea's a dud.
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Anyway, excuse the wall of text;
and have a nice day.
- Ruben
A old but active topics in the algebra, i am combinatorist. i am totally sure that Lorentzian lattices are hot topics nowdays.
He's my hero🥳🥳
This is gold. Thank you Sir!
Legend
we appreciate you sir.
Thank you for your content.
"Your text here."
The first clickbait 😅
There is a big problem arise when you start looking at the metric corresponding to this reflections and rotations, and the added constant + deformation compared to the eigenvalues. You get 2 completely different picture hard to reconcile. I try to think about this more how to understand the connection such as why these physical manifestations arise. Seems like the projective hilbert spaces arise from the ray spaces experience their own spacetime as wordline but no background space required as fundamental. On the other hand the metric now show up as part of spacetime correspond to the point of origin correspond to the momentum generation.
brilliant
so cool!
Nice
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