Lie Algebras and Homotopy Theory - Jacob Lurie

[@AdrienLegendre]

I like his enthusiasm. He is actually out of breath presenting mathematics. There is so much that is so important to present.

[@christianlapointe1678]

How amazing of a time we live in, where amateurs like me can catch a mere glimpse of our times greatest geniuses!!

[@ryanjbuchanan]

Yep

[@anam.caballerowilson9421]

He sounds so excited about this topic lie algebra. Good.

[@joemoeller1442]

At the end he mentions that the derived category of the universal Lie algebra is equivalent to the derived category of the category of functors from FinSurj to Ab. Where can I read about this?

[@duckymomo7935]

What you’re looking for is look up operads and universal algebra Start with P Vogel’s paper I hope this helps

[@duckymomo7935]

Jin Guu Northwestern paper by Eva Belmont might help (look up operads applications)

[@tedward191]

Perhaps this is yet to be published material from Lurie? As I cannot find any text about this anywhere

[@danyeol1]

What a Nice lecture...

[@joebloggsgogglebox]

I don't understand the comments at 11:30. The result of the commutator map is a loop of dimension a followed by a loop of dimension b, followed by their inverses, which is not the same as a loop of dimension a+b, right? Or am I misunderstanding something?

[@joebloggsgogglebox]

@Connor Malin I think I understand the relationship between the loop space and the base space (the right hand side dimension increases by 1 not 2). It's the dimension of the right hand side when a,b>0 that I don't get. If we have a=b=1 then on the left hand side we have a pair of 2-loops, and the commutator of those 2-loops is surely another 2-loop (the first followed by the second, followed by their inverses), not a 3-loop!?

[@joebloggsgogglebox]

OK, after thinking a bit more about the comments at 16:40 and reading the Wikipedia page about the Whitehead product, I think I get it; one of the dimensions is used by the commutator map for joining the loops (p, q & their inverses) together, and the other dimensions are used for identifying the particular 1-dimensional loops within each part. So he is treating the dimensions a bit differently in pi_{a+b}; they don't correspond with spacial dimensions as they could do for pi_a & pi_b when I try to imagine an example in my mind.

[@noellundstrom7447]

What a great talk/lecture

[@hhhhhhhh6008]

G cross g space to the identify put your identity in me(I know you know what the identity is)

[@j1d2e3l4l5]

Jacob is always good.

[@kaushaltimilsina7727]

Wow! Thanks very much for the really interesting talk!

[@hhhhhhhh6008]

Good

[@perguto]

Why does this video have so many views (relatively speaking, for a maths lecture) after just a few hours? Is it just the prominence of the speaker plus the rather simple title?

[@ХыуБаоВыонг]

I think it is youtube's algorithm, I came here because I saw it the first video recommended and it from IAS, so just curiosity. I intentionally want to watch another lecture :)

[@PGouges35]

Same here. I have viewed other videos on Lie algebras and the KZbin algorithm recommended this video to me

[@harrywilson1660]

IAS has 40k subs.

[@johncharles2357]

Jacob Lurie is currently a big name in mathematics. Check out: www.quantamagazine.org/with-category-theory-mathematics-escapes-from-equality-20191010/

[@giuliocasa1304]

@@johncharles2357 they should give those money and prizes to really competent people working in many technological fields. I'm a programmer and I see the mathematical concepts that a good developer like me has to apply to implement good abstractions in the working business context. There is an exaggerated worldwide marketing sponsorship for these golden positions, where one can enjoy playing with exotic topics and earn so much without any just comparison to the real market outside, with reference to other intellectual workers

[@SidharthSisawesome]

At 5:35, How does the differential of the commutator map give the Lie Bracket?

[@duckymomo7935]

math.stackexchange.com/questions/806498/the-diffential-of-commutator-map-in-a-lie-group

[@SidharthSisawesome]

@@duckymomo7935 So it's the zero map then?

[@duckymomo7935]

Sidharth S Yes, that’s why it’s really not an interesting Lie algebra

[@rtravkin]

@@duckymomo7935 To get the Lie bracket on the tangent space to a Lie group, one should take the second derivative, e.g.: [ dx/dt (0), dy/dt (0) ] = d^2/dt^2 ( x(t) y(t) x(t)^{-1} y(t)^{-1} ) for two differentiable paths x(t), y(t) starting at the identity element x(0) = y(0) = e .

[@adityaekbote8498]

@@rtravkin what happens to the first derivative?

[@hhhhhhhh6008]

Simply laced algebras

[@Bagatatatoken]

From Higher topos theory to higher cosmoi muchzuki theory

[@hhhhhhhh6008]

Jacob is always good

[@wacksparrow88]

Was thinking about CubeB inscribed in CubeA. CubeA is fixed and CubeB rotates around one point. Vectors move through each cube. What is interesting to think about is that there will be at times in which the vectors can either hit the imaginary barrier. Still working on it but interesting to think about in terms of shapes, boundaries, and properties that can be applied.

[@kenichimori8533]

Lie Algebras Lie Lie Lie cosmotopy.

[@MasterKenfucius]

Ops... wrong video...

[@johnrichardson3297]

The answer should be Alpha Constant

[@NothingMaster]

Agitated, breathless, uninspiring, uninsightful, and regurgitative.

[@waynewalls5033]

But that’s enough about you, onto the subject at hand...

[@nadeembajwa8530]

And that's just your comment