Members' Seminar Topic: Lie Algebras and Homotopy Theory Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: November 11, 2019 For more video please visit video.ias.edu
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?
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?
@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!?
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.
@@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 .
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?
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 :)
@@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
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.
