Imagine having the possibility to view lectures from people of this quality of intellegence, one honor we should all admire! Thanks for posting this video.
I hope someone has already given feedback along these lines, but I am quite bothered by the constant shifting of the camera to follow Professor Lurie instead of staying steady on recent things he points to or writes. The constant movement strains the eye, but does not provide anything (I can't speak for everyone, I guess, but I was not able to recover anything meaningful from the pattern of his back-and-forth pacing).
The camera-person is trying to make the image large enough to be seen, while including Jacob. Perhaps it would be better if they zoomed out while jacob is talking without doing any writing.
I liked his style. The movement conveyed his enthusiasm for his topic. There are alot of great stories out there about genius Professors and their quirks. I had one professor show up to the first day of Diff E Q and just stand there looking at his notes for like 5 minutes. And then he asked the students "What class is this?". Everyone laughed. The professor was just kidding around and he often did hilarious things like that.
If you have an equivalence between two categories, it could imply that similar tools or ideas from one category can be applied to problems in the other category. Like modular forms and elliptic curves, to take a "well-known" example
Another example might be the duality of locally compact Hausdorff spaces and commutative C*-algebras, which gave rise to the field called noncommutative geometry, where (noncommutative) C*-algebras are regarded as some sort of (functions on) "noncommutative"-spaces. Much of the mathematics of modern quantum field theory is written in the language of NCG, which wouldn't exist if the equivalence of 2 categories (namely LCHaus^opp and abC*-alg) wouldn't have been discovered.
If you understand it you don't need notes, I had a lecture course on Geometry and the professor didn't refer once to notes in 30 hours because he either knew it or could do the calculation on the spot to re-derive a result.
BG typically refers to the classifying space of a group G. You can construct it by defining a one-object category whose morphism set Hom(•,•)=Aut(•)=G. For example if G=Z/2Z then the category would have a single object and one non-identity morphism f such that f•f=id. Then you take the geometric realization of the nerve of this category and get a topological space that you call BG. This process actually defines a functor from groups to topological spaces.
Instead of using his incredible genius to improve his own egoistic gaining, he is using it for man kind. Thank you for existing. You are a perfect role model for everyone.
All numbers are abstractions. In category theory however they are actual objects as items and not collections of objects like sets, nor collections of operations and properties like fields or groups.
One of the great thing's about Lurry's presentation style is that the board is just supplemental. I listen to him while cleaning or driving and don't suffer any dizziness from watching him 😉
Your Fourier transform us classic for all vectors and sub vectors spaces are isomorphic or isotopic and abelian translation but it is wrong cause the conumdrums are not usi specific depending on which topographical relations interconplexes non abelians C we are dealings with .quite impressive teachings if great havard teachers .but Fourier transfirm us just numbers of maze abstracts teachings but not apps to real life specifics assets of hi tech researches futures if solving abelian and non abelians complexes vectorings designs of conumdrums .Fourier transform is only a tool nit the lever apps .sorry to be so non compliant to an classics but in life the classics are not compute classics .still havard must be right somewhere along the lines .you have great teachers but a little bit fonctionnaires .if Fourier transform apps to future aeronautics or not would it be the same .the answer is quite impressive fir nit to say hyoerdumbs even fir masters if the masters 45 dumbs.
His lecture is not interactive as if he is reviewing for himself. Very traditional way of teaching that only a few students can follow the teacher. Reviewing is not teaching. And also his constant navigation makes me distracted.
