The Atiyah quote he shares at the end is: "No one fully understands spinors. Their algebra is formally understood but their significance is mysterious. In some sense they describe the 'square root' of geometry and, just as understanding the square root of -1 took centuries, the same might be true of spinors."
Love the style and general idea of this sort of lecture. Great work. Minor correction, maybe it even was made in the video and I missed it, but in a Lie Group only the part of the Lie group near identity can be written as the exponential of a Lie Algebra element. Products of exponentials will generate the connected component of the identity. However, generally, a Lie group can be disconnected and we'll need something more than a matrix exponential to write the non-identity components of the group. For example, the orthogonal group O(3) has determinant 1 and -1 matrices and those form sets which are disconnected. Physically, the determinant -1 give orientation reversing transformations whereas determinant 1 give rotations which preserve right-handedness of triples...
I see that Alex passed away. I've only watched this lecture --- but I am sure the others (which I will watch) will be just as informative and inspiring. This mentor's passion is remarkable and rare. He light shined briefly --- but no doubt very brightly for his students. One hopes the past is solid and real and Alex is eternal.
I haven't watched the previous lectures in this series, but you've a very pleasant style of communicating to the students. They are definitely not afraid to engage and it has a nice cliff hanger on spinors. Very warm, very welcoming. Thank you!
*The Group Norwegians* The adjective 'Abelian' is named after the Norwegian mathematician Niels Henrik Abel. And 'Lie group' is named after the Norwegian mathematician Marius Sophus Lie.
Off topic: The first Secretary-General of the United Nations was Trygve Halvdan Lie, also he Norwegian. But I don't know if he was related to Marius Sophus Lie. (Probably he was, but distantly so.)
yacine benaida I just know that if you replace the intake manifold on a 1972 Buick Skylark with a Calabi-Yau manifold, you also have to switch from "unleaded" to "Ricci-flat" or you're screwed. 🤔
Just found these lectures - I love the style and presentation. He leads the class so well that you feel all the time a couple of steps ahead of where he's going. (Does that make sense? :D ) Wish I'd had this quality of tuition when I was a student.
It's so weird to me that this is a 3rd or 4th year university physics course, but he says things like 'you might know the definition of cosh(theta)' and 'in case you've forgot, i is the square root of minus 1'. Any Americans out there; is this typical?
It is sadly typical for hyperbolic functions to be downplayed in American University calculus. There is tremendous pressure to dumb down university courses and little pressure to maintain excellence or scholarship in many locals. Of course, in his context, it may well be a joke. As a point of personal experience, I don't think cosh or sinh was mentioned in my calculus although I champion their utility now in my own teaching.
@@jmckaskle we certainly should do that. But, all too often parents and administrators and students lobby for medocrity for the masses. It doesn't seem to bother them that those most deserving of knowledge have to seek it out as if it was countercultural in school. It's a shame. One size fits all makes us dumb.
Prof. Flournoy, is it possible to change the angle a little bit in such a way that the camera captures the full black board in the straight manner? Right now, the left side, from the perspective of the black board reflects quite a bit.
Is there any way you could post homeworks and answer keys? I know I would appreciate it and assume others would as well. If its too long ago or there are other reasons I understand.
He lost me with the multiplication table @12:27. An odd number times an even number is even. An odd number times an odd number is odd. Oh, a minute later a student called him on it. --wow his reaction wasn't very helpful, since the operation with even-odd is addition, and the operation with + and - is multiplication. It's hard to associate two groups as identical when subjecting them to two different operations!
@nishant jangid Hola. It's the hamiltonian for a harmonic oscillator. The first two terms represent position and momentum, but the eigen (energy) values always go like (1/2 + n) n=1,2,3... so it's never zero with two terms. The third term I say is Force because why not? Position, momentum, force are all just extending derivatives in time. But as it turns out the third term is the Pauli spin operator and that let's you take energy down to zero. Which is cool because you'll have uncertainty if your energy is not zero. I don't know why we only use position and momentum as equation of motion for ALL oscillations.
The students should wait until they know enough to ask helpful questions. He's wasting lots of time addressing irrelevancies. Trust your instructor to show you what you need to know!
Yes! You should definately not ask questions if you feel confused during a introductory group theory lecture for undergrads. My god that could send a honest signal about your current understanding to the professor, and worse to your fellow students who might sigh from all the time wasted. Not to mention all the people watching on youtube whose time you are wasting. Remember that the course is for them not for you who paid tuition (stupid student). I'll even take it a step further: I think the course should preferably only be taken by people already fluent in the thought structure of groups and representations and any non helpful-comitty aproved questions (that the professor obviously ironically said you were welcomed to ask) should, if not by you yourself, collectivey be squashed before uttered by an agressive student culture. Everyone becomes a better student with a really harsh an elitist learning enviroment.
@@HilbertXVI the lecture you commented on is literally a part of lectures introducing group theory to undergrads trying to learn about particle physics.. Sorry if my comment hurt your feelings making you feel less advanced. Lots of love (the only non-embarrassing usage of “lol” if you are over the age of 15).
Guys, is it just me, or us this guy kinda not a great lecturer. Like he's good, but you have an underlying feeling that he didn't do any preparation for anything throughout the semester
I disagree. He made it very clear even using non-trivial examples without going off into axioms and definition based proofs. They are very non transparent. See ABSTRACT ALGEBRA for example. This is a GREAT PROFESSOR , your lucky to have digesting hard subjects for you. BRAVO, BRAVO AND HATS OFF.
Knowing that this man is teaching despite having BRAIN CANCER ........stirs great(est) respect for you SIR...
How did u know
@@adscft7597 Check the description of this channel....
Wish the best for him
and this is when the cancer was unknown to him, just growing
The Atiyah quote he shares at the end is:
"No one fully understands spinors. Their algebra is formally understood but their significance is mysterious. In some sense they describe the 'square root' of geometry and, just as understanding the square root of -1 took centuries, the same might be true of spinors."
Love the style and general idea of this sort of lecture. Great work. Minor correction, maybe it even was made in the video and I missed it, but in a Lie Group only the part of the Lie group near identity can be written as the exponential of a Lie Algebra element. Products of exponentials will generate the connected component of the identity. However, generally, a Lie group can be disconnected and we'll need something more than a matrix exponential to write the non-identity components of the group. For example, the orthogonal group O(3) has determinant 1 and -1 matrices and those form sets which are disconnected. Physically, the determinant -1 give orientation reversing transformations whereas determinant 1 give rotations which preserve right-handedness of triples...
Professor James! nice to see you here as well. Your lectures are also awesome!
I see that Alex passed away. I've only watched this lecture --- but I am sure the others (which I will watch) will be just as informative and inspiring. This mentor's passion is remarkable and rare. He light shined briefly --- but no doubt very brightly for his students. One hopes the past is solid and real and Alex is eternal.
I haven't watched the previous lectures in this series, but you've a very pleasant style of communicating to the students. They are definitely not afraid to engage and it has a nice cliff hanger on spinors. Very warm, very welcoming. Thank you!
*The Group Norwegians*
The adjective 'Abelian' is named after the Norwegian mathematician Niels Henrik Abel.
And 'Lie group' is named after the Norwegian mathematician Marius Sophus Lie.
Off topic:
The first Secretary-General of the United Nations was Trygve Halvdan Lie, also he Norwegian. But I don't know if he was related to Marius Sophus Lie. (Probably he was, but distantly so.)
excuse me sir,what does it mean ''manifold''
yacine benaida I just know that if you replace the intake manifold on a 1972 Buick Skylark with a Calabi-Yau manifold, you also have to switch from "unleaded" to "Ricci-flat" or you're screwed. 🤔
I always wondered about that, thank you
You forgot about Sylow.
Just found these lectures - I love the style and presentation. He leads the class so well that you feel all the time a couple of steps ahead of where he's going. (Does that make sense? :D )
Wish I'd had this quality of tuition when I was a student.
I was just about to post the exact same comment lmao... this guy is like the Prof. Leonard (another great) of graduate level mathematics
No Morgan Freeman could not have pulled off this level of explanation
Full bodied approach is great!
Really interesting, clearly presented, and well developed lecture!
Prof Alex Flournoy is no more.... RIP Alex Flornoy
It's so weird to me that this is a 3rd or 4th year university physics course, but he says things like 'you might know the definition of cosh(theta)' and 'in case you've forgot, i is the square root of minus 1'. Any Americans out there; is this typical?
@DY_Physics joking about students not knowing basic differential geometry (tangent vectors to the group at the identity) is still really bad.
It is sadly typical for hyperbolic functions to be downplayed in American University calculus. There is tremendous pressure to dumb down university courses and little pressure to maintain excellence or scholarship in many locals. Of course, in his context, it may well be a joke. As a point of personal experience, I don't think cosh or sinh was mentioned in my calculus although I champion their utility now in my own teaching.
James Cook You learn about imaginary numbers and hyperbolic functions in highschool.
@@jmckaskle we certainly should do that. But, all too often parents and administrators and students lobby for medocrity for the masses. It doesn't seem to bother them that those most deserving of knowledge have to seek it out as if it was countercultural in school. It's a shame. One size fits all makes us dumb.
B
Prof. Flournoy, is it possible to change the angle a little bit in such a way that the camera captures the full black board in the straight manner? Right now, the left side, from the perspective of the black board reflects quite a bit.
I love learning, thanks, subscribed.
Is there any way you could post homeworks and answer keys? I know I would appreciate it and assume others would as well. If its too long ago or there are other reasons I understand.
Sir,you must have your telegram group for students
Pfo，so cool. Like the Iron man.
I don't know why anyone would herd sheep into any waters at all, let alone troubled ones.
Somehpw I always end up calling it the CEVI LIVITA.
Now I want to punch Robin too!
He lost me with the multiplication table @12:27. An odd number times an even number is even. An odd number times an odd number is odd.
Oh, a minute later a student called him on it. --wow his reaction wasn't very helpful, since the operation with even-odd is addition, and the operation with + and - is multiplication. It's hard to associate two groups as identical when subjecting them to two different operations!
Do you guys like my new harmonic oscillator? I made it from three generators instead of two :)
H = (1/2)kX^2 + (1/2m)P^2 + (1/2)gF^2
Can you explain it?
@nishant jangid Hola. It's the hamiltonian for a harmonic oscillator. The first two terms represent position and momentum, but the eigen (energy) values always go like (1/2 + n) n=1,2,3... so it's never zero with two terms. The third term I say is Force because why not? Position, momentum, force are all just extending derivatives in time. But as it turns out the third term is the Pauli spin operator and that let's you take energy down to zero. Which is cool because you'll have uncertainty if your energy is not zero. I don't know why we only use position and momentum as equation of motion for ALL oscillations.
I want to invite you to a whats app discussion
The students should wait until they know enough to ask helpful questions. He's wasting lots of time addressing irrelevancies. Trust your instructor to show you what you need to know!
I think the students would benefit from a first course in abstract algebra, a lot of these questions would be very quickly covered there
Yes! You should definately not ask questions if you feel confused during a introductory group theory lecture for undergrads. My god that could send a honest signal about your current understanding to the professor, and worse to your fellow students who might sigh from all the time wasted. Not to mention all the people watching on youtube whose time you are wasting. Remember that the course is for them not for you who paid tuition (stupid student). I'll even take it a step further: I think the course should preferably only be taken by people already fluent in the thought structure of groups and representations and any non helpful-comitty aproved questions (that the professor obviously ironically said you were welcomed to ask) should, if not by you yourself, collectivey be squashed before uttered by an agressive student culture. Everyone becomes a better student with a really harsh an elitist learning enviroment.
@@an2nkr Lie groups and Lie Algebras are very far from "Introductory Group Theory" lol
@@HilbertXVI the lecture you commented on is literally a part of lectures introducing group theory to undergrads trying to learn about particle physics.. Sorry if my comment hurt your feelings making you feel less advanced. Lots of love (the only non-embarrassing usage of “lol” if you are over the age of 15).
Guys, is it just me, or us this guy kinda not a great lecturer. Like he's good, but you have an underlying feeling that he didn't do any preparation for anything throughout the semester
I disagree. He made it very clear even using non-trivial examples without going off into axioms and definition based proofs. They are very non transparent. See ABSTRACT ALGEBRA for example. This is a GREAT PROFESSOR , your lucky to have digesting hard subjects for you. BRAVO, BRAVO AND HATS OFF.