I have never clicked on a UA-cam notification faster than this.Thank you good sir for posting again. I need to go get a cup of coffee first as it is almost midnight here :D
Dr. Borcherds, your excellent lectures on UA-cam make me study math again. I have a BS in math degree, but I always want to study math again because I think I don’t study math hard in college. Thank you for sharing your excellent lectures on UA-cam.
17:30 - 18:45 We probably need to do step (2) first and then step (1)? Although there's no elliptic function with only one pole on L, but we haven't shown that yet. So it might happen that in step (2), such a hypothetic function = P' times a function with two zeros on L, and poles not on L. Then we have to perform step (1) again.
When removing the poles from F, you can show that there are only finitely many poles in the repeating region to remove as the region is compact. If there were infinitely many, this would necessarily result in a convergent sequence of poles to a point within the region by the topological properties of compact spaces, and this point would fail to be holomorphic while not being an isolated point, contradicting F being meromorphic.
(Somebody) Tell us more about 4x**3 -g_2 x - g_3 - y**2. What is being identified? oh at 23:10 you answer this ... (p(z), p'(z)) is a phase space ... in C ... I didn't do so well at complex diff.eqs in college ... I almost want to say this is starting to make sense ...
19:48 I don’t understand why subtracting a linear combination of these would result in an expression with no pole at 0, surely the + … remains at the end and results in a high order pole still being present at the end?
Guessing that Liouville of Liouville's theorem is the same person mentioned in a quote attributed to Lord Kelvin. The quote is related to the result that the that "integral from plus-infinity to minus-infinity of e to the power of minus x squared dx is equal to the square root of Pi". Lord Kelvin said that "A mathematician is one to whom that is as obvious as that twice two makes four is to you. Liouville was a mathematician."
19:10 - 19:50 What's the point for assuming F is even, if we subtract by combinations of P and P'? I think the logic should be, since F is even with poles only on L, it is c z^{-2n} + ... near 0, so agrees with P^n up to constant.
I love the graphs in Janke's and Emde's book so much. I hope to be able to reproduce them somehow for a given complex function. Maybe somebody has done this already. I would like to know if this is the case.
18:39 what if the second even periodic function has poles at the zeroes of p'(z)? I'm not sure how we can conclude it has no poles except on the lattice.
Hi Richard. I already watched some of your oldest videos about the same subject....very interesting. My comment is : elliptic *curves* only with complex numbers ? ... I learned about elliptic functions for Poncelet Closure Theorem, where the space is the couple of (P,T) where P is a point in projective space P^2 on one conic and T a tangent to the caustic. How to "map" to complex numbers ?
When the world needed him most, he returned
😂
Math bender :)
He was busy playing Prince Philip in The Crown and one of the popes in The Two Popes.
Can we call you Professor Aragorn, because truly this is the Return of the King
The return of the jedi!!! Was waiting for this 1,5 years. Professor Brocherds is my favourite teacher!!!
Saw this on my recommended and clicked IMMEDIATELY! The GOAT of math lecturing; we are so privileged to have you Professor Borcherds
we missed you professor!! I wish you a great health and long life! much love
Glad to see you're back. Love the new beard.
Wonderful to see you back ❤
The legend returns!!!
Thank you for coming back to us, in such difficult times !
Let's goooooooo
I am from a thrid world poor country and i am sure that one day all of your free lectures would be helpful for me, thanks for that
This channel is a sanctuary. Welcome back Prof.
He has risen from the depths of Evans Hall! I love you. Thank you Jedi Borcherds
Yay! You have no idea how happy seeing the notification for this video made me! Thank you prof. Borcherds.
Sir, so happy to see you back. I was sad that we might have lost you as you have not posted much in a year.
The return of the king.
Good to see you back professor!!!
Return of the king!
wonderful to see You back Professor, best wishes.
Ecstatic that you're recording more lectures. Such a unique lecturing style and perspective. Thank you!
Good to see you professor.
I have never clicked on a UA-cam notification faster than this.Thank you good sir for posting again. I need to go get a cup of coffee first as it is almost midnight here :D
Welcome back professor
Great to see you back professor!
Let's go, glad to have you back!
So nice to see you again
Welcome Back professor and thank you for everything
Welcome back!!
you coming back is the best thing happened within this month! Thanks sir.
Good to have you back man !
It's awesome to see you back. Hope you are fine. Thank you Prof. Borcherds ❤
I think you just covered an entire term of lectures I took at undergraduate in 30 mins (and did it remarkably well!)
Dr. Borcherds, your excellent lectures on UA-cam make me study math again. I have a BS in math degree, but I always want to study math again because I think I don’t study math hard in college. Thank you for sharing your excellent lectures on UA-cam.
The best thing that ever happened to UA-cam!
Amazing!!
Thank you for making my life more positive...your videos give me the necessary inspiration to continue down this path
Welcome back! Love your videos
finally, our legend is back!
its great to see you back professor
@Richard E Borcherds
Great to see you back on UA-cam!
Keep up the good work!
--- Rich
master 👏👏
Reallly happy to see you making more of these! Your lectures are excellent
Glad to see you again Professor !
sir? Sir..!? SIRRR...!?!?!? WELCOME BACK 🗣️🗣️🗣️
Richard, Thanks for sharing this rare and specialized knowledge!
Even though I’m just an undergraduate Comp Sci. student I still love your videos professor!
So glad you are back!
Thats a great surprise :)
We missed you so much man, where did you go?! Have you been working on solving the Riemann hypothesis?😅❤
So glad to see you back !!
Welcome back Professor. Do you plan to continue the Algebraic Topology lecture series?
Welcome back sir , please if you can, post remaining vid lectures on alg topology , really looking forward .
Very interesting lecture. I'm a physics student, so this is the type of math that I miss out on. Thank you for putting this out there!
babe wake up new Richard Borcherds lecture just dropped
17:30 - 18:45 We probably need to do step (2) first and then step (1)? Although there's no elliptic function with only one pole on L, but we haven't shown that yet. So it might happen that in step (2), such a hypothetic function = P' times a function with two zeros on L, and poles not on L. Then we have to perform step (1) again.
Amazing lecture!!! ❤
Welcome back to UA-cam, prof. Borcherds !
The return of the chosen one
He’s back!
When removing the poles from F, you can show that there are only finitely many poles in the repeating region to remove as the region is compact. If there were infinitely many, this would necessarily result in a convergent sequence of poles to a point within the region by the topological properties of compact spaces, and this point would fail to be holomorphic while not being an isolated point, contradicting F being meromorphic.
The Return of the King
Great to see you again sir👍
Lord 🙏🏻👑⚛️♾️
If possible for you, could plz share link of video lectures of classroom courses which u had taken in UCB.
this is just what I needed today
(Somebody) Tell us more about 4x**3 -g_2 x - g_3 - y**2. What is being identified? oh at 23:10 you answer this ... (p(z), p'(z)) is a phase space ... in C ... I didn't do so well at complex diff.eqs in college ... I almost want to say this is starting to make sense ...
❤❤❤❤❤❤
What a nice intro. Thank you 😻
The GOAT is back
Return of the king!
Welcome back Prof!
19:48 I don’t understand why subtracting a linear combination of these would result in an expression with no pole at 0, surely the + … remains at the end and results in a high order pole still being present at the end?
Guessing that Liouville of Liouville's theorem is the same person mentioned in a quote attributed to Lord Kelvin. The quote is related to the result that the that "integral from plus-infinity to minus-infinity of e to the power of minus x squared dx is equal to the square root of Pi".
Lord Kelvin said that
"A mathematician is one to whom that is as obvious as that twice two makes four is to you. Liouville was a mathematician."
my guyy is backkk!!!!
The goat is back???
19:10 - 19:50 What's the point for assuming F is even, if we subtract by combinations of P and P'? I think the logic should be, since F is even with poles only on L, it is c z^{-2n} + ... near 0, so agrees with P^n up to constant.
Let’s goooooo🎉🎉🎉
I love the graphs in Janke's and Emde's book so much. I hope to be able to reproduce them somehow for a given complex function. Maybe somebody has done this already. I would like to know if this is the case.
Oh im excited for this!
why did we assume b to be an integer at 8:03 and does p(z) also generale all eliptic functions with noninteger poles?
happy t osee you return btw
At 19:50 it should be p, p^2, p^4, etc ... I take it ? Given that F is even and we just did the observation about the even powers of p
Instant subscribe, really interesting stuff
18:39 what if the second even periodic function has poles at the zeroes of p'(z)? I'm not sure how we can conclude it has no poles except on the lattice.
❤❤❤❤🎉🎉🎉
Welcome Back Professor! can any one tell me what's book he mention at 4:00 around?
The book is by Jahnke and Emde
not gonna lie, compared to measure theory ive been drowning in this is kinda relaxing.
He's back!!!
what are your favorite POVs in asoiaf?
6:30 second line: is it g in G or g in V?
In the example (with L) it becomes clear that it should be g in G
Hi Richard. I already watched some of your oldest videos about the same subject....very interesting. My comment is : elliptic *curves* only with complex numbers ? ... I learned about elliptic functions for Poncelet Closure Theorem, where the space is the couple of (P,T) where P is a point in projective space P^2 on one conic and T a tangent to the caustic. How to "map" to complex numbers ?
I can't understand the authors of the book mentioned in 3:53 (I'm sorry, I'm not English native speaker). Could somebody please tell us?
Welcome back!
❤❤❤
Nice
welcome back! :)
I remember this same content uploaded previously
终于更新了，呜呜呜
yeeeeeeeeeeeeeeeeee (take that apophis)
yeeeeeeeeeeeeeeeeeeeeeeeeeee
Maths is love
Thank you