I have never clicked on a TH-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 TH-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 TH-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.
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?
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.
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.
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.
(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 ...
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.
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."
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!!!
Glad to see you're back. Love the new beard.
we missed you professor!! I wish you a great health and long life! much love
Wonderful to see you back ❤
Saw this on my recommended and clicked IMMEDIATELY! The GOAT of math lecturing; we are so privileged to have you Professor Borcherds
Let's goooooooo
The legend returns!!!
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.
Thank you for coming back to us, in such difficult times !
The return of the king.
Return of the king!
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
Good to see you back professor!!!
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.
Welcome back professor
Let's go, glad to have you back!
Good to have you back man !
Good to see you professor.
Welcome back!!
finally, our legend is back!
Ecstatic that you're recording more lectures. Such a unique lecturing style and perspective. Thank you!
Great to see you back professor!
So nice to see you again
wonderful to see You back Professor, best wishes.
So glad to see you back !!
I have never clicked on a TH-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
Amazing!!
The best thing that ever happened to TH-cam!
master 👏👏
Welcome back! Love your videos
It's awesome to see you back. Hope you are fine. Thank you Prof. Borcherds ❤
Welcome Back professor and thank you for everything
@Richard E Borcherds
Great to see you back on TH-cam!
Keep up the good work!
--- Rich
I think you just covered an entire term of lectures I took at undergraduate in 30 mins (and did it remarkably well!)
you coming back is the best thing happened within this month! Thanks sir.
sir? Sir..!? SIRRR...!?!?!? WELCOME BACK 🗣️🗣️🗣️
its great to see you back professor
Dr. Borcherds, your excellent lectures on TH-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 TH-cam.
Reallly happy to see you making more of these! Your lectures are excellent
Thank you for making my life more positive...your videos give me the necessary inspiration to continue down this path
Glad to see you again Professor !
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!
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!
Thats a great surprise :)
What a nice intro. Thank you 😻
We missed you so much man, where did you go?! Have you been working on solving the Riemann hypothesis?😅❤
Amazing lecture!!! ❤
Welcome back sir , please if you can, post remaining vid lectures on alg topology , really looking forward .
The return of the chosen one
Welcome back to TH-cam, prof. Borcherds !
The GOAT is back
He’s back!
Return of the king!
this is just what I needed today
Great to see you again sir👍
babe wake up new Richard Borcherds lecture just dropped
The Return of the King
Welcome back Professor. Do you plan to continue the Algebraic Topology lecture series?
Welcome back Prof!
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.
my guyy is backkk!!!!
Instant subscribe, really interesting stuff
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?
Oh im excited for this!
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.
The goat is back???
welcome 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.
He's 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.
(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 ...
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
Lord 🙏🏻👑⚛️♾️
Welcome back!
not gonna lie, compared to measure theory ive been drowning in this is kinda relaxing.
If possible for you, could plz share link of video lectures of classroom courses which u had taken in UCB.
Welcome Back Professor! can any one tell me what's book he mention at 4:00 around?
The book is by Jahnke and Emde
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.
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."
Let’s goooooo🎉🎉🎉
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
❤❤❤❤❤❤
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 remember this same content uploaded previously
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?
Nice
终于更新了，呜呜呜
Thank you
❤❤❤❤🎉🎉🎉
Maths is love
❤❤❤
yeeeeeeeeeeeeeeeeee (take that apophis)
yeeeeeeeeeeeeeeeeeeeeeeeeeee