One of the mysteries for a young person encountering modern mathematics is "what happened to continued fractions?" It is helpful in the pedagogical context to explain that continued fractions are just iterations of GL2(C) in another language, because the maps (az+b)/(cz+d) are just the 2 by 2 matrices (a b ; c d)under composition, so that the theory of GL2(F) is really the theory of continued fractions modernized. But many of the classical results don't have obvious translations to the modern abstract form, where you are talking about the group properties mostly, for instance, the representation of various analytic functions by continued fractions is mysterious (at least to me). I believe some of the classical results could still give something new in the modern language, if translated.
I think that QFT has bested him, like it has bested every mathematician. But I agree that it would be nice having Prof borcherds talk about his interactions with QFT.
He talks about it in his interview with Curt Jaimungal on the Theories of Everything channel. But he just says a few scattered remarks about QFT specifically, mainly about how it doesn't make sense from a mathematically rigorous point of view. This makes it very intriguing for me why it nevertheless gives such amazingly accurate results
Thank you very much for these very insightful videos. I appreciate the clarity and lucidness of your presentation. You never sacrifice those in favor of "formal rigor". I am wondering if you could cover the subgroups of GL(2), namely the maximally compact subgroups and the groups corresponding to simple Lie algebras? I understand that the topic is highly dependent on the field in question, but your insight and explanations are extremely valuable nonetheless.
RETURN OF THE KING
Gandalf the white teaching us math
Lord of the Fields
Wish u long healthy life! Thank you for this 🙏
Please never ever retire
seeing a new upload from you, Professor, is always a pleasant surprise; wish you the best in your mathematical endeavors.
One of the mysteries for a young person encountering modern mathematics is "what happened to continued fractions?" It is helpful in the pedagogical context to explain that continued fractions are just iterations of GL2(C) in another language, because the maps (az+b)/(cz+d) are just the 2 by 2 matrices (a b ; c d)under composition, so that the theory of GL2(F) is really the theory of continued fractions modernized. But many of the classical results don't have obvious translations to the modern abstract form, where you are talking about the group properties mostly, for instance, the representation of various analytic functions by continued fractions is mysterious (at least to me). I believe some of the classical results could still give something new in the modern language, if translated.
The legend...
Missed your vidoes :)
we all missed you ;) ❤
I enjoy all of your lectures and courses, thank you for your generosity and god bless you. Wishing you the bests. Farhad Abdi
He's back people
Your videoes are so nice and clean!
Hey Prof . Borcherds, can you please explain your current work on QFT?
I think that QFT has bested him, like it has bested every mathematician.
But I agree that it would be nice having Prof borcherds talk about his interactions with QFT.
He talks about it in his interview with Curt Jaimungal on the Theories of Everything channel. But he just says a few scattered remarks about QFT specifically, mainly about how it doesn't make sense from a mathematically rigorous point of view. This makes it very intriguing for me why it nevertheless gives such amazingly accurate results
Welcome back me lord. 🍻
Thank you King
Please do not leave us alone!
Thank you very much for these very insightful videos. I appreciate the clarity and lucidness of your presentation. You never sacrifice those in favor of "formal rigor". I am wondering if you could cover the subgroups of GL(2), namely the maximally compact subgroups and the groups corresponding to simple Lie algebras? I understand that the topic is highly dependent on the field in question, but your insight and explanations are extremely valuable nonetheless.
Love it! Do you have plans to finish the Lie group series?
Thank you
The GOAT
yup, another richard e borcherds classic
ye
yeeeeeeee
'a bit like the complex numbers - only more so' very open ended