Thank you so much for taking us through the K-theory wanderland! This is my first exposure to K-theory and oh ! This is beautiful ..! This will stay with me forever!
Thank you for this nice first video on algebraic K-theory, I'm looking forward to more! While I don't think this is suitable to a "general audience" (most of the friends I have who specialize in applied math would be lost at certain places, I'm sure), I believe this is really a cool project for people interested in this kind of math! I really need to start picking up some algebraic K-theory...
Nice! This is what I was looking for. I am a physicist trying to study k-theory for my thesis project, and literature on this topic is kind of hard for me, but this video encouraged me to keep going :D I will follow the next videos!
I'm curious about how one proves that K_0(Z[t_1,...,t_n]) = Z. Does one do it by legitimately understanding modules over that ring or is there some kind of "contractibility" going on?
It's admirable that you're trying to popularise an advanced maths topic. However I don't think this is accessible to anyone without at least a solid undergraduate maths foundation. You would have lost everyone at the group completion stage. It's not an intuitive concept at all for people without formal maths training. I doubt even someone with a maths PhD in a different field would easily follow the arguments in computing \pi_0 and K_0.
yes, I am more or less assuming that people have a math undergrad degree, and it still won't be fully accessible for everyone, but I hope to share some ideas nonetheless
@@math-life-balance As someone with a degree in theoretical physics, this has in one short video been the best introduction to K-theory I've seen. I hope you make more, especially about Bott Periodicity! My interest in K(x) comes from needing it to understand modern papers on topological superconductivity. If I can't encourage you to make more videos, can I pay you to tutor me?!
folks, I was afraid to open the comments section for 3 days, and they turned out to be so sweet, thank you!!
Thank you so much for taking us through the K-theory wanderland!
This is my first exposure to K-theory and oh ! This is beautiful ..! This will stay with me forever!
These are wonderfully Helpful...
Gives me the courage to pick a textbook.
I think this is an exceelent video! Great content, great editing, great presentation. Thank you so much! I am excited for the next one!
We need more videos bringing down advanced topics back to Earth like these. The RH series coming out now is also amazing.
Thank you for this nice first video on algebraic K-theory, I'm looking forward to more! While I don't think this is suitable to a "general audience" (most of the friends I have who specialize in applied math would be lost at certain places, I'm sure), I believe this is really a cool project for people interested in this kind of math!
I really need to start picking up some algebraic K-theory...
Please keep doing this! Thank you
Nice! This is what I was looking for. I am a physicist trying to study k-theory for my thesis project, and literature on this topic is kind of hard for me, but this video encouraged me to keep going :D I will follow the next videos!
great, good luck!
i am soo looking forward to this series
Loved the video, and actually understood some parts of it!
great! :)
Thank you. That was the first time in my life that I understood more than 2% of any K-theory material hahahaha
I enjoyed this video, thank you so much 💜
Only reason I have heard of K theory because D brane Ramond- Ramond charges can be interpreted in K theory terms but that is as far as I know.
Anyone know if Peter Haine and Eduard Heine are connected? What about Will Cavendish and Henry Cavendish?
Very fine video.
I still understand almost nothing about algebraic K-theory, but I feel intrigued.
Math-life crisis is the best crisis I'll ever have!
Awesome video!
Is the K_0 of a (lest say compact) smooth Manifold always a finitely generated group?
I'm curious about how one proves that K_0(Z[t_1,...,t_n]) = Z. Does one do it by legitimately understanding modules over that ring or is there some kind of "contractibility" going on?
This follows from a theorem due to Quillen and Suslin stating that:every finitely generated projective module over a polynomial ring is free.
It's admirable that you're trying to popularise an advanced maths topic. However I don't think this is accessible to anyone without at least a solid undergraduate maths foundation. You would have lost everyone at the group completion stage. It's not an intuitive concept at all for people without formal maths training. I doubt even someone with a maths PhD in a different field would easily follow the arguments in computing \pi_0 and K_0.
yes, I am more or less assuming that people have a math undergrad degree, and it still won't be fully accessible for everyone, but I hope to share some ideas nonetheless
@@math-life-balance As someone with a degree in theoretical physics, this has in one short video been the best introduction to K-theory I've seen.
I hope you make more, especially about Bott Periodicity! My interest in K(x) comes from needing it to understand modern papers on topological superconductivity.
If I can't encourage you to make more videos, can I pay you to tutor me?!