Richard E Borcherds
This is mostly mathematics lectures for graduate courses on algebraic geometry, commutative algebra, and group/rings fields. There are also a few math talks at an undergraduate or high school level and a few short courses on other topics such as complex analysis, theory of numbers, modular forms, category theory, representation theory.
For the current list of courses, see the playlists page for this channel.
For anyone who wants to copy the format of the lectures, I'm using a program called OBS studio with a logitech webcam and a document camera and a yeti microphone. I use sketchpad for the thumbnails.
Richard E Borcherds
Curt Jaimungal has just posted another interview with me on his channel:
3 years ago | [YT] | 103
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Richard E Borcherds
The winner of the poll for next topic is "algebraic topology". I will not be following any particular book, but will recommend "Algebraic Topology" by Allen Hatcher, because he has generously made the pdf freely available from his home page pi.math.cornell.edu/~hatcher/
I'll be taking a break before starting the lectures for this, and will probably produce lectures less frequently than before.
5 years ago | [YT] | 447
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Richard E Borcherds
This is the poll for the topic of the next few lectures. If you have any suggestions not on the list below put them in the comments, and they may appear in the next poll.
I will take a break after the modular forms lectures, and probably produce videos less frequently for a while, so the lectures for the next topic will not appear immediately.
5 years ago | [YT] | 211
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Richard E Borcherds
Curt Jaimungal (independent film maker with a background in math and physics) recently interviewed me for his youtube channel, and you can see the result here: https://youtu.be/xu15ZbxxnUQ
(I have not dared to watch it, but I think it consists of me rambling on about math, the universe, and everything, in answers to various questions from his viewers.)
The first modular forms lecture should appear on Saturday March 20 if all goes well.
5 years ago | [YT] | 219
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Richard E Borcherds
The clear winner of the poll for next topic is "modular forms" so I plan to start on this in a few days, after doing a few topics in complex analysis needed for modular forms.
I will not be following any particular book, but if anyone wants a recommendation for an introductory book I suggest "A course in arithmetic" by Serre or "Modular functions and Dirichlet series in number theory" by Apostol. (You should be able to get free pdf files of these from springerlink if you belong to an institution that subscribes.)
5 years ago (edited) | [YT] | 325
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Richard E Borcherds
This is a poll to help me choose the next topic for lectures. The possible topics below are based on the previous polls and comments to the post from a few weeks ago. If you prefer something not in this list mention it in the comments: if someone suggests something in a comment you would like to see then you can "vote" for their suggestion by "liking" the comment, and if enough people "like" a suggestion I may add it as an option to the next poll.
5 years ago | [YT] | 194
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Richard E Borcherds
Q&A
As an experiment, I'm thinking of producing a Q&A video where I answer questions suggested by viewers. So if you have a suitable question, ask it in the comments below.
This channel is mainly about university-level mathematics, but non-mathematical questions are also OK.
UPDATE: Thanks to everyone for the questions. To avoid the video getting too long, I am cutting off questions now, and will be making the video soon. If you have a question please keep it for the next Q&A video.
Another update: I've now made the video (so I really wont be able to include any more questions). It should appear soon.
5 years ago (edited) | [YT] | 305
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Richard E Borcherds
The winner of the poll for the next lecture course is complex analysis, which will probably start on Saturday and run for a few weeks. This will (at least initially) be an introductory undergraduate course. I will not be following any particular text, but if anyone wants a suggestion for something to read I recommend "Complex analysis" by Ahlfors.
The Lie groups course is not finished and I will probably return to it sometime.
On Friday in the gap between lecture series there will probably be a one-off lecture on Maryna Viazovska's use of modular forms to solve the sphere packing problem in 8 dimensions (suggested in the comments to the previous post).
Correction: As several people pointed out to me, the occasional spikes in numbers of new subscribers to this channel are nothing to to with youtube's algorithms, and are caused by mentions on social media.
5 years ago (edited) | [YT] | 329
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Richard E Borcherds
This is a poll to help me choose the next topic for lectures. I'll probably pause the Lie groups lectures in a few days (but intend to come back to it later). The possible topics below are based on the comments to the post from a few weeks ago. If you prefer something not in this list mention it in the comments: if someone suggests something in a comment you would like to see then you can "vote" for their suggestion by "liking" the comment, and if enough people "like" a suggestion I will add it as an option to the next poll.
(On an unrelated topic, can anyone explain why the number of new subscribers was so high yesterday (about 20 times normal) while the number of views stayed much the same? My guess is that it may be some strange side effect of youtube's algorithm for detecting fake subscribers.)
5 years ago | [YT] | 164
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Richard E Borcherds
Stavros from the channel www.youtube.com/channel/UCjUs...
has written up some notes for some of the Lie groups lectures and is kindly making them available in the comments for the videos, starting with https://youtu.be/pAuRWd8dpvE
I'm having trouble getting the links to his notes to work properly, so until this is sorted out you have to cut and paste the links. I have recently changed the settings for comments so that anyone can post links, but for some reason youtube rejects his link. If anyone can see what the problem is please let me know in the comments.
If anyone else wants to post their notes on the lectures this does not need permission from me: my videos are released under a Creative Commons license that allows anyone to create derivative works, and you should now be able to add links in the comments (except that for unknown reasons this sometimes doesn't work...). If I notice any notes I will try to "pin" them so they appear at the top of the comments sections.
A minor downside to allowing links in comments is that this channel is now getting linkspam. If it annoys you, you can report it to youtube by moving the mouse to the right of the comment until 3 dots appear, and clicking the dots to bring up a menu with an option to report the comment. (I'm not sure what effect this has; maybe it helps to train some AI that youtube uses to filter spam.)
5 years ago | [YT] | 31
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