As a way of spitting in the face of the current crisis, I am thinking about having an online “course” based on these notes.

Estimated start time:  in about 3 weeks (early to mid May 2020).  That gives some time to figure things out.

How will it work?  My initial thoughts are this.  It would be held on zoom, in the same “webinar” format as, for example, WAGON.   Much of the way in which I would like to explain things is already in the notes, so rather than just reading things out loud, I’d want to give a gloss on the notes, to set people up for reading them.   I’d also release “current” versions of each week’s reading.   (The notes have been steadily advancing since their last posting, but because there are sections that are temporarily in a mess, I haven’t reposted the entire thing in quite some time.)

Now for this to be useful and effective, most the action has to be done by the audience.  You have to think about things, ask questions, do problems, and get feedback on your solutions.   We need groups meeting to discuss the material, and problem sessions.  How could this work?  If you have ideas, please put them below.

My initial idea is something along the following lines.  Those who sign up to take the course in some serious way need to be organized into cells (better name needed!) of about ten people to start.  The group would be roughly at the same level, and might even know each other.  (Over time, the group might shrink; once it drops below 3 it might have to merge with another.)   The group would make a joint dropbox folder for their solutions.  They would somewhat randomly “grade” each others’ solutions, and more important, critique and give advice to each other.   Along with each set, they would decide on the questions and comments they found most important, and pass them “upward”, to the next level.  (There might need to be a next level, depending on numbers — perhaps 10 cells in each of the bigger organism?)  Then these would be posted here, or otherwise collected, and I could answer some in the next “class”.

In the “class”, we’d want some ways for people to ask questions.  Likely people could ask just in chat, and some other designated organizers could just ask them in real time when they feel it makes sense.  (I can think of a bunch of people who would be great at things like this — helping make this work.)

Perhaps there could be problem sessions, perhaps not necessarily run by me, and perhaps at the level of the groups of cells.

The final lectures could be put on youtube to be freely available.  (Still, I feel it is important that people try to watch things in real time, but don’t see how to encourage it.)  Perhaps start with one lecture per week (to let people jump on the train before it gets too far), then up to two lectures to week.  Ending at some indefinite point in the future.  Perhaps somewhat episodic (the first episode might be mainly things like “geometric spaces”, and we’d get to algebraic geometry only later.  Maybe some people might do a side “course”, perhaps developing complex algebraic varieties using the same road map.

(I’d ask that solutions to problems not be posted to the public.  Making them available can only make things worse for future generations — you’re not doing them any favors.  But questions on individual problems, of the sort that have come up on mathoverflow, seem good, because they generate genuine mathematical discussion and conversation.)

Intended audience:  I would want this (like the notes, and the courses they are based on) to be good for people at many levels.  From the high end:  experts in other fields who want to learn algebraic geometry.  Experienced algebraic geometers who want to see things in new ways (and who also would likely make very enlightening comments).  Graduate students in any area of mathematics wanting to get a deep look.  Graduate students with a good background who are considering working in or near algebraic geometry.  Undergraduates with particular backgrounds and experiences.   But I’ll assume a lot of mathematical maturity, and I would guess that many people wanting to follow along won’t be fully ready for this.  They shouldn’t waste their time, but some undoubtedly will.  I will deliberately not worry about them — they can get what they can from the experience, but you get what you pay for.

Caveats:

My personal bandwidth (as many of you know) is quite limited, and sometimes can suddenly disappear.  So I make no promises about anything.

Well, except:  because of possible volume, I can basically promise not to answer most emails related to this experiment.   I will deliberately deprioritize responding to such emails, because of other commitments (on which I am already overextended).  It’s best to then write to the community in the comments if you have something to say.

 

Things to figure out next…

Most important:  How to get the audience (self-)organized. 

How to get a list of people interested, and find out enough about them.

When to hold the lectures.  (Probably around 8 am Pacific will reach the highest number of people?)

and many many more questions…