Hi all,

I forgot in the last post to say that I wouldn’t start today (May 23) because I’m still wading through survey answers.  My intent is to start on May 30, but it is taking me long enough to go through the pseudo-registrations that I fear it will be the first Saturday in June before I’m ready.

Here’s where things stand.  I’ve largely gone through around 800 so far.  I’m surprised to report that the adjective I’d most use for this rag-tag collection of people is “charming” — it is really interesting seeing where people are coming from (mathematically, intellectually, geographically).

I’m hoping to start setting up groups, in the “Algebraic Geometry Syndicate” discord server, in bits and pieces, starting with the groups that are already built.    I will let you know when I think I have placed *everyone* who said they wanted to be involved at a level higher than “include me on mass emails” into some sort of group.  (There are some people who said they didn’t want to be involved, yet also asked to be in groups — I’ll figure out what to do on the fly.)    I’ll also let you know when I’m ready to announce the first lecture (so don’t count on it being May 30).  If you haven’t heard from me (at least indirectly) when I said everyone interested was put into a preliminary group (and you thought you told me you were interested), *then* let me know.

I’m going to give the lectures using zoom webinars, which I think allow 1000 participants.  This plausibly won’t be enough at the start, so I’m a bit nervous; but I’m going to put the lectures on youtube anyway, so possibly even at the start, the number of people watching live will be safely within the number allowed.  (I don’t think this will be a long-term problem.)

I think at least one person can’t access discord in their country.  This probably doesn’t matter much to them in particular, but if this affects other people who want to be in a group to discuss things, let me know, and possibly we can figure something out.

As I’m getting things ready to go, I’ll probably keep posting every few days to let you know where things are, even though these will be less substantive posts.

Hi everyone,

I’m gradually reading through everyone’s registration, and the numbers are large enough that it’s going to take me some time to do this (and put people into groups).  I’m done for tonight, and I’m through 453 of them.  But I may as well take advantage of this time to also give a few thoughts before things get fully underway.

(1) One question to throw out there:    when I put people into group (who aren’t already coming as a group), it makes sense for me to group people at similar levels who are in the same university, or national educational system, or geographical region.  Except maybe that’s not wise —having some random people from the same university thrown together may not be ideal.  I’m really not sure, and things will be pretty random, but I am open to suggestions (as long as you are open to my not taking your suggestions.)

(2) The group of you is very diverse — what you know and what you want to know varies hugely.  So what to do?  I know the number of participants will drop quickly once we get going, and people realize that they do not have the background to enjoy it, or the time to enjoy it.   But I don’t like the idea of being unwelcoming, and I know that people unused to this sort of thinking may feel that I’m being deliberately obtuse and needlessly forbidding.

One of the most important things while learning is to know why you care.  Someone else can tell you why you should care, or at least why they think you should care, but you should not take what they say on faith.

The problem with this project is that at the outset, I’ll have to assume that you already know why you care.   This is bad for a first course, which is why I do not recommend this as a motivating first course in the subject.  I don’t mean that you need to have taken a course in algebraic geometry per se — you just need to know enough to know why you might desperately want to learn about it.  Very many of you know why you care (and your reasons are appropriately not varied).  To the rest of you — I deeply apologize.


Hi everyone,

I’m just writing to clarify:

I’m now wading through the registrations.  The number of them (and the fact that I want to read them all, and then make groups, and then set the groups up) mean that it will be some time before I’m done (especially as I’m just doing it when I have some spare time late at night).

If you haven’t “registered” and still want to, please feel free to do so.

 Here (again) is the form.

At some point I’ll add you to the pool (although the longer you wait, the later I’ll get around to adding you, as it is far easier to bulk-process these all at once).

If you cannot access google products (in particular, this googleform), then you can send in your answers by email (and I’ll deal with them when I have time).

If by some chance we later find out that you thought you’d registered, and I don’t have it, then that’s no problem at all anyway.

(Keep in mind that this isn’t a competitive process — my intent is that everyone who wants to participate can participate.  What you get out of it is up to you.)

At some point I’ll likely figure out how to send email to everyone who registered, and certainly to those who wanted to be on the email list.  (This is one of the things you’ll have to deal with — one of many things I promise not to do promptly.)  I don’t want to send out masses of emails in general.

Thus:  If you *have* registered and haven’t heard anything back, don’t worry.   Nobody has.

Hi everyone,

Thanks to all of you who have filled it out. Googleforms does not send acknowledgements when you’ve submitted the form, so if later (after it is clear that I’ve written to registrants) by some miracle you think you’ve registered and haven’t, just let me know. Although I expect the number of participants will settle in the low triple-digits, the number of registrants is in the quadruple digits, so I’m really not going to be able to manage to deal with everyone individually, much as I would like to.

If you can’t access googleforms because of your location, please email me the answers to the questions (which are on this pdf), and I’ll copy them in by hand.

I’m going to extend the googleform “deadline” by one day (to 23:59 Pacific on Sunday May 17) because there are a few people who heard only recently about it.

I will certainly leave the form open after, but please understand that due to sheer volume, I don’t expect to be able to add people particularly efficiently.

Because of the numbers of people I’ll have to sort into groups, the first lecture is currently intended to be Saturday May 30 (two weeks from today).

More before long!

Time to launch.

It’s time to jump in and see what happens — with this post, we’re officially launching this experiment!  We’ll aim to meet roughly  8-9:30 am Pacific time (maybe with a 15-minute break in the middle?) on most Saturdays, hopefully starting on Saturday, May 23, or more likely on Saturday May 30.  (More details later, on this wordpress site.)

I’ll quickly discuss my plans.  Then, if you’re interested in joining in (at least at the start), please fill out the googleform here by midnight of Saturday May 16 (say, 23:59 Pacific time on that day).  The week after that, I will attempt to set up the working groups, along with some “field marshals” to help make it work, and depending on how this goes, I’ll post a version of the first few chapters of The Rising Sea by a few days before the first lecture.

The plan.

The initial plan is vague:  see who might be interested, and then try to make it work.   We have a diverse group of people with very different backgrounds in very different timezones.  I want to make this work as best as possible, given that my personal resources (time, attention, energy) are in particularly short supply.   I am doing this unofficially on top of other things, and my life is such that I expect there to periods when complications arise, and I’m forced to deal with other things for a few weeks,

So while I have an idea of what would make a good course for this kind of group (based on some embryonic ideas I tried out with an excellent bunch of students in an undergraduate algebraic geometry class not too long ago), instead I’m going to present what I can in the amount of time I have.  So I’m going to work through part of the Rising Sea notes.  

Here’s the problem.  I’ve worked through this material in a year-long class with a class that, while diverse, was much more homogeneous than the group we have now.  We covered the material in 30 weeks, with 3 to 4.5 hours of classes each week; let’s call it 100 hours.  So a one-hour lecture each week would mean two whole years, going at the same rate.  I’ve also heard that attending virtual lectures is more draining than attending actual lectures, so I’m reluctant to start at 1.5 hours per lecture.    But because there are no rules, I’m thinking of having a course on part of the material, hopefully (but not necessarily) followed by another, and another.  In particular, this isn’t a “summer course”; it will just be a (pseudo-)course, whose “first part” may take place roughly this summer.

The first part isn’t really then an algebraic geometry class.  I think I’d like to make a case for how to work with certain kinds of “geometric spaces” (schemes, varieties, complex analytic spaces, even manifolds), and then to apply that to develop the notion of a scheme or a variety.   Because the notes already exist, I don’t intend to just read them out — I’ll probably try to talk “around” them and motivate them, and expect you to read things in detail.

It would be easy for you to just watch lectures passively, and nod your head, but then you would get very little out of them.  This material (like much of mathematics) you only learn by actively grappling with it.   What you get out of this will depend on you more than me — I can try to set up the environment for it to make things as accessible as possible, but you have to do all the work.    For most people,  some sort of accountability makes a big difference — that, for example, is one reason we have grades in “real” courses.  In this case, I’m going to try using peer accountability.  I’d like many of you to work in groups, to write up problem sets, to grade each other’s problem sets (meaning: give feedback), to decide together what you think I should do.  Even if you’re working alone, if you have a larger group to which you periodically give updates to can only help.

So here’s the plan, to first approximation (and to be refined as we see who signs up).  I’ll try to put those interested into working groups (some of you already have groups).  You’ll have a reserved channel to chat on the Algebraic Geometry Syndicate discord server (don’t worry if you don’t know what discord is — it is trivial to use), on which you can chat synchronously or ascynchronously, by text voice or video.  You’ll ideally share a dropbox folder where you will hand in your solutions, to swap and grade.   The groups might somehow be parts of dekagroups, and “report” upwards with questions and ideas; the dekagroups might have channels too, and then one channel on top of them all to which everyone can post.    Perhaps there will be people who will serve as “field marshals” or “precinct captains” to help a dekagroup.      Questions, proposals, and ideas can be posted on the discord server or on the wordpress blog.  Your own group’s channels will be pretty private; it would be a place for you to chat (synchronously or asynchronously), and perhaps a few other people like me could drop in.

Ideally you’ll watch lectures (and side explanations, and problem sessions) in real time, and pose questions there in some way (I’ll figure that out — perhaps on the discord server, and some of the field marshals will just interrupt me).  Many of you will only be able to watch after the fact (the videos will be posted somewhere).  Each lecture will have an accompanying post on this wordpress blog.

What’s expected of you.

A lot; as much as possible.  And even more:  you are expected to watch out for others taking the class — help them learn, and be kind to them.  (It is easy to be unkind in these situations without realizing it, and mathematicians can be more socially clueless than most.)

What you should expect from me.

Remarkably little.   In order to make this workable to me, I think I will deliberately promise to not do a number of things.  Volume means that I’m already slow on email, so on things that are AGITTOC-related, don’t expect a response (although you might get one, even if late).   The better place to write to me will be on this wordpress blog or discord channel, as others can then reply too.  I think the best way for me to communicate with you is by blog post.  You won’t get a grade for the pseudocourse, or even a certificate of completion or participation.   I will not write you a letter of recommendation.     Lectures may be cancelled on short notice due to periodic crises here.   Indeed, the entire thing may suddenly stop, or be on indefinite hiatus.   The videos are going to be unprofessional and unpolished.   (I’ve never given on online lecture before!)    I may later deny being at all involved in this experiment, and when presented with evidence, will claim that my account has been hacked, and I will blame you.

… Okay, let’s see what happens!

Hi everyone,

This is a short update on the online course.    I’m sure it’s going to happen, in some form, although I’m finding the thought a bit scary.   My plan:  The next thing that will happen (publicly) will be a “let’s get going” post here, potentially in about a week, giving details and structure, and likely announcing the first lecture.    I have an email list (consisting of those who asked to be on it) which exists for a single use:  to let people know when this “let’s get going” post has gone up.  If you’re already following the blog, you’ll already know, so you needn’t be on the email list.  But feel free to ask to be on it.

I’m basically settled on technology.  (WordPress, discord, dropbox, zoom, youtube, googleforms.)  So right now I’m (in the interstices between other things) setting things up, and sketching out how this can work.

Standing caveats (I’ll be slow or unresponsive on email due to volume, etc.) apply.  (At the moment, I have ten emails on this topic needing a response, for example.)

One thing  on my mind I may as well ask now, as long as I’m here — are there any platforms that people will have trouble using?  (Everything I mentioned is free to use, but there may be countries that are unable to access some sorts of things.)  This is not going to be perfect, but I’d prefer to make things as accessible as possible.

Another thing to ask now:  if 8 am Pacific, once per week (say for 1 hour, but maybe as much as 1.5 hours), what day of the week?  I am wondering if it would be too radical to have it on the weekend — because people might have the most flexibility in their schedule.  I don’t know if this would cause obstructions for religious reasons, for example.     Or if on a weekday, it’s not at all clear to me what my own preference would be.  (One necessity is that the plan be workable for me most weeks.)

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.


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…