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…
April 19, 2020 at 12:50 pm
It’s been a few years since I’ve tried to make significant headway in this material, but this sounds like a great idea.
In the interest of self organization, anyone else interested in this can reach me at [deleted by ed.]. I was a math graduate student for a short time before I switched to computer science, if that helps anyone to match background/expectations
April 26, 2020 at 10:06 am
Thanks Chris! I’m going to delete your email address from your post so you don’t get spam, but add you to the list for the “initial email”, which will hopefully go out in the next week.
April 19, 2020 at 3:46 pm
Putting the videos up on youtube (or your website) relatively quickly might be helpful to people in timezones that are inconvenient for the course, whatever hour it ends up being given.
April 26, 2020 at 10:10 am
Good idea. I’m not sure how fast a turnaround might be regularly possible. Probably fairly fast. (I don’t know if it makes sense to quickly edit it — that depends on (i) how much editing is needed, and (ii) how much time I have)
April 28, 2020 at 2:02 am
I don’t see any particular reason why it should be necessary to edit an online math lecture. Are you planning to put a Stanford header on them (or special effects)?
April 30, 2020 at 11:36 am
Things often don’t appear as perfect as they appear after polishing!
May 2, 2020 at 10:06 pm
Perhaps to say more: if an eight-year-old were to wander in to show me something entertaining and interesting, it might not need to be saved.
April 19, 2020 at 3:56 pm
I think maintaining a forum dedicated to the course might be the best way to collect all questions and discussions into a single pool, where all participants can see and think about them.
April 26, 2020 at 10:10 am
Makes sense. Discord tentatively seems a natural home for such a forum.
April 29, 2020 at 9:22 am
Perhaps we could even choose a platform where people can “upvote” questions they like to make it easier for Ravi to choose what to address in lecture?
April 30, 2020 at 11:34 am
Is there something off-the-shelf that would do this? The downside is that I wouldn’t want to just listen to the top votes, as the participants are going to be coming from a wide variety of backgrounds.
April 30, 2020 at 1:15 pm
Perhaps if we end up using Discord and have a dedicated #questions channel, we could have people to react to their own messages with a :check:. Then if people have the same question, they can also react to the message with a :check: so you get a rough idea of how prevalent the question is.
May 2, 2020 at 1:24 am
Is it possible to set up a stackexchange forum for this? I haven’t used Discord much, but I would worry that a chat format might make it easy for questions to get lost in a flood of later messages. What happens if there are different people trying to answer different questions roughly simultaneously? Do the messages all get mixed together?
Something that “pins up” questions (with or without votes) might be a better medium to make all questions visible.
May 2, 2020 at 6:54 am
Maybe something stackexchange-like, but stackexchange itself has a pretty length community process for creating new sites, and they hold to it pretty strictly. I’ve spoken with some people at SE, and having a vibrant, ongoing community for each site, and the purpose of the site, is pretty core to their success. This would be somewhat different than their usual purpose and usual community. So while their technology might be useful for this course, I imagine they would simply say “no” to a request like this.
What about Disqus? $9/mo.
May 2, 2020 at 10:08 pm
So far, Robin Truax’s discord suggestion is winning (in my mind). (One criteria is: ease of use and lack of stress for myself.) ( I’m going to see what Disqus is about, not for this, but just in general.)
April 20, 2020 at 4:34 am
I would love that! I know some algebraic geometry even though I work in a different field – I did my master’s thesis on the proof of the Weil conjectures (based on Milne’s lectures) but somehow I never got the patience to learn schemes thoroughly (and my university didn’t offer a course in it).
April 26, 2020 at 10:11 am
Great, thanks! I’ll post here before long about next steps (meaning: hopefully in the next week).
April 22, 2020 at 5:26 am
Brilliant idea. I am a third-year undergrad student and was going to study Algebraic Geometry on my own. Learning things this way would be fun and much better!
May 2, 2020 at 10:15 pm
Thanks!
April 22, 2020 at 11:58 am
That’s amazing to read, I’ve studying he notes by my own and doing exercises in hartshorne as well. Now I’m finishing part 3, it would be amazing to have a class on this and discuss with other students, since there’s not a course in AG in my college. I’m very glad that you’re considering doing this.
May 2, 2020 at 10:15 pm
Thanks!
April 24, 2020 at 11:02 am
This seems like a great idea, I would love to get to start learning AG with a group of people instead of alone and solely from a textbook.
As a side note, 8 AM Pacific seems like the perfect time for me personally, but I also think that it would be best to fit into most people’s schedules. As someone living on the West Coast, most classes that I know of start around 10:30 AM Pacific, so there’s plenty of time.
April 26, 2020 at 10:12 am
Okay, so far 8 am seems the right choice….
April 26, 2020 at 3:11 am
One obvious question would be if there is a mailing list to be notified when the course starts, and to measure interest?
April 26, 2020 at 10:13 am
At this point, it should definitely happen, and I’ll post here (hopefully in the next week) to discuss next steps (probably to propose details, and a starting date). I’ll also email anyone interested to let them know when the post is up (people can just email me if they want to receive that first email).
May 2, 2020 at 10:09 pm
Also, I should have been clearer: the mailing list will be used (I think) only once, to let people know when things officially get going here. So if you’re watching this blog, you needn’t be on the list.
April 26, 2020 at 12:15 pm
Thank you so much! This is very exciting!
As for the timings, 8AM(Pecific) seems to perfect with the point of view of Indian time zone!, Since it’s already 8:30PM and further delay would only mean a lot of night owl’s in your class!
May 2, 2020 at 10:15 pm
Thanks — it looks like we have a tentative plan! (A follow-up question on which day of the week is best for people is in the next post.)
April 26, 2020 at 7:56 pm
This sounds awesome. (I’m a professor working on the algebraic side of theoretical computer science.)
A few logistical suggestions:
– Google form to gauge interest and collect emails. Could also collect time zone info, time availability, and relevant mathematical background (series of checkboxes with an “other” option probly preferable to open-ended) for later use in organizing cells
– Password-protected Piazza for group Q & A. Piazza has the option to ask anonymous questions (there’s an admin setting as to whether they’re truly anon or whether only admin can see who asked – generally I do the latter to prevent spam, but maybe not an issue here?). Anon questions can help people feel more comfortable asking.
– while live is certainly better, it’s important to recognize that, esp. during the pandemic, not everone has access to working mics, videos, or high-bandwidth enough internet access to participate live (beyond just time zone differences). So it’s important for those people to *also* have asynchronous options, ie recordings of lectures and asynchronous forum discussion
– in the interest of keeping momentum, it might make sense to try to coordinate sessions for the cells. Several could even take place simultaneously in a single Zoom using breakout rooms (giving more experienced people the chance to float like butterflies between rooms and offer advice/insights, or conversely giving a group that has a question a more immediate forum to ask some other groups “anyone know why blah?”)
April 27, 2020 at 7:46 am
Many thanks! I was already thinking along these lines, and your suggestions have helped clarify things a lot. In particular, they have the goal of being as easily as possible for both me and different levels of participants. Things are simple so as not to break; and also robust. The main variation I’ll end up proposing to what you say is to use discord instead of piazza. (Also, dropboxes for each of the delocalized working groups will allow people to do problem sets, and “grade” each others’ within the group.)
April 27, 2020 at 12:03 am
Thank you Prof. Ravi Vakil for providing everyone this fantastic opportunity to participate in learning Algebraic Geometry!
I am a mathematics faculty member at IISER Pune, India. I work in Automorphic forms and representation theory and I am very much interested in attending the proposed webinar on Algebraic Geometry.
I will coordinate a google classroom group devoted to this webinar with about 20-25 people (mostly advanced undergraduate students, some phd students and a couple of post docs) in my institute who are also interested in the webinar.
All of us will independently register and attend your talks online. We also plan to run some internal problem solving sessions ourselves in between your lectures. This can be synced with the activity (forming small cells and solving exercises) which you have suggested on the this forum.
If you plan to have a mailing list, I will be happy to email you with the list of all interested people in IISER Pune which can be added to the mailing list.
Early morning pacific time will suit us the best considering the time difference of 11.30 hours between pacific time and Indian standard time
Chandrasheel Bhagwat
April 27, 2020 at 7:42 am
Thanks! It looks like 8 am in California might be the best option — I probably can’t go earlier. It makes things difficult in some important time zones of course, but makes things possible at least as far as India.
May 2, 2020 at 10:10 pm
Also, I owe you an email response. Although perhaps it may be clear what it will say: basically, yes to everything.
April 27, 2020 at 12:38 am
Very exciting! Do you plan on uploading recordings of the lectures?
April 27, 2020 at 7:40 am
Yes, I do. I think there is great added value in seeing things in real time, but of course that is not always possible.
April 30, 2020 at 8:56 pm
Interesting! Why is there great added value for the student in seeing things in real time in a lecture course, as well as in a seminar?
May 2, 2020 at 10:25 pm
This is the beginning of a long (and in my opinion, important) discussion. But for now, I’ll say a couple of things, which might not be particularly surprising. First, it depends very much on the student (in many ways), the lecturer (in many ways), the subject material, and more. So this may not apply to you — or at least you may not believe it applies to you. Second, if anyone is unconvinced, I won’t strenuously argue against them — they are welcome to just watch recorded things.
But for those wanting to think about this, I’d suggest some questions to mull over, related to how we learn, and how we learn best. Probably most people will agree that (all things being equal) learning actively is more effective than learning passively. Learning in a conversation is in many ways more effective than learning watching a TV screen. (On the other hand, being able to pause a video, or take a break from a book to scribble in the margins, provide different advantages.)
So the interesting question is: if you are likely not going to ask a question in a lecture because the audience is big enough, what is the advantage of seeing it live rather than just watching the recording?
The related questions I’d want you to ponder: how do you get yourself into some active learning mindset? Why might it help being in the same room as other people? Or the same virtual room? Why do people go to see live music, even if they have bad seats? Why do people go to theater? Why do people go to community theater when they could watch the same things with highly experienced and talented performers? Why do people go to see live music, when they could instead listen to much better recordings?
My point isn’t that there is no value to recorded lectures — it is just a *different* value — a much more individual and less communal experience. Similarly, there is a lot of value in books! But there is a reason why we don’t tell undergraduate students: just go and read these books — all the information is in there.
May 3, 2020 at 1:58 am
Your book is a bit daunting because it has a lot of theorems and exercises which I’m sure you don’t cover it all in lectures and homeworks. I would watch your lecture just to see a stripped down and self-contained version of it so that I am then more easily prepared to tackle the rest of it.
May 16, 2020 at 10:10 pm
Sounds good — whatever works for you!
April 28, 2020 at 1:56 am
Have you thought about what technical format you plan to use for the course? I assume making slides for every lecture is too much work to be feasible. Will you be using a screen share + note-taking program on a tablet?
April 30, 2020 at 11:35 am
Yes, I’m intending screen share and note-taking on a tablet.
May 2, 2020 at 12:59 am
Sir, i m an ntegrated phd student in IISER MOHALI, India. Please add ke to the mailing list. My email id is [deleted]
May 2, 2020 at 10:29 pm
Thanks! I’ve deleted your email address from your comment to help avoid spam, but I’ve added it to the list where I’ll announce when we start.
May 2, 2020 at 1:29 am
Will you be testing out different options?
I’ve found that the choice of hardware + software makes a huge difference in terms of readability, amount of writing that can fit on the screen at once, etc.
May 2, 2020 at 10:31 pm
I’m certainly investigating different options, and it’s true that choice of hardware and software makes a huge difference. I’m making choices that I think are reasonably good, but far from perfect — one serious constraint is doing it in a way that allows me to do this around many other duties and obligations. So everyone should have very low expectations (which is already the case for those who know how little time I have around other duties and obligations…).
May 22, 2020 at 12:02 pm
On the subject of technical implementation…
What format will be used to run the online sessions? I think a normal Zoom meeting fits up to 300 people. There are formats like Zoom webinar which fit more, but make it more difficult for people to ask questions mid-lecture.
April 30, 2020 at 10:35 pm
Sir, I am a grad student in IISER Thiruvananthapuram, India. Please add my email in your mailing list (I think you can see my email I’d, in case you can not see, it is koushik16@iisertvm.ac.in). Should I send an email in your institute email address?
May 16, 2020 at 10:09 pm
Thanks! Hopefully the later posts clear all this up; let me know if not.
May 2, 2020 at 1:04 am
Sir, I have just finished a Master Thesis on Del Pezzo surfaces of degree 4 at the University of Basel, Switzerland. And plan to start of a PHD at the LSGNT in september 2020. The proposed course would perfectly match my interests, I indeed started reading your notes a few days ago to rigorously learn about sheaves and schemes.Please let me know once you have decided about the starting point of your online class and many thanks in advance to provide a broad audience with the chance to learn about the fundaments of modern algebraic geometry.
May 16, 2020 at 10:08 pm
Hopefully the next posts have answered your questions!
May 2, 2020 at 1:22 am
Just got to know about this recently. I hope it is not too late to register for it though. A bunch of us (advanced undergraduates and graduate students) want to join in from India. Could you clear up how do we sign up for this? Should I (and a few more people who are keen to join this) send you an email with all our email ids?
May 2, 2020 at 2:47 am
Hi! I’m an undergraduate at Harvard and would love to join this course! I took Math 137 this semester (Harvard’s undergraduate algebraic geometry) if that helps match levels. I have a couple of friends from Harvard who might be interested too. How can we join the mailing list/could you add me, please? Also, has the initial email you mention above been sent out already? Thank you! 🙂
May 16, 2020 at 10:06 pm
Hopefully you’ve now happily filled in the googleform!
May 16, 2020 at 10:35 pm
I have, thank you!
May 2, 2020 at 7:02 am
Just recently came to know about this course. Several students(upper undergraduates and graduate students) from my institute and I are keen to join this but I couldn’t find a way to sign up for this here. How do I do that? Should I email you the email ids of everyone in my place who want to be added to the mailing list?
May 16, 2020 at 10:06 pm
Hopefully this is now clearer — just see a later post, and write to me again if you have any questions. (I now have a number of emails regarding this pseudocourse that I’ve not had a chance to respond to.)
May 2, 2020 at 8:31 am
Good afternoon!
My name is Michela, I am a postdoc and I would be interested in your course. How can I join the mailing list? May you please add me too?
Thank you very much!
May 2, 2020 at 10:33 pm
Thanks for the email too — as I mentioned there, you’re now on the list! (Everyone in these comments will be on the list before long — I’m just doing things in bits and pieces when I get a moment.)
May 2, 2020 at 11:32 am
Hi, I’m a PhD student from Brazil. Since São Paulo time zone is UTC -3 and Pacific time is UTC -7, I wouldn’t be able to watch the live classes, but I could watch them if they were posted online. By the way, I’m starting chapter 8 of your book and this course would be very helpful to me both for the classes and the possibility to talk with another students about it.
If the mail list is already one could you include mine? And about discord, it has the advantage of creating as many rooms as one wants to, this would be helpful with the study groups.
May 2, 2020 at 11:56 am
Hi Fernando. I’m also a Brazilian studying algebraic geometry. If you would like to talk about it, feel free to email me at gabriel.ribeiro at polytechnique.edu. 🙂
May 2, 2020 at 5:20 pm
Hi, I’m graduating from UC Berkeley this semester and have taken undergraduate abstract algebra, plus a look at the content in our undergraduate algebraic geometry course (which uses Miles Reid’s UAG/UCA)… Fairly thin background, maybe, but I have a small community of friends, also interested in your course, with whom I should be able to form a support network. I also have a lot of free time for the next couple of months. I think I could get something out of the course… Worth at least a try to assess whether it would be a waste or not. I have checked the various boxes and I look forward to receiving updates. Thanks!
May 16, 2020 at 10:07 pm
Backgrounds are going to vary hugely. But having a group to work with makes a huge huge difference (which is why I am hoping that people who don’t know anyone will find new friends in their working group.)
May 4, 2020 at 3:24 am
Hello Ravi, I’m a graduate student from Institut Fourier (Grenoble, France), I would be interested by following the course ! I will start a PhD in AG this summer, but I would like to strengthen my knowledge in algebraic geometry (which I mostly learned through Positivity, Intersection Theory and Complex Analytic Geometry) by following one more course like yours.
And thank you for all your work, I found your notes very useful for my comprehension more than once !
May 16, 2020 at 10:05 pm
Thank you! (You probably have already seen this, but you can pseudo-register using the googleform announced in a later post…)
May 4, 2020 at 8:45 pm
Hello, I am an undergraduate student at the University and Vermont and I was interested in taking this course. Could you add me to the email list? Thank you for offering this!
May 16, 2020 at 10:04 pm
Thanks — please see the later posts with information on how to pseudo-register!
May 7, 2020 at 11:32 am
Hi,
I am an undergraduate student at the Chennai Mathematical Institute(CMI). CMI is renowned for C. S. Seshadri and algebraic geometry. I am interested in this subject. I am reading commutative algebra from Michael Atiyah’s book and beginnings of Algebraic geometry from Hartshorne’s classic text. I am eagerly waiting for this course. Please let me know how can I join the mailing list and this online course.
May 10, 2020 at 4:39 pm
Info now in the next post!
May 10, 2020 at 2:51 am
Thank you Prof. Ravi Vakil for providing everyone this fantastic opportunity to participate in learning Algebraic Geometry!
I am a Phd student studying Algebraic Geometry at Trento, Italy, and my supervisor is Prof. Roberto Pignatelli which send you an email some days ago about the request of our group to take part to the webinar.
I found a group with about 15-20 people from italian universities interested.
We also plan to run internal problem solving sessions ourselves in between your lectures. This can be synced with the activity (forming small cells of 4-5 members and solving exercises) which you have suggested on the this forum. Then we will exchange the solutions between us to correct them.
If you plan to have a mailing list, I will glad to email you with the list of all interested people or, if you prefer, you can add only me on your list and I’ll send the email of the meetings to my group periodically.
Early morning pacific time will suit us the best considering the time difference of 9 hours between pacific time and italian standard time
Kind regards,
Federico Fallucca
May 10, 2020 at 4:39 pm
Hi Federico — the announcement is now on the next wordpress post. (saving myself an email…)
May 25, 2020 at 12:04 pm
Hi! Thank you so much for the opportunity! I am an undergrad from UIUC and learning AG rn. It would be great if I can study it with other people! 8AM Pacific Time will not be a problem for me.
I was wondering if this course has started right now? If so, to where has it processed so far? If not, how can I register for it? Besides, can you add me to the mailing list if you have already set up one?
Thx!
May 29, 2020 at 6:08 pm
Later posts might say more, but: as of this writing, it’s looking hopeful (but not certain) that Saturday June 6 will be the first “meeting”. To sign up, go to the post titled “Further update”, and click on the link you find there.