**EDIT**: Please click “AG Seminar” above for information.

This term I’m doing research, taking a course, auditing a course, and helping coordinate another. In this post I’ll discuss the last point.

This was mentioned a while ago on the PMC group, but for anyone who’s not aware, I’m part of a little group of students planning to coordinate a kind of “seminar” on algebraic geometry this term. As a disclaimer, please note that what follows is merely intended to represent my own opinions and feelings, and none of this has really been discussed at length with others in the group. I’m certainly open to ideas or criticisms from others.

We can call this [seminar/interest group/whatever it is] “PMATH 899” for reference purposes even though it’s not a real course. I choose the number 899 not because I think it’ll be comparable to actual 800-level PMATH courses, but rather to suggest that one of its purposes is to serve as a prelude to PMATH ~~900~~ 955, which is being offered this coming Fall.

We don’t exactly have a detailed outline of what we want to do, but we’re trying to encourage as many interested people to participate as possible. We will strive to make the material comprehensible even for those who haven’t taken PMATH 764. Indeed, PMATH 764 spends a lot of time on topics which are rather orthogonal to what we plan to discuss — topics such as intersection theory, for example. Hence, it seems like the plan is to spend the first couple of meetings mostly getting familiar with the machinery of algebraic varieties (affine and projective), coordinate rings, function fields, and so on. There’s no need to grind through any difficult theorems relevant to this material; we can simply take on faith any facts we need. If you’re taking 764 this term, it will probably end up filling in those details anyway. Even if you’re not, there’s not much need to worry since the technicalities of those proofs won’t be of much importance in the context of 899.

The tentative plan is to book a room, and meet Wednesdays 4:30 — 6:30pm, starting next week, so that the first meeting is on the 15th. There will be some amount of material presented, but ample time will be left for discussion amongst the group. The speaker will probably change each week depending on interest and availability. Of course, I intend to contribute as much as I can (or as much as I need to — the of the two, haha) in this regard. If it’s more convenient, we could try meeting twice a week.

Here’s a general idea of what kind of material the first few meetings might contain:

- algebraic varieties, coordinate rings, function fields… (basic machinery from 764)
- categories, functors, natural transformations… (will be as brief as possible)
- presheaves, sheaves, morphisms of sheaves…
- spectra of commutative rings, locally ringed spaces, affine schemes… (working towards the definition of a “scheme”)

If anything above sounds intimidating and you feel like everyone else is already going to know this stuff and breeze through it, I assure you that’s far from the truth. In my case, at least, I’ll have to work diligently to grasp these new concepts, especially since I’ll be one of the people speaking during the first few meetings.

Please get in touch if you’re interested in participating. I think we’ll have no problem making this a success with all the inspiring people around. And of course, feel free to share it and stuff, to spread the word. Further details about the meeting location will be posted on this blog (probably later this week), and likely scrawled on the blackboard of the PMC as well for good measure.

Do you think you will be posting any notes or resources online? I would love to follow along, but I am unfortunately away from Waterloo this summer.

For that matter, what are your thoughts on setting up some collaborative online resource?

I may look into setting up a discussion forum or something along those lines. If taking notes doesn’t become too formidable a task, then I will be posting those as well. Others have asked about video recordings, but it’s unlikely that will occur, mainly since we are trying to keep things informal and collaborative.