@BrianMScott I don't think there is any good answer given the SE platform. However, if we developed our own software then we could easily accomodate everyone's viewpoint. I've actually given much thought to this. I wonder if we have enough volunteers that we could start a sourceforge project...

@MarianoSuárezAlvarez My first concern by a large margin is to answer the OP's question. I try to do so with an eye towards future utility of the answer, but that's very much a secondary consideration.

@BrianMScott How would you describe a good hint?

Hello everyone! Could anyone outline the requirements for Ravi Vakil's notes on algebraic geometry? Just a broad outline will suffice, and when I say requirement I mean only the 'logical' ones, not counting familiarity with something that might help. Thanks for any help!

@BillDubuque I'm afraid that will bleed quickly to death...

Here other people give us software and servers. It might not be perfect but at least it is pretty decent.

@BillDubuque A sourceforge project with our "own" software.

@skullpatrol One that isn't too obscure and seems likely to point the OP in the right direction. I tend to give pretty broad hints, because I've found that it's very easy to overestimate how much information one has actually given.

@FortuonPaendrag Thanks!

@JonasTeuwen Servers are easy to come by.

@LovrePešut It's longer than the Algebraic Geometry I have on my shelf! I think it would be easier if you explained what your background is...

@ZhenLin I must confess that I didn't find (1) particularly obvious either.

Okay, but expensive, and somebody needs to be an administrator and we are mathematicians (not that I claim that a mathematician cannot do that, but I think a mathematician prefers to do mathematics).

But it might be an idea, I would be in for that.

@BrianMScott Hm. Maybe I'm weird then. Because to me, (2) is the non-obvious one.

@ZhenLin I didn't actually think about it; it may be that I'd have found both of them non-obvious! :-)

@BrianMScott Could you provide me with a short example please?

@JonasTeuwen Mathoverflow already does all this. It's not difficult. What's difficult is corraling enough competent software developers.

Okay, fine :-).

MO is completely run by SE

@MarianoSuárezAlvarez By an old much simpler version of SE. And at least one person is working on a possible replacement.

yes

but it is completely run by SE.

I probably don't understand what you mean by "MO already does all this"...

@ZhenLin I wasn't specifically interested in whether it is the right book for me, but I'm rather interested in the 'logical' prerequisites (for the future).

@skullpatrol This answer is a fairly good example. Here is one at a higher level that I thought had to be more extensive.

@Lovre: So you want to study the subject, rather than the notes?

@MarianoSuárezAlvarez I was talking about the servers, and some admins stuff, which I thought was not originally all at SE. In any case my point is that that is far from the most difficult part of such a project.

all that is done by SE and has always been

a couple of MO users have the equivalent of mod-access to it

I used to do a lot of server administration, but I wouldn't do it for free 8-).

Unless it is really cool...

@BrianMScott Thanks, I now understand :-)

Hard drive fail -> go to the data center (or use dedicated servers, more expensive).

@skullpatrol Ha.

@JonasTeuwen I suspect that we do already have enough software expertise in the community, but probably not enough combined spare time.

Server admin work is not too rewarding, indeed.

@ZhenLin: Not really, I'm interested in prerequisites for those notes, but not necessarily because I want to learn from them (or learn right away), which is why I don't think my current background is too important.

@JonasTeuwen what's that suppose to mean?

Yes, I am pretty sure that is correct that we have enough capable people. But get them do this...

But it's quite fun to have lots of machines at one's fingertips.

@ZhenLin Yeah, go at 2 AM to a data center to replace a bloody hard drive!

@LovrePešut: I don't think you need much. Those notes are very comprehensive and cover a huge range of material. You probably only need a decent undergraduate algebra background, and maybe a bit of point set topology.

@Jonas: I admit, I haven't actually had to do on site work...

@ZhenLin: I see, thanks for the help.

Okay :-). We had about 150 servers and two people. Then I get called: "HD failure. Your turn! Good night!"

@Lovre: But, the thing is, just because the logical prerequisites are low doesn't mean it's going to be easy to learn. You should probably do an introductory algebraic geometry course first – something with varieties, or at least, curves. See my answer here.

@ZhenLin: Yeah, I am aware of that. Your post is pretty helpful, thanks. ;)

@ZhenLin Hahaha, the compliments your answers get you :) . Are you a graduate student?

Still not yet...

@ZhenLin Do you already have your eye on something? :-).

Should be easy with your qualifications, if you're willing to move.

@Jonas: Yeah, I've more-or-less secured a Ph.D. place in Cambridge now.

@ZhenLin Great!

That's really cool.

Thanks!

Indeed. Congratulations!

@ZhenLin Beautiful place to be, especially along the Backs on a sunny day.

But I can imagine it can be quite though to work there. I already now experience quite a lot of stress... I hope it's worth it in the end 8-).

Hah, yes! After 4 years of being in a city-centre college I'm going to be in a college on the river!

@ZhenLin Where have you been up to now?

The same Cambridge.

Convenient!

Verily.

@BrianMScott KP is teaching a course on topologies on function spaces :-).

@JonasTeuwen Sounds like fun.

I think it is based on the stuff in Engelking's book. I have seen it nowhere else.

Not my very favorite kind of thing, but his tastes are a bit broader than mine.

He's been sneaky. He calls the course: "Advanced topics in analysis".

So how many suckers amongst the analysis students will fall for that?

Two.

Me and some other guy :-).

(There are no analysis students, only two PhD students).

Ah, I see. That does make it simpler.

People here like applied stuff...

shudder :-)

We had a 24-lecture graduate course last term about "Topics in Calculus and Algebra". I dare you to guess what it was actually about!

"Topics in Mathematics", essentially.

@ZhenLin Something to do with $\sigma$-algebras and measures?

It was a course on $(\infty, n)$-categories and topological field theory...

heh

Good grief!

The lecturer said that the choice of title was so that he could get away with lecturing just about anything.

So Dylan was more or less right!

Indeed.

@DylanMoreland +1

I quote from the official description, "This course is an introduction to basic homological algebra and deformation theory as it occurs in algebraic geometry, topology and physics." "We might also study the fundamental work of Kontsevich on the B-model, and the Tamarkin-Tsygan idea of ”calculus”. (The somewhat flamboyant title is theirs—it refers to the structures for arbitrary algebras that generalise the differential forms/vector fields package that are attached to smooth manifolds.)"

"There will be no particular prerequisites, other than the basic courses."

For a suitably generous definition of basic.

Oh, hey, I know those people.

Very generous indeed.

@BrianMScott Something like "for sufficiently small values of 1"?

@Dylan: That's better than me then, and I went to the first half of the course!

@JonasTeuwen More like 'sufficiently small values of $100$', I think.

Er, just Tamarkin and Tsygan, I guess. They're faculty here. They both seem to be outrageously good at thinking about homological algebra.

Hi everybody!

hi

@PeterTamaroff You sound distressingly cheerful and energetic. :-)

Anyone knows how can I acces this article?

Ah. I'd quite like to find out more about this "calculus" they are purported to have invented.

@BrianMScott Really? Maybe it is the plushies that convey that feeling. I'm rather in for a good coffee and I have to study for my midterm tomorrow, which isn't really cheering.

@ZhenLin Are you going to Michigan, by the way?

@Dylan: No, I'm going to Cambridge now.

Ahh. Big mistake :)

I just remember that you had an offer from there.

that calculus is the mixture of two things: the fact that the usual calculus can be expressed in terms of differential forms and multivector fields on a manifold, and the fact that the Hochschild homology and cohomology of the algebra of smooth functions on a manifold are precisely the forms and multivector fields, respectively

so if you now start with an arbitrary algebra $A$, Hochschild homology and cohomology provide you with a calculus based on $A$ instea of on $C^\infty(M)$.

this works even if $A$ is non-commutative, or a DGA, or...

@MarianoSuárezAlvarez That sounds interesting. And I'm sticking to that thought!

the interesting this is that it is not purely formal, of course

(they have used it to get local index formulas and other wond'rous things)

@Mariano Ah. That explains the comments my Lie Algebras lecturer was making w.r.t. that course. I have completely forgotten what Hothschild cohomology is though (but not that I ever even knew the definition)!

for this purpose, it is the abstraction of what forms and multivctor fields are :)

Hochschild (co)homology is to algebras what de Rham cohomology to manifolds, very very roughtly, and group cohomology to groups

So, it's derived functor cohomology for some functor...?

sure

You people talk about scary stuff :-).

saying that never explains anything, though :)

Is it possible for anything good to come of this?

@Mariano: Sure, but it's a starting point!

Actually, I take that back. I've just opened Weibel and the definition by simplicial modules is more convincing.

@DylanMoreland Are you saying my answer is no good?

@DylanMoreland Hmm, those things make me think people think more about doing something than actually think while doing it...

Avoid visual mathematical calculations while driving!

@ZhenLin, that definition is almost disjoint from applications :)

@MarianoSuárezAlvarez You make that sound like it is a bad thing?

@Mariano I can't really say I can tell either way. I've only known the definition for... 15 minutes!

And who knows how long it took to make the definition ...

and now it is past midnight; time to sleep.

«Mathematics of Vexillology and Heraldry»

Where?

math.stackexchange.com/questions/92380/… just got revived