But I assimilate very little from his book on complex manifolds.

@TedShifrin Hopefully Chern was a little less short-tempered than Gromov (from what I have heard).

:P

He was one of the sweetest people, @Balarka. Totally not Gromov.

Ah, wonderful.

It's a tough little book, @Frank. Plus the first edition had errors, which I corrected for the second edition :P

@BalarkaSen: I found a play recorded from BBC for The Physicists online. You want it? :P

It's roughly 1.5 hours

Sure.

A few somewhat rude mathematicians like Lang used to pick on Chern a bit, but he took it very good naturedly.

@TedShifrin Did your study overlap with my adviser (Gompf) at all? I think you graduated 5-years apart.

Lang used to pick on everyone.

@BalarkaSen: do you have an email address I can use?

I've known Gompf for years, @PVAL, but I think we crossed in my years helping run the Georgia Topology conference. I believe he arrived when I left.

yeah, give me your e-mail, and I'll mail it to you.

@BalarkaSen see my profile

But say hi to Gompf for me, @PVAL. I haven't seen him in 20+ years.

I don't see your e-mail.

check my website then

@TedShifrin There's a second part in that book, maybe something on geometry on characteristic classes? I didn't manage to read it.

also not there

:D

boo

k.

That was the appendix taken from elsewhere, yes, @Frank. That's what @MikeM has been trying to find to read. I gave him the source; he never told me if he found it.

I've taught a lot of that stuff in graduate courses, @Frank, so I have made it through most of it.

@Huy by "me" you mean "me", not "huy", right?

y

I found Chern's book tougher than, say, Huybrechts book, used in the previous semester as a textbook of an undergraduate class.

done.

Well, the book is written in the old-fashioned terse style, @Frank, and the appendix was taken from a journal article, basically.

Yes. Chern's book was assigned by one of my professors.

I had a hard time to read, but digested almost nothing.

Only remember some notations like $D\theta=\theta\wedge\omega$.

connection matrix, etc.

it seems to very accurately follow the original German play so far

Have you learned the moving frames approach to real geometry, @Frank? Connection matrix, etc.?

who were the actors?

@BalarkaSen: do you mean in the original play or ?

this one.

just some people from Edinburgh Music School afaik

@TedShifrin A bit from practical usage. From Singer & Thorpe, and Do Carmo.

@TedShifrin: I found a copy but haven't read it. No time.

DoCarmo avoids forms. Singer and Thorpe does principal bundles for the surface case, which I find annoying.

OK, @MikeM. I'm glad you found it. I can cross that off my memory.

No, I mean do Carmo's thin book.

Differential forms and appplications.

that one.

Oh, that book. OK.

Not Riemannian Geometry.

@Ted: There are about a hundred things I've listed as "going to read eventually", aka, in about 20 years. Thats' on the list.

One of them is the new Kronheimer-Mrowka 4-color theorem paper; luckily we're doing that in seminar next quarter, so I can cross that off.

There are about a hundred things I was reading that I stopped reading because they'd take 20 years for me to read.

Just heard one of the secretaries say "Just put it in the grad fridge, they'll eat it." I mean, she's right, but I'm still a little :(

LOL ... I never read as many papers as I should have.

I didn't learn Riemannian Geometry from Do Carmo. I learnt from Gallot & Hulin & Lafontaine.

But now I forget most of them.

I've been reading too much lately, to the exclusion of getting enough done.

One needs lots of exercises. The moving-frames approach is very powerful for certain proofs and computations, but not for everything.

@MikeMiller Do you have a candidacy exam?

Our ATC exam is just us giving a talk about our work. Everyone passes.

Did you do this already?

off to bed. n8 everyone

No. You usually do it into your third year or so.

night, @Huy.

Night, @Huy. Night, sick @Balarka.

Yes, exercises are very necessary, so my undergrad years are mostly of failure.

I officially scheduled mine yesterday.

Congrats, @PVAL. Very exciting.

Nice. Good luck.

It may or may not come before a note on the arXiv, which may or may not be written by me.

Though it seems like it would be quite sad if no one wrote this note.

Any more "may or may not"s you can throw in?

Such uncertainty.

This is what we were talking about, yes, @PVAL?

Now I leave analytic methods alone and go into algebraic theory.

Well, @Frank, to each his own. Ultimately, the really powerful mathematicians know it all :P

It's frightening to see my advisor absorb both halves of a talk about Hilbert schemes and Ricci flow.

@MikeMiller There's actually a "trivial" proof to get examples which work with either orientation. Which is kinda nice. "Trivial" means VERY easy given a VERY standard result, which is not necessairly very easy.

I wonder whether it's a rumor that the criterion/syllabus in U.S. is reduced now than decades ago.

Thereby confirming what I just said, @MikeM :)

what syllabus/syllabi, @Frank?

re:"the really powerful mathematician" I had a mental image of a very tall bald man saying "Take sheaf" in a deep voice.

@TedShifrin For math major.

The really best math majors at the best places still take a thorough curriculum. But a generic math degree means very little.

The mathematician whose response to any problem is "Let's use sheaves" is not much of a mathematician.

Hey, I actually had to use sheaves nontrivially in several papers!

I don't understand what the OP wants here .. He seems to have understood Girschgorin Thm just like that won't prove the inequality ..

Of course, I am not much of a mathematician.

I acknowledge, of course. I didn't hear the rest of his statement.

@MikeMiller Depends on how good this person is at using sheaves.

Since in France, it's pretty reduced.

@PVAL: Well, if their response is "use sheaves" without any further input...

There seems to be many very good mathematicians who know very little or nothing about almost everything.

I would argue they're not really "very good," then, @PVAL.

But that does describe the mean/median mathematician. I'm not falling in that trap again :P

Twenty years ago, there were examinations on Liouville's theorem on impossibility of elementary indefinite integral of some elementary function.

@TedShifrin Mean mathematicians?

I'm glad people aren't forced to learn mathematics they find neither interesting nor relevant anymore.

Some of the exam questions Hippa had to do for his prep school exams I honestly couldn't do easily.

@TedShifrin Well in terms of being able to produce papers with outstanding results... My perception of these people may be very incorrect of course.

I know some topologists whose first responses are "Use sheaves". Most of their papers on the subject do not seem very exciting.

Maybe I'm pickier than you about "very good" and "outstanding," @PVAL :)

Now the program for the first year master only contains something like Galois theory in algebra, basic functional analysis, etc.

@MikeMiller Interesting, there are topologists using sheaves on everything?

OK, I'm outta here for now. Bubye.

That is a completely meaningless sentence. But yes.

In my defense, I'm ill and sleepy.

I'm the one who said it...

Not sure which statement is meaningless and which isn't anymore. But ok.

@MikeMiller I am not really arguing for sheaves in particular. I just think there are some people who are amazingly gifted within their specialization, that they rarely need to pull results out of others to get super non-trivial theorems (like say disproving a 30 year old conjecture on knot concordance for an example).

I think we're thinking about the same people.

I find it dififcult to read any of this A infinity stuff.

I don't really know the person I am thinking about personally, but I doubt he could define a sheaf.

Or at least none of his work suggests he could.

Maybe not, then.

@MikeMiller I read Abouzaid's paper on surfaces for a seminar, and got a lot out of it. There's very little background assumed. The theorems are cute and well-motivated, but there aren't any REAL applications floating around (that I know of).

I mean, all the bordered theory floating around lives in A infinity stuff. I feel like that should eventually give some applications.

Goodbye!

I think both Tye and Jonathon gave excellent talks about a lot of the algebra, which helped me a lot.

Not that I know much about this kind of stuff.

I heard one from Liam recently which helped me understand it a little bit, but it was all in terms of the bimodule language they talk a lot about.

Jonathon is giving a class on HF this semester which I suspect will be fantastic.

Sucharit is permanent faculty here starting next year. I assume he'll do the same.

Sucharit? Do you mean Sucharit Sarkar?

The graph manifold L-space result is great. I hear there's no reason to believe the result will extend for other sorts of manifolds.

Yes.

Oh, fun. I have heard of him.

@PVAL Yeah, I couldn't figure out who you meant. Oh well.

Unless you mean K&M, but they're in a league of their own.

@MikeMiller I meant Yasui. All his work is highly specialized in one area.

Fair enough. I don't know much about the contact geometry people.

@MikeMiller The Abouzaid paper I mean (Fukaya Categories of Surfaces or something) is really just for Floer theory of surfaces. Maybe in the the g=1 case this could give 3-dimensional invariants (which wouldn't be interesting anyway) but for higher genus stuff I don't see how. It isn't a Heegard Floer paper really, but I felt like I had some understanding of the Aoo relations of a Fukaya category after reading it.

I think it's the same story you do for every Floer theory. There's a monopole for surfaces that has been in perpetual work for ten years and Lipschitz has a bordered Floer theory.

I think Ciprian has a cornered Floer theory but I don't know where that lives.

Nobody has done this for instantons but I don't think anyone is about to.