Sigh... I'm going to try for a couple hours again.

Good luck @BalarkaSen Just relax and try to forget about everything

@BalarkaSen That's a rather black-and-white way of looking at it..

@Mahmoud: You need to show $x+y\ge 0$ and $x+y\le 4/3$.

I suggest completing the square to see the first one. Your equation can be manipulated to show that $x+y$ is equal to the sum of two squares.

Rehi @Danu

Heyo

Home from having some beers

Perfect preparation :P

> time to math

I do like working after getting a bit drunk

you get in a sort of mode where time passes easily

I generally had several martinis while grading exams :)

Like.. sitting and doing math for 3 hours doesn't feel like a long time

Hahaha

Time passes too quickly as it is.

Soon I'll be starting my first teaching job :D Quantum mechanics

Cool, Danu.

@MikeM: I know. It seems like a few yesterdays ago that I was a grad student.

And Danu keeps asking me questions about stuff I haven't taught since 1980.

I already did the problem sets for the coming two weeks, so that i'll be able to present them better (we also get the solutions given to us, so you don't technically have to do anything but rewrite them)

@TedShifrin I can also start asking about symplectic geometry, if you prefer? :P

Sometimes solutions are flawed ... and just copying something on the board is hardly the model of good teaching.

Also, my course on 4 manifolds is looking pretty cool right now

I don't know much symplectic geometry.

we're already using sheaf cohomology though I think nobody there except me and 3 others know it lol

The teacher is a really cutesie guy who just kinda shyly said... "uhh.. yeah... we'll need some... ehh sheaf cohomology..." then gave an intro to sheaf cohomology in 20 minutes

and proceeded to use it :D

I know more about that than complex geometry. PVAL knows more than me.

It's not too bad to give an intro to sheaf cohomology quickly as long as people have seen some homology/cohomology. I've taught it to undergraduates who didn't know any algebraic topology, so I belabored things a bit more.

I think about half or so of the people attending know (co)homology

But it's a bit perverse, I guess, to do a course on 4-manifolds without assuming a little bit of knowledge in that direction

who signed up and doesn't know about cohomology lol

Not to mention perverse sheaves ...

@MikeMiller Everybody who was not in my topology class (mostly physicists :P)

The course is officially called "mathematical gauge theory 2" :P

So they lured in the physicists

Do the physicists make snide remarks calling you a traitor?

Yes, yes.

LOL

You love it.

Also, I constantly bitch about how they don't know shit about what they're saying :D

Oh, definitely the way to endear yourself to friends.

Yes, yes, indeed

Establishing dominance is the first step to true friendship

You may receive a few smacks ....

Whoever shouts the loudest, right? I learned from watching US TV ;D

Mostly, though, I try to drag them into taking math courses with me :)

I'm pretty much the only one who is still enthusiastic about taking courses :\

I'd rather sit in (reasonably decent) lectures than read books/articles. But I suspect most researchers are the opposite.

Should I stop writing $\wedge_\text{eval}$ for the wedge (+ evaluation) on bundle-valued forms?

@TedShifrin I'm with you!

And I also like teaching, I think

Oh, you're doomed to fail, then.

Yes, I know. You've heard me whine many times already about my bleak prospects ;D

Oh Hey @TedShifrin

Sorry /afk

Huh? @Mahmoud

My girlfriend is studying to be a high school math teacher... Not quite as nice but ehhhh.... maybe?

@Ted I disagree. People can simplify the ideas in talks down to their essential pieces. But the details are in the papers.

I was away from keyboard

The problem is that I don't wanna teach people who don't wanna hear it

@Danu: The wedge is needed. The matrix product or pairing of $E^*$ on $E$ can be inferred without a big deal.

@TedShifrin So I should just default to $\wedge$? :\

@TedShifrin What did you mean by completing the square ? :)

@Danu: I loved most of my university teaching experience, but I don't think I would have lasted long in the high schools (in this country, anyhow).

I think I don't like it because my Riem. geom. professor consistently wrote $\wedge_\text{eval}$

I know how to do it but where

Complete the square on $x^2+xy+y^2$, @Mahmoud.

Note that your equation says that's $x+y$.

((x+y)^2)-xy=0

That (xy) ...

That's not the right way to complete it. That's taking too much and subtracting.

Hint: Start with $x+y/2$.

Just write wedge.

Hmkay..

Yup, just write wedge.

Differential geometry is full of Lie brackets, and I tend to just write wedge of matrix-valued forms.

Now that I think about it again, my initial reaction to insist on $\wedge_\text{eval}$ was probably caused by the fact that when I initially learned about this stuff I was not ready for it so it all seemed really hard---but now it seems pretty okay.

It all took me a while. But extra notation just makes things worse.

@PVAL Apparently Bob Edwards is going to tell us how Casson handles work.

Yeah, in the end I guess you're right. Just at that initial stage it's good to constantly be reminded.

Sure, @Danu, just like for the first months of abstract algebra I insisted on having my students write $\bar a$ for the equivalence class in $\Bbb Z/m$, but eventually I dropped it once they actually knew what they were doing. (And because we started modding out polynomial rings by ideals, so there were too many equivalence relations going on.)

Well, I guess I need to start packing up all my food to take .... You all have a good evening/night.

What'd you make for dessert, @Ted?

A sour cream apple coffee cake.

@TedShifrin I followed what @Semiclassical said and arrived at a tricky part

I'm about to leave, @Mahmoud, so ... quickly?

4-3(x+y)<0 and x+y>0

or

Ah ... or switch the signs.

@TedShifrin Hmm... Coffee is not really my thing for cakes

But completing the square the way I showed you (or hinted) will show you that $x+y\ge 0$.

@Danu: It's called coffee cake. There's no coffee in it.

I don't know how such cakes are called in Europe.

@TedShifrin I thought it'd mean at least some kind of coffee flavor is involved.

It's meant to go well with coffee or tea. :)

If not, all the better :D

Ah, hahaha

NO, no.

@TedShifrin Thanks everyone !

This is the first one I've made, though, that had a yeast-based dough. Streusel on top. I think it's gonna be yummmmmy.

Congrats, @Mahmoud.

Yeast... Hmm, interesting.

:)

Anyhow, I need to push off ... Bye, all.

I love working with "live" yeast for breads

aw, bye!

Bye. :)

I hate the stress of waiting after writing an email.

Must be great if you're a prof, and you know people are waiting for you to reply ;D

You are going to receive one and only one message at the end, so why bother yourself, if something is out of your control let it be.

Mm. At most one.

^

Expectation value hovering around... 0.5? :D

No math needed 1=1

But maybe that's some Math over there.

I don't know anymore, Math is everywhere :D

anyone here ?

@MikeMiller

Yeah?

Oh, do you think you can help me with another problem ? :)

Just say no if you're not interested.

Probably not right now. Sorry.

It's okay, :)