@BalarkaSen So you're interested in topology, you're interested in modular forms, maybe you should be interested in topological modular forms? :P

oh?

interest

"the spectrum of topological modular forms (tmf) describes a generalized cohomology theory whose coefficient ring is related to the graded ring of holomorphic modular forms with integral cusp expansions." SHIT

sounds fun

More fun : "tmf was first constructed by Mike Hopkins and Haynes Miller"

a coincidence, I promise

I want to product two subsets $A$ and $B$ of $\Bbb R$ such that $int(A \cup B) \neq int(A) \cup int(B)$. $A = (0, 1]$ and $B = [1, 2)$ works, right?

$int(A \cup B) = (0, 2)$ while $int(A) \cup int(B) = (0, 2) - \{1\}$

yes

great

Hi @DanielF @Pedro @Mike @Balarka

And @Jasper

@TedShifrin Hi. Say, do you know how Rene S. got himself suspended?

@DanielFischer Sounds very familiar...

You mean how I got him suspended?

Ah, that fellow!

@TedShifrin You did? Nice!

He told Ted to go stalk little boys, LOL.

He was abusive and homophobic to me, yes.

in general, I would actually advise doing the opposite

@TedShifrin Oy. He was lucky to get off with a month then.

I suspect he'll say some crap which I will correct and he'll go off worse ....

Oh he is that mathematician turned bartender!

I want to watch that, @Ted.

@TedShifrin Do you know why he said those stuff to you? Did you have a fight with him before that?

I don't. I hate this.

@TedShifrin For $n>1$, is there always a closed $n$-manifold that cannot be embedded into $\Bbb R^{2n-1}$?

@TedShifrin It seems as if he knew you in person.

Yes, @Jasper, I corrected him before, and he told me to leave him alone. He thinks he has the right to say whatever he wants. He's a pathetic character.

No, @Jasper.

Characteristic classes detect such things, @Mike.

@ted Are there many homophobic people in the US? There are quite a lot here...

Sure, not so much among the young, but among the older, @Jasper.

How so, @Ted? I know that given the Stiefel-Whitney classes of $M$, I can use that to detect whether $M$ can immerse in $\Bbb R^{n+k}$ based on the class of the dual to $w(TM)$. But this is only immersion and I need to have candidates in mind beforehand.

I'm rusty, @Mike.

Me too, @Ted.

I am thinking of changing my username to Justin Bieber, but I have already promised not to change it anymore, lol.

sott.net/article/… WTF!!!

@Mike: You barely know this stuff. You can't be rusty :) Chern's 1951 Princeton notes say that for $M$ to embed in codimension $m$ we need that $\bar w_r = 0$, $r\ge m+1$, and $\bar p_k=0$, $2k\ge m+1$. (If I remember correctly, the bars mean the dual classes, i.e., the Poincaré duals of the dual Schubert cycles, but I'll have to review.)

Ah, right, these are formal inverses in the power series sense, but they do correspond to dual Schubert cycles.

Oh man. What's going on in here? :(

@KajHansen Nothing, Matt!

Hi, @Kaj ... To what do you refer?

@Ted, lots of math that's way over my head :O

Well, sure :)

:P

I'm annoyed. I lost 1 point on my 4700 test due to stupidity -_-

Only 1? You used to lose 30 on mine :)

Let's just say your tests we're much harder. And we'll see about Dr. Fu on Monday.

hello @TedShifrin

Oops, guess you get me fired fir FERPA violation now ...

Hi @Alizter

I guess it's at this point I should consider Doug's blackmail question @Ted ;)

@TedShifrin How are you?

Which one? He has so many ...

Fine, @Alizter, and you?

Good point!

@TedShifrin I am good thank you. I have been reading number theory. I have given probability a break.

Good choice @Alizter

LOL

I've enjoyed learning it ... And so have some of my students ...

@TedShifrin It is definitely interesting.

I feel that it may look too unappealing to people who like to study pure mathematics. I think that the pure and applied mathematics line is silly. A lot of good mathematics comes about from "applied" investigations.

I last did probability in high school, lol.

Good night all!

@Alizter See you in your dreams.

Let $\underline{v}(x,y)$ be a vector field on $ \Omega = {(x,y} : x>0, y>0}$ of the form $\underline{v}(x,y) = g(y/x)(\frac{-1}{x}, \frac{1}{y})$ where $g:\mathbb{R} \rightarrow \mathbb{R}$ is continuous. Find a scalar potential $\underline{v}$ in terms of an integral involving $g$; you may assume that $\underline{v}$ is conservative.

When I tried to answer this, I got 0 as my answer.

Which i'm guessing probably isn't correct as the qestion specifically asks for an integral involving g.