Mathematics - 2015-04-09 (page 4 of 4)

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JC574

23:00

same here (UK)

Ted Shifrin

often, they've have to start graduate work all over, so it's not worth having the M.A.

JC574

ah ok

Herr mann

grüss gott @TedShifrin

evinda

Hallo @Herrmann

JC574

I'm confused by the structure of the US degree, and the layout of the courses

Incurrence

23:06

Hey @Ted @ᴇʏᴇs

Stan Shunpike

@TedShifrin Morse theory? What's that? A quick scan through the Wikipedia article and I saw CW structures mentioned. Is that related? I think Lee talks about those.

Ted Shifrin

heya what's-your-name :P

ᴇʏᴇs

Hi @Incurrence

Ted Shifrin

@Stan: We can talk about it later :P

Incurrence

@TedShifrin I am Committingtoachallenge, not sure if I have talked to you after name change haha

JC574

23:08

I saw something about Morse theory, it's cool you can get things like the Euler characteristic from extrema of real-valued functions on your top. space

Ted Shifrin

yes, I know, @Incurr

Incurrence

@TedShifrin Apologies then :P.

Stan Shunpike

@TedShifrin l'll accept that as a rain check :P

Incurrence

How can I find the elements of the center of some group generally?

What are some useful incites for finding these quickly

Karim Mansour

hi @JC574 so right now I am doing quick build its telling couldn't start bla bla

wat is that

JC574

23:10

@KarimMansour it's been ages since I set it up, i honestly will not be able to help much

there are lots of tutorials onlin

online*

I know this will probably vary school by school, but at grad school are there usually taught courses?

Karim Mansour

alright

yeah

we have courses @JC574

JC574

trying to work out whether I'll be at an advantage coming to the US for grad school with a masters

Incurrence

Chat guidelines | $\LaTeX$ in chat | MSE chat dwellers: pin your location (just for fun)[instructions]

@Ted How do you feel about people pinging you with questions? Dislike it?

Ted Shifrin

What you say, @Incurr?

JC574

@TedShifrin I'm sorry if i'm bugging you

Incurrence

23:15

Math questions I should say

JC574

or anyone else here

Incurrence

@TedShifrin How do you feel about people @ing you with math questions? Would you rather we say them undirected and you will help with them whenever you feel like it

Ted Shifrin

you're fine, @JC574

Incurrence

I'll take no answer as you don't care. So quick question: @Ted, is there a quick way to determine elements in the center of a group?

Ted Shifrin

@Incurr: I'm on the phone ...

Incurrence

23:18

oh whoops

JC574

@Incurrence i think it's probably going to depend on the types of groups you're studying

Incurrence

@JC574 I know, that's why I asked, since it seems that they are obvious or not depending on the group

JC574

i can't remember if you can use the character table to do it

Incurrence

Yes you can

JC574

yeah i remember, they're in the kernel of all the irreducible characters or something. I don't know whether that'd be a shortcut

Disciple of Barney

23:20

Are you talking finite groups? @Incurrence

Incurrence

Yep

Actual no

Well I am interested in both

evinda

Hello @CivilSigma

Incurrence

In a finite group the table will just need equal column and row

but in an infinite group I have no idea

JC574

sorry i meant the character table rather than the cayley table, but i don't think my suggestion was at all helpful really

Incurrence

@JC574 Character table, I don't know this perhaps

JC574

23:25

it's not worth getting into for this, i don't think

it just jumped into my head

http://mathoverflow.net/questions/106729/center-and-representations-of-finite-group-how-are-related

I don't think it's a shortcut, just something i remembered

Incurrence

Fair enough, I'll be back in a min.

Disciple of Barney

23:41

@Incurrence In general it is algorithmically undecidable whether or not an element is in the center of a group. Of course that doesn't hold for finite groups though if that is your main interest.

Incurrence

@DiscipleofBarney True

@DiscipleofBarney Infinite groups are my main interest(at this time)

Is the center of $GL_n(\Bbb R)$ truly only $\{-I,I\}$?

I think there are nilpotent matrices that make that untrue

JC574

$2I \in GL_n(\mathbb{R})$ right?

Disciple of Barney

@Incurrence Nilpotent matrices are not in $GL_n$.

Incurrence

@Disc Can you star the comment of mine above that has the latex in chat and guidelines and crap

@DiscipleofBarney hm?

@DiscipleofBarney $\begin{bmatrix}0&1\\0&0\end{bmatrix}$ is inverible(although isn't in the center)

Disciple of Barney

@Incurrence $GL_n$ are invertible matrices, nilpotent matrices are not invertible

JC574

23:47

@Incurrence what is the inverse of that matrix?

Ted Shifrin

@Incurrence: I'm off the phone. For what group were you seeking the center?

Incurrence

@JC574 Oh now I am embarrased lmao

@TedShifrin I meant in the general case

Ted Shifrin

<-- always enjoys embarrassing people :P

I can't say anything general ... other than basic undergraduate exercises.

Incurrence

For some reason I just thought to myself it was det -1 lmao

Disciple of Barney

Maybe you wanted to be talking about center of $\mathfrak{gl}_n$.. @Incurrence

Incurrence

23:49

Nono, I meant GL_n

But you are right @Disc

JC574

you're right that $I,-I$ are in the centre. Note also that $2I$ is in the centre

Incurrence

So it is only scalar multiples of the identity

JC574

yes :)

Ted Shifrin

yes, for $GL(n)$ ...

Incurrence

Why are you dotting me @Ted haha

Disciple of Barney

23:50

@Incurrence And for $\mathfrak{gl}_n$

Ted Shifrin

Would you rather I crossed you, @Incurrence?

Incurrence

@TedShifrin You mean xoxo?

Ted Shifrin

LOL

dotting i's and crossing t's

Incurrence

What is an infinite group with a more interesting center?

Michael Albanese

@TedShifrin: Would you mind taking a look at an answer of mine regarding the splitting principle for Chern classes? I have some concerns about it.

Ted Shifrin

23:54

Oh, I saw that question, but didn't dally, @Michael.

Michael Albanese

Meaning that you saw it but didn't read it?

Disciple of Barney

@Incurrence What constitutes an interesting center? After all centers are abelian groups, so choose an abelian group and it is its own center.

Incurrence

Ted says the strangest things

@DiscipleofBarney I mean infinite non-abelian groups with a center with numerous elements(which are of different nature, e.g. not just scalar multiples)

Ted Shifrin

I didn't study your answer. Maybe there are some sign issues with the symmetric functions? I would need to think.

@Incurrence: Ted is a strangest person.

What are your concerns, @MichaelA?

Michael Albanese

I didn't show that $c_1(L_1), \dots, c_1(L_n) \in H^*(Y, \mathbb{Z})$ are in the image of $p^*$. I'm not sure how to do this.

Ted Shifrin

23:59

The standard reference is Hirzebruch (which I haven't given away yet), but it's in my office.