Mathematics - 2015-05-24 (page 3 of 3)

3:01 PM

I wonder if there is a connection between tropical geometry and the monomial stuff I did...? One of the purposes of the monomial stuff is that in some sense you are making parts of the problem linear, so it is easy to calculate. @AlexClark

Clarinetist

Did any of you see A Beautiful Mind ?

nj.com/middlesex/index.ssf/2015/05/…

[I haven't seen it yet]

Paul Plummer

@AlexClark Oh and as someone interested in geometric group theory and things related, I feel obligated to mentions this paper "Geometry of the space of phylogenetic trees" By Billera, Holmes, and Vogtmann

Clarinetist

[The link is SFW contrary to what the link may suggest]

user147690

@Clarinetist Yep, great movie

user147690

@PaulPlummer Haha I'll check it out now

Clarinetist

3:03 PM

@AlexClark Yeah, apparently the mathematician featured in that movie died yesterday

Paul Plummer

Hmmm, I don't remember the movie being any good

user147690

@Clarinetist Yeah I saw in the star bar

user147690

@PaulPlummer What? I guess you don't like dramas?

Paul Plummer

Dramas are fine, I don't remember the movie to well, and I am pretty sure it wasn't any good

user147690

@PaulPlummer whhhhhhattttt[you are somewhat right, it isn't very rewatchable]

user147690

3:05 PM

@PaulPlummer Did you like good will hunting?

Paul Plummer

That was good

user147690

@PaulPlummer math.cornell.edu/~vogtmann/papers/Trees/lap.pdf

Paul Plummer

Yup that is it

user147690

@PaulPlummer It'll probably be good to go through

Paul Plummer

Huh, I have not given the paper a read (for some reason I thought it was 60 pg), I think I will read it.

Well I am going to make breakfast and read a bit of this, probably won't be back for 30 minutes, I suspect you will be sleeping @AlexClark

user147690

3:12 PM

@PaulPlummer I hope so

user147690

@PaulPlummer So goodnight to goodmorning!

Paul Plummer

Yes goodnight,

user147690

@PaulPlummer Before you go, I ruined my chat graph

Paul Plummer

Haha

crl

@crl Does someone have a good way to solve this? or to prove the unicity of the solution?

$a_1+(13*a_2/a_3)+a_4+12*a_5-a_6-11+(a_7*a_8/a_9)-10=66$ with $a_i$ elements of $\{1,2,...,9\}$ non-repeated

user147690

3:29 PM

@crl Move $10$ and $11$ over to the right, and consider what numbers leave $\frac{a_2}{a_3}$ integer and same with $\frac{a_7a_8}{a_9}$

user147690

Three options for the first(including a class of options for 1 on the denom), more for the latter

crl

for the first there are: 9/3, 6/3, 8/4, 8/2, 4/2, and i/1 for any i>1

user147690

@crl True, apologies I gave it very little thought

user147690

It's 1:30am and I am normally asleep

crl

hehe no problem

Clarinetist

3:34 PM

Really basic linear algebra question. If $X \in M_{n \times p}$, I would like to prove that $N(A^{T}) = C(A)^{\perp}$, $N$ being the nullspace, $C$ being the column space. I have the following: we have $$A^{T}x = \begin{pmatrix}
c_{11} & \cdots & c_{1n} \\
\vdots & \ddots & \vdots \\
c_{p1} & \cdots & c_{pn}
\end{pmatrix}\begin{pmatrix}
x_{1} \\
\vdots \\
x_n
\end{pmatrix} = \sum_{i=1}^{p}\sum_{j=1}^{n}c_{ij}x_i = 0$$
where $c_{ij}$ is the value of the $i$th column and $j$th row of $A$.

Now $C(A) = $span of the columns of $A$, so there I'm a bit stuck.

crl

~~I would have called them $a_{ij}$ then~~ ith column and jth row of $A^T$ you mean ^

Clarinetist

Okay, that makes more sense :P

evinda

@crl How did you delete a part of your sentence?

Clarinetist

@crl Wait, I indexed them wrong?

crl

@evinda ---I would have called them $a_{ij}$ then---

Clarinetist

3:42 PM

Is there an easier way to show $N(A^{T}) = C(A)^{\perp}$ rather than play around with matrix components and sums?

evinda

I tried it but I don't get that what you wrote.. @crl Where else did you use $$ ?

@crl Or did you write exactly this: ~~I would have called them $a_{ij}$ then~~ ?

crl

@evinda chat.stackexchange.com/messages/21813080/history

Ted Shifrin

Yes, @Clarinetist. Either understand constraint equations for $Ax=b$ to be consistent, or think about why $N(A) = R(A)^\perp$ and apply this to $A^\top$.

Hint: $Ax=0 \iff x$ is orthogonal to all the rows of $A$.

evinda

@crl A ok.. Thank you!!! :)

Balarka Sen

meh.

I think this question deserves a good answer.

I haven't thought a lot about it, but I always thought that Mayer-Vietoris can actually be derived algebraically from doing homotopy theory on chain complexes.

Paul Plummer

3:56 PM

@BalarkaSen Lol, I was reading the question and was about to say here "ten quatloos that RB posts something about one of his books", then I saw the answer below.

Balarka Sen

haha

Paul Plummer

Although it looks like it could be one of the more relevant posts he has done (I am not familiar enough with the ideas to say if it is or not)

Karim Mansour

hi guys

Balarka Sen

It might or might not be, but I am not gonna look through each of his books to check if it is or not :P

Paul Plummer

Haha, look at the comment on his answer @BalarkaSen

Balarka Sen

3:59 PM

lol at the comment

yeah, I was just looking at it.

Paul Plummer

I think he has only two books (Topology and Groupoids and the free one he mentions)

I actually own topology and groupoids and so far I like it

Balarka Sen

bah.

Paul Plummer

although the behaviour on math.se is sort of annoying

Well the comment was removed... @BalarkaSen

Mike Miller

His book isn't bad. His spam, and posts on essentially unrelated questions, are.

Paul Plummer

I agree @MikeMiller

Clarinetist

4:18 PM

@TedShifrin That makes sense, so $A^{\prime}x = 0 \Longleftrightarrow x$ is orthogonal to all of the columns of $A$... is it really that simple?

0

Q: Orthogonal complement of column space is orthogonal to null space of transpose

Let $X \in M_{n \times p}$. $C$ denotes the column space, $N$ denotes the nullspace. I would like to prove $C(X)^{\perp} = N(X^{\prime})$. Let $X = \begin{bmatrix} x_{11} & \cdots & x_{1p} \\ \vdots & \ddots & \vdots \\ x_{n1} & \cdots & x_{np}\end{bmatrix} = \begin{bmatrix} x_1 & x_2 &\cdots &...

Ted Shifrin

Yes, @Clarinet.

Clarinetist

So it just follows immediately. Wow. Thanks @TedShifrin

Ted Shifrin

Hi @Balarka

Goodnight @Mike

Mike Miller

@TedShifrin: Morning. That submersion question is mostly solved now; there remains the question of whether there are submersions $S^{4k-3} \to S^k$ for $k \geq 4$, $k$ even. Qiaochu solved most of the cases; I, uh, solved $S^5 \to S^2$.

Ted Shifrin

Qiaochu is impressive.

Clarinetist

4:27 PM

Now to learn about SVDs, Genearlized Inverses, PPOs... fun stuff

Teddy

hi

Ted Shifrin

But, then, @MikeM, all of us MIT/Berkeley folk are. :D

Mike Miller

:(

Ted Shifrin

Awww ... :)

That was not a serious remark.

Mike Miller

I know, I'm just kidding.

Teddy

4:30 PM

math.stackexchange.com/questions/1270940/… if my field have 10x 15 units and if I fix a startposition, the starting position is standing up

AlpArslan

Aha, right. May I ask a small question regarding complex analysis?

nullgeppetto

Hi everyone! I am interested in visualizing the convex cone of symmetric positive-definite $n\times n$ real matrices. Could please help me? I have just asked a question, if you like to take a look. Thanks a lot in advance!

David Cardozo

Hello everyone, one question: Do you happen to know how to construct the lattice of S5? Is it possible? I try GAP but it says no 1st choice method found for `MaximalSubgroupsLattice'. Has anyone been able to do the lattice of S5

Clarinetist

Does anyone know if Dummit and Foote plan to release another edition? I noticed the plethora of errata...

Mike Miller

After all, you came from Berkeley... how good could they be?

Teddy

4:30 PM

can I move my 1x2x4 cuboid to every endposition ?

Ted Shifrin

Sorta my point, Mike.

Mike Miller

Oops

Ted Shifrin

ask, @Alp

Karim Mansour

how good are people in Berkeley @TedShifrin ?

Ted Shifrin

Varied, @Karim. You mean students?

Karim Mansour

4:32 PM

yeah

AlpArslan

Right. So, say, p(z) is an even polynomial, all the roots of which are of modulus < R, for some R.

Ted Shifrin

Yeah, varied. Some superstars, many duds.

Karim Mansour

oh

AlpArslan

I need to try and define a holomorphic function h(z) on the region { |z| >R} such that, h^2 = p.

Clarinetist

You know what baffles me? A lot of people that I saw on the actuarial forum that I used to go on have been asking the question Should I go to UCLA or UC-Berkeley for a career in actuarial science and I was just like... facepalm

AlpArslan

4:34 PM

Now, I need to, in a sense, talk about why this exists and is well-defined.

Karim Mansour

why @Clarinetist?

AlpArslan

I know, I can say, h = e^{ (1/2) log(p(z)).

Ted Shifrin

Ok, @Alp. Think about Morera's Theorem, perhaps.

Karim Mansour

I guess its same as if you go to ucla or berkley as long as your good in what you do then its the same

Ted Shifrin

I wouldn't go that route.

Clarinetist

4:35 PM

@KarimMansour IDK, if you manage to get into *any* of those schools, I would imagine you would have other options. Most people pursue actuarial because they feel that have no other options.

Actuarial puts little stock into what you actually do at the institution you go to, and as long as you have a GPA of 3.5+, you have a good chance of getting hired.

LeGrandDODOM

@Ted Salut, j'ai vu ton message concernant la courbe d'hier. Dommage qu'on puisse pas arriver à caractériser le cercle de cette manière

Clarinetist

@KarimMansour Of course, that's assuming you pass a decent number of exams

Ted Shifrin

Salut, @LeGrand.

Karim Mansour

oh

AlpArslan

Hmm, fair. Morera says that if every integral of a continuous function around a closed loop in my domain is 0, then, the function is holomorphic.

Karim Mansour

4:36 PM

I might go to US in my phd

I am still debating

AlpArslan

But, I'm puzzled by why I need the polynomial needs to be even?

Or, do odd polynomials work just fine, as well?

Ted Shifrin

Peut-être symétrie de toutes ordres?

Karim Mansour

@Clarinetist you live in US?

Clarinetist

@KarimMansour Yes I do

Ted Shifrin

No, @Alp, with odd you need a branch cut to infinity.

Karim Mansour

4:38 PM

@TedShifrin would it make a difference if I stay in canada for phd or go to US for it?

I see

Clarinetist

@KarimMansour I'm interested in knowing the same. My impression is that Canadian standards are on average higher than U.S. standards, but maybe I'm wrong

AlpArslan

What do you mean, you need a branch cut to infinity?

Karim Mansour

@Clarinetist so after your done your actuarial degree are you planning to do degree in math or just as a hobby ?

Ted Shifrin

Actually, the main thing is well-definedness, @Alp.

AlpArslan

Of the logarithm, yes?

Karim Mansour

4:40 PM

yeah I wanted to know if I go to like university of Toronto or mcgill is it same as going to one of ivy league in US

Clarinetist

@KarimMansour I quit my actuarial degree after 3.5 semesters, switched to statistics in my last semester and graduated exactly a year ago (concidentally :) ). Worked in actuarial science for the last year, got bored of it, and am now starting a M.S. statistics degree while working in healthcare technology.

Karim Mansour

@Clarinetist

nullgeppetto

It's not a good time to ask question here, I think :P

Karim Mansour

oh I see

Clarinetist

@KarimMansour IDK. It seems that people only know about those if they try applying for them where I'm from...

Ted Shifrin

4:40 PM

Try $\sqrt z$ versus $\sqrt{z(z-1)}$.

N3buchadnezzar

@Clarinetist Heya!

Clarinetist

@N3buchadnezzar Hey, got more spreadsheet stuff?

Karim Mansour

I see

N3buchadnezzar

@Clarinetist You read my mind ;) How can i update A2 when A1 changes? But I want to also change A2 manually

Clarinetist

@KarimMansour You know, if there's one thing I've learned in the last year, it's that I need to do what I actually enjoy during the day or I'll go insane

Ted Shifrin

4:42 PM

Depends on quality of place in US, @Karim, and quality of your adviser and thesis.

Clarinetist

@N3buchadnezzar Pretty sure you can't do that. Either manual or automatic (lol)

Karim Mansour

like for example comparing berkley to UOFT

N3buchadnezzar

@Clarinetist After some hectic googling, I came to that conclusion as well :p

David Cardozo

Hello everyone, one question: Do you happen to know how to construct the lattice of S5? Is it possible? I try GAP but it says no 1st choice method found for `MaximalSubgroupsLattice'. Has anyone been able to do the lattice of S5?

Clarinetist

You know what's funny @KarimMansour. People ratted me out on the actuarial website I was on because I don't like putting my time into things I don't enjoy. :P

Karim Mansour

4:44 PM

people from your class ?

Ted Shifrin

If you write a top-notch thesis at Berkeley, you win. A mediocre one ... Meh. What isUOFT?

Karim Mansour

university of Toronto

Ted Shifrin

Confusing, @Karim.

Clarinetist

@KarimMansour Not necessarily, there's an actuarial forum of a bunch of people who want to remain anonymous. A small minority (myself included) choose not to. It's breeding grounds to be mean to each other

Wait UOFT, how do you get University of Toronto from that?

Mike Miller

U of T

Karim Mansour

4:46 PM

yea

I don't know we always refer to university here by first letter like mcgill UOFM

Clarinetist

@KarimMansour Another suggestion

Rachmaninoff-Richardson - Vocalise (with sheet music)

►

And this one is absurd. Just absurd. I don't know how anyone can play piano like this.

Rachmaninoff's "Moment Musicaux Op. 16 No. 4 in E minor" (audio + sheet music)

►

Karim Mansour

nice

Clarinetist

I think I'm going to make an omelet

Btw @KarimMansour, this is the original version of the first one I sent you (the Vocalise). It was originally written for Soprano and orchestra.

Vocalise

►

Karim Mansour

I like the vocal one better

Clarinetist

Then you'd probably like this, the Zdes' khorosho by Rachmaninoff

Zdes' khorosho (Op 21 No 7, RACHMANINOFF) - Anna NETREBKO (score animation)

►

N3buchadnezzar

4:55 PM

@Clarinetist Perhaps a bit more advanced, but... How can I automatically import a CSV file? The problem is at the website, one has to download the file. I have problems using =IMPORT(vinmonopolet.no/api/produkter)

Clarinetist

@N3buchadnezzar OOH fun. Well, in my experience, I usually have to download it to my computer. You really only have two options: 1) learn how to code in VBA (a pain to do for this sort of task) or 2) import it manually

N3buchadnezzar

I guess I will ask some of my computer geek friends to give it a go :p

Clarinetist

@N3buchadnezzar Importing it manually isn't terrible. What are you using? Google Docs?

N3buchadnezzar

@Clarinetist Yeah, I was able to import it just fine after downloading it ^^

Clarinetist

:) Good.

N3buchadnezzar

4:59 PM

Having to filter out what I need from 5000 entries is going to be a bitch though

Karim Mansour

very nice I do @Clarinetist

Clarinetist

@N3buchadnezzar Imagine working with about 500,000 and filtering that out. During my last few days at my job, I would be waiting for three hours! I mean THREE HOURS! to get a filtering job done

And then a filter on top of that filter....

:P

N3buchadnezzar

@Clarinetist Say I know that the row i want contains 1039001, how can I get that row in another spreadsheet? I know I can google this, but since it seems this was your horribly? boring job. I might ask you :p

Clarinetist

Haha @N3buchadnezzar Let's see, what you would do is go into your new spreadsheet, let's say you want to put what is in row 1039001 into row 1 of your new spreadsheet

Assuming the values start at column A, in A1 of your new spreadsheet, type =A1

Then press ENTER

and then you should get the value

Then click on cell A1 again but don't double-click it

You should see some sort of little wedge thing on the bottom right on the cell.

Click and drag it to the right as far as you want and you will get the row values

It's horribly inefficient, but that's Excel for you

OOPS

Actually, it should be =[WorksheetName]!A1

But everything else should be right

WorksheetName is the name of the worksheet you reference

N3buchadnezzar

@Clarinetist Not working, sigh

Clarinetist

5:11 PM

@N3buchadnezzar Step by step

So your values are in row 1039001, right?

N3buchadnezzar

@Clarinetist Oh no, that is its reference number. I am actually looking for the row that contains that value.

Clarinetist

@N3buchadnezzar Okay now THAT is a different question

Oh I misinterpreted you Sorry @N3buchadnezzar :P

N3buchadnezzar

Pardon my horrid English. I tried " =SEARCH(1039001,'products!'B3000:B5000) "

Clarinetist

@N3buchadnezzar So you want the row number for 1039001 and it's somewhere in B3000:B5000?

N3buchadnezzar

@Clarinetist Yeah, I tried with B2:B first, but I got an error, so I tried narrowing down the range.

Gives me #VALUE , "Error In SEARCH evaluation, cannot find '1039001' within '1301'."

Clarinetist

5:16 PM

@N3buchadnezzar I'm gonna try this one out... let you know what I find

@N3buchadnezzar This looks like a textbook case for VLOOKUP. What are you using this 1039001 value for?

N3buchadnezzar

@Clarinetist I need to extract a few column values from that row

Clarinetist

@N3buchadnezzar Yeah, VLOOKUP is your best friend

I'm going to work inside your Sheet2 @N3buchadnezzar

N3buchadnezzar

@Clarinetist Yeah no problem =)

Clarinetist

@N3buchadnezzar See what I did? I extracted the column after the number

N3buchadnezzar

@Clarinetist AJ4190?

Clarinetist

5:21 PM

@N3buchadnezzar B1:AJ4190 is the entirety of your table

N3buchadnezzar

Ah right =)

I think I can manage the rest now, I tried hard doing this using SEARCH but alas to no avail.

Clarinetist

@N3buchadnezzar So how you should think of this is VLOOKUP(reference_key, table_reference, column_number, FALSE). Always use FALSE at the end for an exact match on the reference_key.

N3buchadnezzar

VLOOKUP, looks earlly nice. Yeah, I looked up the definition ;)

Clarinetist

The reference_key should always be unique if possible. @N3buchadnezzar Once you get really good, you can start using INDEXMATCH, but VLOOKUP is a nice start.

N3buchadnezzar

Yeah, the number I see now is unique.

Clarinetist

5:25 PM

@N3buchadnezzar What's even more fun sometimes is that it's not unique and you need to do a VLOOKUP. In these cases, I would have to create a concatenated column of some sort so that the key is unique... Man, I do not miss those days

N3buchadnezzar

:p

Clarinetist

@N3buchadnezzar Once you get used to VLOOKUP, you may want to learn INDEXMATCH. See here: randomwok.com/excel/how-to-use-index-match .

INDEXMATCH is just a more efficient VLOOKUP.

N3buchadnezzar

@Clarinetist Can I do a HLOOKUP as well?

Clarinetist

@N3buchadnezzar Yes, you can, but I have rarely had to use it. Usually it's good principle to create new values on rows, as in the worksheet you have

N3buchadnezzar

@Clarinetist Concretely I was thinking of using =VLOOKUP(B3,products!B1:AJ4190,2,FALSE) and wanting to get the price "pris" but say I do not know what column this lies in. How can I figure out that it is the 5th column?

Karim Mansour

5:32 PM

what the hell

physics book derive some equation by resorting to magic

Clarinetist

@N3buchadnezzar I see what you're trying to do. Could I modify your sheet for you?

N3buchadnezzar

No problem =) Basically the goal is to get a simplified version of the big spreadsheet, only having the relevant colums.

Clarinetist

@N3buchadnezzar I had to insert another row

N3buchadnezzar

@Clarinetist Yea, I saw. clever use of HLOOKUP

Clarinetist

@N3buchadnezzar There you go, that should be right

N3buchadnezzar

5:45 PM

@Clarinetist Indeed. I think "=COLUMN(HLOOKUP(C2,products!$A$1:$AJ$2,2,FALSE))-1" Might be a tad shorter for retriving the number though, also no need for letters

Clarinetist

Yep @N3buchadnezzar Notice also that I changed the reference_key to $B3, so that the column remains fixed

@N3buchadnezzar One thing to be careful with that is you want to change C2 to $C$2

I should probably change those as well

@N3buchadnezzar To test this, I'm going to insert another one

And it looks like dragging works, so the code should be good @N3buchadnezzar

N3buchadnezzar

@Clarinetist Thanks a bunch =)

Clarinetist

@N3buchadnezzar Np, anytime

N3buchadnezzar

A last question. If I update the first sheet, does the second one also update. Or is there a button I must push?

evinda

Hi @Alessandro
Wie geht es dir? :)

Clarinetist

5:50 PM

@N3buchadnezzar For your VLOOKUP, as long as you don't put it on manual calculation mode (I don't think Google has that), it should update automatically

Pedro Tamaroff

Anyone wants to compute some group cohomology?

Balarka Sen

@Pedro of what group?

Pedro Tamaroff

$C_p$ acting on $C_{p^2}$.

Balarka Sen

what's the action?

Paul Plummer

Oh look a group theorist @BalarkaSen :D

Pedro Tamaroff

5:54 PM

Actually I want for $A=\Bbb Z[C_p]$ and $M=C_{p^2}$, ${\rm Ext}^2_{A}(Z,M)$.

Suppose that $\xi$ generates $C_p$ and $\sigma$ generates $C_{p^2}$, and assume that $i=1\mod p$. Then $\xi\sigma=\sigma^i$.

Alessandro

hallo @evinda jetzt besuche ich einen anderen Deutschkurs und muss deswegen sehr früh morgens aufstehen, apart from that (how do you say that in German?) very good :D und dir?

Pedro Tamaroff

For $M=C_p\times C_p$, I proved there are two nonisomorphic structures up to isomorphis, the trivial one and $\xi(x,y)=(x+y,y)$, the one given by $\begin{pmatrix} 1&1\\0&1\end{pmatrix}$. For $M=C_{p^2}$, there are $p$ nonisomorphic structures up to isomorphism, which are $M_i$ under $\xi \sigma=\sigma^i$ for $i\equiv 1 \mod p$.

Balarka Sen

OK, no idea. All I know about group cohomology is that $n$-th group cohomology of a finite $G$ is the singular cohomology group $H_\bullet(K(G, 1))$.

Pedro Tamaroff

Well, there is a canonical free resolution for $\Bbb Z$ as the trivial $A$-module, given by $$\cdots\stackrel{1-\xi}\longrightarrow A \stackrel{\nu}\longrightarrow A \stackrel{1-\xi}\longrightarrow A \stackrel{\epsilon }\longrightarrow \Bbb Z\longrightarrow 0$$

Where $\nu=1+\xi+\cdots+\xi^{p-1}$.

If you apply $\hom_A(-,M)$ to this complex, you get a cochain complex, and you can calculate the second cohomology group of that, which is ${\rm Ext}^2_A(\Bbb Z,M)$.

evinda

Aha.. You can say it ansonsten in german. @Alessandro
Am 5 Juni fangen bei mir die Prüfungen an.

Pedro Tamaroff

6:03 PM

And since $\hom_A(A,M)\simeq M$ naturally, it follows that ${\Ext}^2_A(\Bbb Z,M)$ is $\ker(1-\xi)/{\rm im}\,\nu$.

Mike Miller

@BalarkaSen: That's only true if your coefficients are in $\Bbb Z$ with the trivial action, which I guess is what Pedro is saying right now. You can actually generalize this to other coefficients, but this involves working with what are called local coefficients on your space $K(G,1)$, and this is essentially impossible to compute.

Pedro Tamaroff

But I want to describe that as explicitly as possible.

Ted Shifrin

Mr @Pedro!!

Damn, @Pedro's turned into a homological algebra.

Pedro Tamaroff

For example, in the nontrivial case $M=C_p\times C_p$, $\nu$ acts by $0$ and $\xi-1$ acts by sending $(x,y)\to (y,0)$.

Ted Shifrin

Hey, Pedro, did you get that job?

Pedro Tamaroff

6:04 PM

@TedShifrin No news so far. =/

That means I haven't been told yes or no.

Balarka Sen

Which job?

Pedro Tamaroff

Doesn't matter.

Ted Shifrin

Darn. Well, I'm leaving town Wednesday at 5 AM, so if you need to me to do an email, I should do it soon.

Pedro Tamaroff

Personal things.

Ted Shifrin

Guten Abend, @Alessandro.

Alessandro

6:06 PM

Hallo @TedShifrin wie geht es dir?

Ted Shifrin

Ganz gut, danke, und Dir?

Pedro Tamaroff

@TedShifrin How's the moving going?

Ted Shifrin

No one's been to look at the house in 16 days now, so I'm worried. We'll lower the price on Tuesday. ... Going to hunt for an apartment Wednesday AM.

Alessandro

mir auch :)

Ted Shifrin

Studies almost done for this school year, @Alessandro?

Alessandro

6:13 PM

I'm not studying this year, I only attend German courses, I will (hopefully) begin the university in october

Ted Shifrin

Oh, I misunderstood what was going on ... When do you find out?

Alessandro

I need to pass a german proficiency test

Ted Shifrin

Die Mathematik ist schwerere auf deutsch :)

Heya @Fargle

Karim Mansour

@TedShifrin how many languages do you know ?

Ted Shifrin

Only a few, @Karim.

Karim Mansour

6:15 PM

4?

Alessandro

english, french and german at least

Ted Shifrin

Not really ... some knowledge of Russian and Latin, but basically French, German, English.

But I've forgotten too much of all of 'em.

Balarka Sen

You're forgetting math, @Ted :)

That's also a language.

Ted Shifrin

I am forgetting most of my math.

I'm going to try to learn some Spanish, though.

Balarka Sen

Why do my sentences always get misinterpreted?

:P

Ted Shifrin

6:17 PM

Your sentence was deliciously ambiguous, @Balarka.

Alessandro

Italian is much better than Spanish, in my totally unbiased opinion :P

Ted Shifrin

I would agree, @Alessandro, but I will have to converse with Mexicans, so Italian won't help :)

Mike Miller

A bunch of math grads are learning Russian next year, @TedShifrin

Ted Shifrin

Learning learning, @MikeM, or reading to pass a math exam?

Mike Miller

The first. You don't need to do anything to pass the language exam.

Alessandro

6:18 PM

i was joking, Spanish is much more useful :)

Ted Shifrin

I think Italian is a beautiful language, @Alessandro.

Karim Mansour

I need to learn italian

Swedish and romanian and hungarian

Mike Miller

My advisor lectured me on how to pronounce Hungarian names a few weeks ago.

Karim Mansour

spanish too

Mike Miller

"If you want to work in this field, you need to know how to pronounce these."

Ted Shifrin

6:20 PM

Good @MikeM

Karim Mansour

my gf is of hungarian origin so she is teaching me the language xD

loool

must be alot of good hungarian mathematician in your field @MikeMiller

Mike Miller

Yes.

Balarka Sen

I know of only one Hungarian mathematician.

Ted Shifrin

Lots of Hungarians in combinatorics and number theory.

Paul Plummer

Why are they going to learn Russian? Just interest? I was originality planning to learn Russian or German as a language requirement, but it seems more important to learn French nowadays @MikeMiller

Mike Miller

6:22 PM

Interest, yes, @Paul.

Paul Plummer

Okay, wondering if there is a Russian come back :)

Mike Miller

If your goal is just to read mathematics you don't need much more than a little bit of understanding of the language. I can read French without a dictionary perfectly well because I've had some amount of French training; I can read Spanish with some more effort...

But of course there's a lot to get out of a language than the ability to read math papers.

Ted Shifrin

indeed ... I still plan to reread some French literature in my time.

Balarka Sen

I don't know French :(

Ted Shifrin

You barely know English, Balarka .o.

Balarka Sen

6:25 PM

glares

Ted Shifrin

I love a good glare.

Samuel Yusim

when you take the wedge sum of spaces, does it ever matter which points you identify?

Balarka Sen

I still get the best grades on English in my exams, mind you.

yes.

Samuel Yusim

I guess if one space is a disjoint union of spaces then it does

what if none of them are

Balarka Sen

It does for very pathological spaces too.

Mike Miller

6:28 PM

@SamuelYusim: It matters if the spaces look different near some points than others, for one thing, like for $S^1 \vee S^1$. What you really want, for this operation to not matter, is if you're thinking of $X \vee Y$, there to be a homeomorphism on $X$ that takes any one point to any other point.

We say that the homeomorphism group acts transitively in this case. This is true, for instance, for connected manifolds.

If this is true, it doesn't matter what point in $X$ you pick; if it's true for $Y$, it doesn't matter what point in $Y$ you pick.

Balarka Sen

I guess you can whip an example up using infinite earring.

N3buchadnezzar

Bah

Balarka Sen

Or the cone over it.

Mike Miller

But, for instance, consider $S^1 \vee S^1$. If I wedged on another circle at the wedge point, it would look different than if I wedged on another circle away from it.

Samuel Yusim

true

Balarka Sen

6:29 PM

Oh, yes, I was thinking of spaces upto homotopy equiv.

Samuel Yusim

why, then, does the notation seem not to encode this information

Balarka Sen

Abuse of notation.

Samuel Yusim

to abuse notation you first need a good notation to abuse

Ted Shifrin

you do?

Samuel Yusim

in my mind you do

Mike Miller

6:31 PM

@SamuelYusim: 1) One often does this with manifolds. 2) The operation is most useful for pointed spaces (for obvious reasons); the wedge sum is the coproduct of pointed spaces. So often $X \vee Y$ is written in the case that $X$ and $Y$ are pointed spaces...

Samuel Yusim

ah, I didn't know what a pointed space was but I just looked it up

Balarka Sen

they are a useful notion.

Mike Miller

don't throw a riot about connected sums later, which is only unique if one of your manifolds is non-orientable or if they both are and you demand that the sum be done in an orientation-preserving way... and even then it takes some work to show uniqueness... and we write it $M \# N$ :)

Samuel Yusim

I dunno what connected sums are yet but I'll keep it in mind when I eventually see them

Mike Miller

it's similar to wedge sum, but done in a way so that it actually spits out a manifold

Samuel Yusim

6:36 PM

makes sense

Balarka Sen

Chuck a copy of disk from each manifold, and glue the two resulting spaces along the bd of the removed disk

Samuel Yusim

neat

probably a more important question: how should I be thinking about open sets in a quotient space?

Mike Miller

The simplest example of a quotient space is where you just pick a subspace $A$ and identify it to a point. In this case, there is a correspondence between open sets containing $[A]$ and open neighborhoods of $A$ in $X$. This is indicative of the general case.

In general points of the quotient space correspond to sets of points in the original space, and neighborhoods of points in the bottom space correspond to neighborhoods of those sets in the original space.

This is going to be hard to visualize if your equicalence classes aren't nice. $[0,1]^n$ is a quotient of $[0,1]$.

Samuel Yusim

6:51 PM

so what happens to a neighbourhood of a strict subset of those points?

to use your first example, if $S \subset A$ and $N$ is a neighbourhood of $S$, what does $N$ correspond to in $X/A$?

I actually have to go, sorry

I'll be back later though

Mike Miller

It doesn't correspond to anything, unfortunately.

evinda

@Alessandro Hast du dir gestern eurovision angeguckt?

Alessandro

@evinda Was ist das? Ich sehe fast nie fern :(

evinda

7:09 PM

Es ist ein internationaler Musikwettbewerb. Italien hat den dritten Platz belegt. Schweden hat gewonnen: youtube.com/watch?v=5sGOwFVUU0I

@Alessandro Wie findest du das Lied?

Semiclassical

hi chat

Alessandro

Das Lied gefällt mir gut, und das Bühnenbild auch (can you use Bühnenbild for this kind of show or is it used only for the static elements of the scenery?)

evinda

Yes, you can use it... :) @Alessandro

LeGrandDODOM

7:55 PM