Mathematics - 2014-12-15 (page 9 of 10)

Daniel Rust

10:00 PM

What you do have is an action of $\pi_1(S^1)=\mathbf{Z}$ on the space, given by the monodromy action.

Balarka Sen

sure

Z acts on the cantor set fiber by adding a 1 and acts on the base S^1 by deck transformations

there is a two-fold action of Z on the space

Daniel Rust

I guess I understand the action much better geometrically. You just rotate a point once anti-clockwise 'around' the base circle

Balarka Sen

yikes @Kaj. is that avatar for for new hats?

@DanielRust :/

Kaj Hansen

Nope, just experimenting with avatars :P

Hippalectryon

Can anyone tell me how to use that hint ?

2

A: Splitting the plane to fit convexes

Two hints for the price of one: For the first one, consider the point $P\in K$ closest to the origin, and take $D$ to be normal to the line from $O$ to $P$. For the second one, apply the first one to the set $K-L=\{u-v\colon u\in K, v\in L\}$.

Mike Miller

10:04 PM

@DanielRust are there finite-order homeomorphisms of the cantor set?

Kaj Hansen

Check my hat @BalarkaSen

Alizter

and I have voted

Balarka Sen

ok it's late here and i need sleep. i'll think about what you have said tomorrow @DanielRust.

Daniel Rust

@MikeMiller sure, just take the two 'largest' clopen subsets and permute them.

Mike Miller

gross.

Daniel Rust

10:05 PM

@BalarkaSen No worries. It's fun talking about this stuff.

@MikeMiller Actually I think it might be possible for any finite group to act continuously on the cantor set

Balarka Sen

apparently this monodromy approach would take a hell lot of topology

Alizter

10 days till lie

Daniel Rust

@BalarkaSen Well topology is where I'm most comfortable :P

Mike Miller

I'm most comfortable on a couch

Balarka Sen

i'm negotiating just for algebraic purposes, @DanielRust :P

Daniel Rust

10:07 PM

@MikeMiller Don't talk to me about couches. I went to see a friend in the english department today.... and boy is it a shock to see how the other side live...

Mike Miller

they have them?

Daniel Rust

@MikeMiller beanbags and long sofas in their common room... we don't even have a working coffee machine

Mike Miller

I've long been considering pretending to be a physics student so I can get access to their couches. we don't have any.

4

Daniel Rust

haha

We only have a kitchen. We don't even have a common room.

Balarka Sen

the coffee machines all look like beaten up by a baseball bat in this uni, @DanielRust

they make up coffee every half an hour

sheesh mathematicians

Mike Miller

10:09 PM

well that's universal

Daniel Rust

We have to buy coffee from the library cafe if we want one

Hippalectryon

@MikeMiller Can you hint me regarding the hint above ?

Daniel Rust

Or else make our own with equipment we bring in

Balarka Sen

profs here have personal coffee machines

not to mention how they look like ...

Mike Miller

I don't remember the question, much less the hint, @Hippalectryon

@DanielRust Get a coffee machine but hide it in your office.

Kaj Hansen

10:10 PM

@MikeMiller, it's quite different here. We have the nicest lounge of the STEM majors :)

Hippalectryon

2

Q: Splitting the plane to fit convexes

I'm trying to show the following : Let $K,L$ two closed convexes of $\mathbb{R}^2,O=(0,0)$ If $O\notin K$ then there exists a straight line $D$ going through $O$ such that $K$ is in one of the half of plane defined by $D$ If $K$ is bounded and does not intersect with $L$ then there exists a st...

convex-analysis

@MikeMiller ^

Daniel Rust

Btw, if anyone happens to know group theory beyond an undergrad level, I'd appreciate some help on this question on MO: mathoverflow.net/questions/190789/…

Balarka Sen

@MikeMiller some postdoctoral student brought a tea machine here with him, but then 6 or 7 more students came in asking for tea

Daniel Rust

a tea.... machine?

Studentmath

There is such a thing?

Balarka Sen

10:13 PM

ah you know. a heater

:P

Daniel Rust

surely you just need tea bags / tea leaves and a kettle

Balarka Sen

yeah well electric kettle

Mike Miller

@DanielRust Actually, I recently considered moving a couch into an office nobody uses. But the department sent out an email today saying they were going to inspect our offices once a month to make sure there was no clutter. Maybe they heard the couch rumors.

Kaj Hansen

A "water heater" I guess.

Daniel Rust

I'm in the UK so kettles are standard issue for every office :P

Ted Shifrin

10:14 PM

hi @Hippa, @DanielRust, @Jasper, @Mike, @Kaj ... oh, Kaj has reemerged

Studentmath

Interestingly, there is a kettle/water heater that can cook coffee(!)

@TedShifrin Hullo

Hey @Ted

@Ted \o D:

Indeed! It's been a few days.

Jasper Loy

10:14 PM

@TedShifrin Hi, I am going to bed in 2 hours, lol.

Ted Shifrin

heya @Studentmath

Balarka Sen

Ted is ignoring me for saying "algebra > geometry" :(

3

Mike Miller

hey @Ted

Ted Shifrin

Were you emulsified on Friday, @Kaj?

Mike Miller

You say quite a few frustrating things, @BalarkaSen. I would suspect you're on ignore for a number more than just that.

Daniel Rust

10:15 PM

@TedShifrin I see you're getting into the voting spirit in the election chat

Kaj Hansen

Something like that

Ted Shifrin

Politics just depresses me in general, @DanielRust.

Balarka Sen

@MikeMiller What else O_o?

Ted Shifrin

pulverized, @Kaj?

Jasper Loy

@KajHansen You no longer look like Matt Damon. I guess I am the real Will Hunting, lol.

Kaj Hansen

10:16 PM

hahaha

Mike Miller

@Hippalectryon Was this answer sufficient for your problem, way back when?

Jasper Loy

@KajHansen When did you change your hairstyle?

Studentmath

@TedShifrin how do you survive the US then? Every two years, plus the inbetweens

Ted Shifrin

It's very depressing, @studentmath. One more reason to move to CA ... slightly less so there.

Kaj Hansen

It actually doesn't look much like this right now @JasperLoy

Balarka Sen

10:17 PM

you look like someone with a birthday cake thrown on him @Studentmath

Kaj Hansen

My hair is pretty long right now.

Ted Shifrin

@Kaj: I'm sure my 3500 students feel about me the way you do about you-know-who.

Kaj Hansen

-_-

Hippalectryon

@MikeMiller It wasn't back then (which is why I didn't accept it at that time, because I didn't know the subject well enough) but now it is.

Kaj Hansen

His final wasn't too bad actually.

Ted Shifrin

10:18 PM

No perfect score on the definitions page :(

Kaj Hansen

I got a perfect score on that page! :D

Daniel Rust

@TedShifrin depressing

Ted Shifrin

I saw a version of it, @Kaj. I suggested a few things, but I'm sure he ignored me.

He gave you a definitions page, @Kaj?

Studentmath

@Balarka I thought I look like covered under a huge Hannukiyah

Mike Miller

@Hippalectryon well, in that case let me harass you to go through various stuff you never accepted an answer for and accept it to get it off the unanswered queue :)

Kaj Hansen

10:18 PM

On your definitions page @TedShifrin.

Hippalectryon

@MikeMiller Sure :) please help me with my last question though

Ted Shifrin

Ah, @Kaj ... Good for you. Perfect is quite rare :(

Jasper Loy

@TedShifrin You must be talking about a secret professor in UGA, lol.

Ted Shifrin

@Mike: I get tired of asking people to accept my answers ...

not so secret, @Jasper, but in some ways more notorious than I

Kaj Hansen

I got stuck on the details of one of the problems, but I don't feel too bad since apparently everyone got stuck. Should've gotten everything else though.

Balarka Sen

10:19 PM

UGA sounds like Uganda

Mike Miller

@Hippalectryon Maybe I'll give it a shot.

Ted Shifrin

Well, good, @Kaj, I'm glad to hear that.

Jasper Loy

@TedShifrin I suspect Pete Clark, lol.

Ted Shifrin

No, no, @Jasper, not anyone from here.

Mike Miller

@Hippalectryon Here, I'll make you a deal. If I can decode the hint, I'll post it as an answer. But if you like it, you've gotta accept it before anyone has a chance to upvote. Deal?

Studentmath

10:20 PM

@Hippa what's the question?

Mike Miller

Back off, this is my chance at a hat!

Ted Shifrin

@Studentmath, you ready for your probability final? :D

Balarka Sen

@MikeMiller to get a hat>

Hippalectryon

@Studentmath See above chat.stackexchange.com/transcript/message/19084865#19084865

Balarka Sen

LEL

Jasper Loy

10:20 PM

@MikeMiller You cannot accept an answer too fast on SE.

Daniel Rust

haha

Ted Shifrin

For a f***ing hat, @Mike?

Hippalectryon

@MikeMiller I sense a hat :3

Kaj Hansen

@MikeMiller, what purpose does that serve? The 0-score accepted answer badge or something...?

Mike Miller

@TedShifrin For a f***ing hat.

Hippalectryon

10:21 PM

@MikeMiller Deal

LOL

LEL

Hahaha

"For a hat". I'm dying.

Ted Shifrin

rolls all seven eyes

Jasper Loy

10:21 PM

@BalarkaSen It's hard to distinguish between algebra and geometry when there is algebraic geometry and geometric algebra.

Studentmath

@Ted Excited, I hope I didn't forget too much

evinda

@DanielFischer At the algorithm medianOfMedians we have this command:
for i from 0 to numMedians
So, is i<numMedians or i<=numMedians?

Hippalectryon

@TedShifrin I didn't know you gained the eyes of the infants you eat

Mike Miller

This is how I'm spending my holidays, and I'm enjoying every minute of it.

Balarka Sen

LELELEL @Hippa

Ted Shifrin

10:22 PM

@Hippa ... you've desisted on memes and now you're making up more insidious things about me. Not cool.

Daniel Rust

I got so many hats last year, but I was so disappointed when they disappeared :(... I'm not as enthusiastic this year.

Ted Shifrin

LOL, understandable, @DanielRust.

Daniel Fischer

@evinda When you start at $0$, it should be $<$.

Ted Shifrin

It's only for the holiday season.

Mike Miller

Yes, but I'm currently 8th worldwide. If I slack off, soon I'll be ninth, then tenth...

Daniel Rust

10:23 PM

Also some of the requirements were very arbitrary

Balarka Sen

8th, @Mike?

Hippalectryon

@MikeMiller I've cleaned all my questions. The unaccepted that are left either received no answer, or not good enough ones.

Kaj Hansen

"In hats" I'm guessing, hahhaha

Mike Miller

@Hippalectryon What part of the hint is troublesome?

Balarka Sen

haha

Daniel Rust

10:24 PM

@MikeMiller Wow you got 19 hats already? o.o

Hippalectryon

@MikeMiller I'm not sure how to apply it (especially the first case)

Jasper Loy

@Alizter I got a one line email from Sarah a few days ago, lol.

Kaj Hansen

@MikeMiller, I think if you change your avatar you get a hat (at least I did).

Balarka Sen

undisputed king of hats, @DanielRust

Mike Miller

Okay, I'll write down an explicit solution to the first case.

Alizter

10:24 PM

@JasperLoy Oh really? What did she say?

Ted Shifrin

disappears until the hat craze has passed

Mike Miller

@KajHansen Got that one ages ago. Come on bro. Get on my level.

Jasper Loy

@Alizter Well, I asked her some secret questions, and she replied.

Kaj Hansen

I'm with Ted. Hats are silly.

Balarka Sen

we are c-hating too much about hat.

Ted Shifrin

10:25 PM

Wanna help me grade finals, @Kaj?

Kaj Hansen

Perhaps I'm projecting my sour grapes though.

Sure @TedShifrin. I'll check your definitions pages for minimum wage :P

Jasper Loy

I seldom eat grapes.

Ted Shifrin

Oh, I finished those already.

Daniel Rust

@TedShifrin I had to sit in on 2 hours of oral presentations.... that was too much marking for me already this term.

Ted Shifrin

While I was waiting at the doctor's office 2 hours ago.

Studentmath

10:26 PM

Efficient

Ted Shifrin

Just wait 'til you're an adult, @DanielRust :D

Hippalectryon

Just wait 'til you're a teen, @TedShifrin :D

owait

Daniel Rust

@TedShifrin haha... that day will never come

Jasper Loy

I am looking forward to being a kid again in my next life.

Kaj Hansen

I very much dislike how I cannot check my final grades until Christmas Eve. I HATE this new system. Oasis was much better.

Studentmath

10:27 PM

It's funny, your semester seems to end two months before ours

Daniel Rust

I feel sorry for all the profs that are going to get angry emails on christmas day

Balarka Sen

@Hippalectryon cheeks so much with @Ted, and it has to be I who got ignored? Sigh.

:P

Jasper Loy

@BalarkaSen You sure you being ignored?

Balarka Sen

yes

usukidoll

hats

Daniel Rust

10:28 PM

@usukidoll so much insight

usukidoll

I just have to finish my odds and ends for my pdes and I AM DONE!

Balarka Sen

not with the pee DEs again

Studentmath

I'm off, g'night!

Balarka Sen

Yeah I should go get some sleep too.

Off to bed.

usukidoll

@BalarkaSen yaaaaaaa..........I am getting an above average grade on it x.x I hope no one asks me pdes cuz I don't wanna do anymore

Jasper Loy

10:30 PM

@usukidoll I don't even know how to solve ODEs.

usukidoll

@JasperLoy cuz you suck :P

Jasper Loy

I will have to learn some ODEs though for GRE.

Daniel Rust

PDEs are hard. I'll stick with cohomology groups.

4

usukidoll

odes are fun pdes are ****************!

I have at least over 20 pages worth of pdes and that is per assignment

Jasper Loy

@DanielRust I have seen Taylor's 3 volumes on PDEs, seem to utilize algebra, analysis and geometry as well!

Alizter

10:32 PM

I went to a PDE lecture before

matricies and stuff

Pedro Tamaroff

885 messages since I left.

You guys are chatty.

Jasper Loy

But if I were into PDEs I would mug those 3 volumes.

Alizter

@PedroTamaroff Have you got your campaign logo?

Mike Miller

@DanielRust I'm learning about them next quarter. Terrified.

Pedro Tamaroff

@DanielRust Hehehe.

DEM PDES.

Daniel Rust

10:34 PM

Do you have to do grad level PDEs in the US?

Ted Shifrin

hi @Pedro @Alex

Daniel Rust

I haven't seen a PDE since second year of undergrad

RainyCats

A quick question, just working through a text book. How many ways can you draw 5 cards from a deck and get 3 of a kind. I got C(13, 1) C(4,3) C(49, 2) but the right answer has C(48, 2)

Daniel Rust

@PedroTamaroff Hey!

Pedro Tamaroff

@DanielRust How's the topologist doing?

@TedShifrin Wonders if Ted is still mad at me saying his final was not that challenging.

Ted Shifrin

10:36 PM

@Pedro: You still aren't done ...

Pedro Tamaroff

@TedShifrin I am not.

But I know almost all the answers.

I just have to write them down.

Daniel Rust

@PedroTamaroff Well thanks. This is the glorious week of term where all the undergrads have gone home and I can spend a few hours talking to my supervisor over coffee.

Pedro Tamaroff

As you said, the only problem I might not be able to do is the last.

@DanielRust Nice. =)

@AlexanderGruber The votes for primaries are not showing for me.

I have to click on the 0 to get the scores.

Daniel Rust

negative scores default to 0 I think

Kaj Hansen

They don't show me them either @PedroTamaroff

Jasper Loy

10:37 PM

@PedroTamaroff Why be a mod when you should spend more time on math?

Pedro Tamaroff

@KajHansen Weird...

Mike Miller

This is intentional./

Pedro Tamaroff

@JasperLoy I don't think being a mod will tamper with my math.

Jasper Loy

@PedroTamaroff Did you put up a new pic just for the election?

Pedro Tamaroff

@JasperLoy Someone told me Pollack was boring. I delivered.

Daniel Rust

10:39 PM

@PedroTamaroff the Q&A thread is calling out to you.

Pedro Tamaroff

@DanielRust I am actually answering right now.

@PedroTamaroff :)

@Hippa go

upvotes

@MikeMiller That's a very nice hat you have.

Mike Miller

10:42 PM

you son of a bitch

haha

uuuuugh

flags Mike

@DanielFischer When we have this array:

Daniel Rust

did someone upvote it?

Mike Miller

10:43 PM

Yep

evinda

Daniel Rust

lol... I feel bad for joking about it now

Jasper Loy

@evinda There seems to be no end to you pinging @DanielFischer, lol.

Mike Miller

I'm afraid I'll never achieve my dreams.

Jasper Loy

@Vrouvrou There seems to be no end to you pinging @robjohn, lol.

@MikeMiller That's something I would say.

evinda

10:45 PM

@DanielFischer we will call the fuction partialQuicksort(A,0,1), right?
Then we will get medianIdx=selectIdx(A,0,1,0), but there is no element of order 0.. But what do we do in this case?

Jasper Loy

@MikeMiller There is a couch in my living room. You can rest there if you like.

Mike Miller

Seems a bit far for a nap.

Hippalectryon

@MikeMiller Nice proof

Daniel Rust

@MikeMiller your homeomorphism/diffeomorphism question is strange...

Daniel Fischer

@evinda Why partialQuicksort(A,0,1)? The array has eight elements. And we should pass the range we finally need also as arguments.

Daniel Rust

10:48 PM

@MikeMiller I can't wrap my head around a path of homeomorphisms between two different differential structures....

evinda

@DanielFischer So, aren't there only these 3 parameters? :/

Mike Miller

@DanielRust me neither, but it exists. Note that I'm not looking for an isotopy, just a homotopy.

Daniel Rust

@MikeMiller Oh right, I thought I read isotopy.

Daniel Fischer

@evinda You can also use global variables instead of passing them. But global variables have their problems, so are generally discouraged nowadays.

Daniel Rust

@MikeMiller So is $MCG_{Top}(S^7)$ not the same as $MCG_{Diff}(S^7)$?

Mike Miller

10:50 PM

hell if I know.

evinda

@DanielFischer What other argument should the function have? :/

Mike Miller

that would be a reasonable question too (though I would doubt it's true), but I'm mostly interested in the question of 'can I approximate homeomorphisms by diffeomorphisms?', turning some questions of continuous topology into questions of differential topology. Not particularly effectively, but nonetheless.

Jasper Loy

It seems that Daniel, Jyrki and Pedro are still 1,2,3.

I think it is pretty clear these 3 will be the mods.

Daniel Rust

@MikeMiller Does the simplicial approximation theorem not help?

Alexander Gruber

@PedroTamaroff Maybe nobody voted for you. :P

(I have no idea what's wrong. I'm trying to figure out how to use this Android SE app and it is quite temperamental.)

Mike Miller

10:53 PM

@DanielRust don't see how it would. Now I have some simplicial map that used to be homotopic to a diffeomorphism.

Daniel Fischer

@evinda The range we want to look at after the partial sorting. The $\approx\frac{m}{2}\pm p$. These are needed to skip the recursive calls we don't need.

Daniel Rust

@MikeMiller Well I can imagine a PL map being easier to 'smooth out' than a general continuous map.

although I guess not every smooth manifold has a PL structure

Mike Miller

@DanielRust But I have no trouble homotoping my homeomorphism into a smooth map. The trouble is homotoping it into a diffeomorphism.

Daniel Rust

Oh I see

Mike Miller

Every smooth manifold is PL, and uniquely so (in the appropriate sense) IIRC

evinda

10:54 PM

@DanielFischer And won't this parameter change? Will it be the same at each recursive call?