@TedShifrin Hey Ted! What's new amigo?

ATTENTION: all bounty hunters^ :-)

@skillpatrol ;)

interesting...

Yikes, went to the mods office chatroom, followed one of the star messages, and I realized I have isolated myself so much I forgot there were incredibly annoying people(with entitlement issues) on the internet. Starts thinking what teaching is like

lol

been solving physics all day :D

damn I don't like physics stack exchange its not like here

I prefer mathematicians

brb will go for a walk

@mixedmath For the blog posts what is the notation that is used for math modes, would I be able to use things like \DeclareMathOperator, and other things like that? And is markdown used for the rest, like main? I was thinking of modifying this post for the community blog (like change a bit of notation, maybe remove some remarks, add some details here and there etc).

Do you think the organization of the post is fine? And do you thing that there is enough information in the post to make it relatively self contained for the blog @mixedmath

I think so, it was the one that lead to Ali and his tag war

Do you study physics? @KarimMansour

no math

I am interested in mathematical physics though

I see

interesting subject @MaryStar

Yes, but it is a little difficult (for me) @KarimMansour

@AlexClark Yes, although almost all of them are from Lord Farins

Hi @Stan

Hi @Karim, @Mary

Hi @TedShifrin

I see @MaryStar

Hello @TedShifrin

@TedShifrin Congrats on retiring!

Hi @AlexC, @AlexG, @AlexW

Wooot!

Lol, thanks, Stan. Get my house sold :)

how much you gonna sell it for ?

@TedShifrin

Did you finally get the LM right, Stan? Last message I got was still not right.

Not a meaningful discussion for here, @Karim :)

Flying back to Atl tomorrow morning.

You?

I guess Disciple of Wilma does not get hi...

@TedShifrin

@TedShifrin nah, busy. But I'm almost done. Then I'm going to finish that problem and take your calc exam. I'm done next Tuesday and then have all summer to study math :D but they are offering almost no courses here, so I dunno what to do about that.

Hi Paul :)

Damn, we finished a month ago.

Quarters are always later .... Stan, better not to burn out on summer classes.

That's probably wise.

<--- occasionally wise.

Lolol

Makes sense, since summer is beastly hot, @AlexC

@TedShifrin im hoping to up my knowledge of probability this summer. I tried to learn Lebesgue integration, measure theory, and sigma algebras, but I never found a book I liked that was at my level. I tried an Introduction to Continuous Time Stochastic Processes, but I think it asked too much because, for instance, I couldn't figure out what Borel sets were.

Oh, start with Ash's book on line. Two different books, one undergrad, one grad. Seemed ok to look at.

That's great okay. I'll check it out.

What are you up to this summer?

Cleaning out my office, getting my house sold, I hope, and moving the latter part of July. Just found a place to live and bought a car ....

Nice! Where is your new home?

San Diego

Cool. Why there? I always wanted to visit there when I lived in Pasadena but I never got a chance with Caltech's workload.

@AlexClark oh, @AlecTeal packed me off to a private chatroom yesterday evening where he started explaining stuff to me. and he does a good job of it :)

just finished the free groups section properly. it all clicked, miraculously.

@Stan: I grew up in CA and have longtime, good friends in SD.

Heading off ... G'night.

@evinda No, you can't. You can choose $b$ to be a function that oscillates between $\pm 1$ quick enough to make the integral without $|\cdot |$ converge to any number.

@Dave the roots of $ax^2 + bx + c$ are $\frac{-b \pm \sqrt{\Delta}}{2a}$. If $\Delta$ is zero, what do you think the roots are?

@Semiclassical Is it not possible to do the asymptotics in this regime with the available asymptotics for the Chebyshev polys?

@AlexClark you've been very busy these past two days.

assignment?

@AntonioVargas: didn't say I couldn't do the asymptotics in that case (in fact, i basically did in what i wrote out earlier)

what i meant was that 1) i need to actually write up that case, and i'm being a stick in the mud about it

Ohh haha, gotcha

2) i'd like to find a way of doing so which is more readily generalized to cases where the explicit form of the characteristic polynomial isn't available

You can do it!

Oh ok, I see

particularly ones which amount to promoting the matrix elements to be themselves matrices, i.e. block structure

@evinda actually I take that back for now, my construction is flawed.

which isn't immediately terrible, since i know that there's a lot known about block toeplitz/jacobi asymptotics, albeit less explicitly than in the usual scalar case

i discovered something neat today, though, while looking at the physics side of the literature

what we've been doing amounts to characterizing what's known as the 'free energy' of our system. but what people have been interested in more recently is what's known as the system's 'entanglement entropy'

and with that in mind, take a look at this paper:

insti.physics.sunysb.edu/~korepin/its.pdf

(finally found it in my browser history)

so a paper by Alexander Its talking about the connection between Toeplitz determinants and entanglement entropy of spin chains :P

@evinda, ok, take $b(t) = e^{-ab}c(t)$, where $$c(t) = \begin{cases}\frac{1}{2k+1} & \text{if } 2k \leq t < 2k+1, \\ -\frac{1}{2k} & \text{if } 2k-1 \leq t < 2k. \end{cases}$$ Then we should have $\int_0^\infty e^{at}b(t)\,dt = \sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{k} = \log 2$ and $\int_0^\infty e^{at}|b(t)|\,dt = \sum_{k=1}^{\infty} \frac{1}{k} = \infty$.

@Semiclassical Interesting. I'll take a look at it tomorrow. I should head to sleep tonight :)

kk, talk to you later

cya

anyone here who can help me with a little algebra?

nice stuff @Semiclassical

@PaulPlummer perhaps tragically, the blog isn't in markdown+mathjax like the main site

but I have a utility that I wrote that converts markdown+mathjax that one might find on the site into wordpress-compatible mathjax

it works pretty well, I think, though it's not perfect

it may or may not be more efficient to simply copy the source of the post into wordpress and see how it displays it, and make the (probably pretty small) corrections that occur

Hello@Soham

@PaulPlummer I think the post should be fine. But I should remind you that I do not make all the blog decisions, I just happen to be the lead maintainer. If this is something you'd like to pursue, I recommend that you go to math.blogoverflow.com/wp-admin and try to log in. If it's your first time, let me know after you try and I can give you drafting permissions. Then draft and format the post, and we'll have some others look at it. I would feel confident that it would be well-received

@mixedmath do you think math Ed would be appropriate for the blog?

@skillpatrol I don't know. What do you have in mind?

@mixedmath Alright, I logged in. I will work on editing the post over the next couple of days to get it to around where I would want it.

the elevator pitch is "good content that would be interesting to this community"

which is pretty broad, i think

@PaulPlummer when you look again, you should see that you have new powers

That is pretty broad, haha

@Paul, I need a bit of help.

Need help with what? @SohamChowdhury

Are the final objects in this category pairs $(j,G)$, where $j$ is a function mapping everything to $\ast$ and $G$ is a trivial group $\{\ast\}$?

@mixedmath Cool, It looks like I just do a "new post" and start putting things in there, I am guessing.

@PaulPlummer?

@PaulPlummer yepyep! you'll find that you're unable to publish it yourself -- ping me or another mod (or anorton or leo if you see them) and we'll take a look

@SohamChowdhury, what software you use to take these snapshots? just to know, I use sometimes lightshot but I ilke to know a little about these kind of programs

What? I have not even read it yet, just wait a bit @SohamChowdhury

oh, Ubuntu has a nice inbuilt bit of software, @Masacroso

Sounds good @mixedmath

it's been a while since I was on a Windows box.

@PaulP take your time :)

@SohamChowdhury hmm? a Ubuntu user?

oh, ok, ty @SohamChowdhury

@SohamChowdhury Been planning on moving back to Arch Linux (just put it on a usb stick earlier today)

@mixedmath prefer Arch

I love ubuntu but I dont have enough space on disk to have installed this system too :(

@SohamChowdhury yes, my last box was Arch. Now I'm lazy and am just running debian

but I've been on Ubuntu for around a month because I had to get this laptop up and running quickly after I got a new HDD

I imagine there's a Gentoo user here somewhere. :P

@SohamChowdhury Well does there exist a unique morphism $ \to (j,1)$ for every object $(h,H)$?

1 is a group?

The trivial group

oh.

yeah, send everything to the only element.

@SohamChowdhury Always wanted to try Gentoo, or some source based distro, but figured if I go that far may as well do some linux from scratch

Seems like you answered your own question @SohamChowdhury

:)

so (j,1) are final objects?

nice.

Yes

thanks for checking that for me.

Your intuition is good so far

No problem

so far

crosses fingers

algebra is disturbing... :p

Well for these types of things getting an intuition for the initial object is a bit trickier, not necessarily hard, just not so trivial

but I love Noether anyway :p

@SohamChowdhury Do you know how to pronounce the name Mj?

(speaking of Noether)

Not sure, yet @mixedmath :-)

Thanks for replying.

one quick question, what you think is the value of $\binom{-1}{-1}$??

1?

@PaulPlummer Mj?

"Mye"?

yes, I think is 1 with no doubt but anyway I wanted some confirmation

wait.

Yes, I am guessing it is some sort of Indian name. Like: MAHAN MJ

Not as far as I know.

@Masacroso wolframalpha.com/input/?i=-1+choose+-1

Okay, maybe I will ask Balarka since he knows the guy. Is it pronounced "Mye" or are you just wondering if that is what I meant @SohamChowdhury

yesterday I lost a lot of hours trying to understand 2 pages of a book and, in the end, I discovered that the book was terrible wrong

just cause it assumes that $\binom{-1}{-1}=0$, but I dont think so for any point of view... it doesnt seems any kind of convention here

@PaulPlummer Oh, no.

Maharaj.

That's a short form.

That guy worked with Perelman, yes.

It's a title. He belongs to a certain monastic order.

I've been to a lecture of his, a loooong time back.

This guy

@skillpatrol well, if something strikes you, let us know

So it would be be said as the full name Maharaj, I was wondering where all the vowels went

Wait. @Balarka, do you go to Vivekananda?

Oh.

Interesting guy

I would guess Mj is an abbreviation for Maharaj, sort of like M.J. is for Micheal Jackson :P

Will do @mixedmath

harro

Btw, maharaj means king.

Hi pal :)

One could say M.J. was the Mj of pop music :P

\jk

Maharaja

Maharaj is also a title for the monks of the Ramakrishna Mission.

i think i corresponded w/ someone on MSE that i know in real life

Well, I might live in your village, you never know.

im the only one here who has internet, the rest are hunter-gatherers

:D

@iwriteonbananas watch your mouth, i'm a pure-blood neanderthal.

yikes

what are you doing?

complex analysis

not sure how to proceed in this problem however

what are you studying?

algebra.

doing a set of free groups exercises.

with a lot of nonsense ;)

that's cool

so you're doing this in the language of categories?

@AlexClark yeah, and if it really is him, then he certainly knows who i am. i'll ask him next time i see him haha

@AlexClark quite close, should get there in a day.

@iwriteonbananas Aluffi <3

You get a universal property, he gets a universal property, everyone gets a universal property!

@AlexClark Nope, school's from the 15th.

@SohamChowdhury the free group functor is left-adjoint to the forgetful functor from Groups to Sets

And I have a goddamned huge environmental science project to do.

@iwriteonbananas well. that's not something I understand yet.

@AlexClark 35 bar graphs on the Nepal earthquake plus around forty pages of text.

Aid received per country, etc.

:(

I'm procrastinating hard on this.

Relevant.

@SohamChowdhury yeah, doesnt matter. free group functor is cool because you feed it a set and it spits out a group

yeah, I know that bit.

have to learn about adjoints sometime.

ooh.

so the free group functor adds structure and the forgetful one throws it away?

something like that?

exactly

hmm.

forgetful functor takes a group and just forgets that it's a group

whenever you have an adjoint functor to a forgetful functor, it usually means adding structure, and there is usually some work involved in that

left-adjointness means that there is a family of bijections $\text{mor}_{ \text{Groups}}(F(X), Y) \cong \text{mor}_{ \text{Sets}}(X, G(Y))$ where $F$ is the fere group functor and $G$ the forgetful functor

satisfying a naturality condition

anyways, doesnt really matter. im procrastinating bc i dont know how to do this complex analysis stuff

if you keep doing that, @skill, I'm gonna ignore you.

hello, @iwriteonbananas

any luck defining degree with abstract homology? :P

@Balarka can you help me with something?

why are pairs (e,T) not initial in this category? (where T is a trivial group and e sends everything in A to the lone element of T)

don't ask me anything about categories

i am not the right guy

and was I right? You go to RKMVU?

no, who said that?

you did, apparently.

i don't recall.

chat.stackexchange.com/transcript/14798/2014/5/29/14-16 :P

ok, fine. yes, i do.

you dig up stuff from odd places, @Soham :P

why did you lie? I'm curious.

no, actually, I suddenly remembered that I had been to one of Mahan Mj's lectures.

i was just having some fun, wondering how you came up with it :)

once.

really, @Soham?

you are in xaviers, then?

so I looked him up and saw that he was a topologist and was at RKMVU.

@BalarkaSen nope, it was some sort of public expository thingy

and that is in Howrah, where I believe you live.

eh, not quite a topologist. geometric topologist, sure, but mostly a geometric group theorist.

2 + 2 = ? :P

@BalarkaSen oh.

that's how I got to know about hyperbolic stuff :)

anyway.

gromov?

@SohamChowdhury that guess didn't work.

oh.

never mind.

i don't need to know where you live. :)

so he teaches you stuff as well?

he is not the only professor in rkmvu, you know.

yeah.

"as well"

(personally, i don't think he's a good teacher. but his geometric intuition is great)

haha

cf. Bourbaki/Lang joke

@BalarkaSen That is old news

:P

the title sure is great, disregarding the content of the question.

many many times mathexchange is sooo serious... I hope nobody changes this title, is extremely funny

Humour is relative.

all is relative @skillpatrol :)

True dat bro :)

(phew... you dont started something like "but $\pi$ is $\pi$ no matter what" and this kind of stuff :) )

philosophy.SE is down the hallway, kids.

there is a phylosophy.se?

@SohamChowdhury no, I don't think he worked with perelman.

Yah I don't think so either

Perelman was doing his postdoc when he was doing his PhD

oh, god, ty @SohamChowdhury :)

Perelman was doing his PhD when he was a grad student

That is not the same as working with him @SohamChowdhury

so, yes, not "worked with".

I didn't remember.

I had to check.

He may have been in the same room as him a couple times

Haha.

Maybe even some conversations, if Perelman talks

Good question.

@PaulPlummer haha at "if perelman talks"

I last saw him around four years ago, so I think I might be forgiven for inaccuracy.

man, phylosophy.se is so funny... xDDD, a lot of absurd questions there

@Paul so, planning to do a lot of algebraic topology? or already started on it?

@Paul, can you help me with the question I asked Balarka a while back?

I started reading chapter 0 a bit, and thought a some about the "two rooms"

may have to double check my intuition on contracting it to a poing

oh cool. can you visualize why it's homeo to D^3?

Yes, although I think it is a ball

yes, my bad.

@PaulP?

The clay visualization he gives is nice

What are you having trouble with, try an example an you should see fairly quickly @SohamChowdhury

Did you see the question?

here

Yes, do an example @SohamChowdhury and tell me your thoughts on it

I think they are not initial also when A is a singleton.

Philosophy @Masacroso :P

Otherwise, I've solved the problem.

Like I said, give me an example @SohamChowdhury

oh. wait.

(kids these days, don't listen...)

it's done.

@PaulPlummer what example?

are there any?

(e,T) is pretty much unique, I think.

Just give me any example, I don't care, except not one with the final object

oh.

An example of a morphism

it is a good place to learn to write about philosophy on english @skillpatrol, the classical technical terms at least

well, any morphism has to be a unique group hom from T to G that works for all $f$.

so.

Yep @Masacroso

I dunno, there are no morphisms that work, I think. Except if A is empty.

That's what I have to prove.

Okay lets say we have $ \{a\} \to \mathbb Z$ with $a \mapsto 1$

{1} is T?

Wikipedia too pal @Masacroso

oh.

no, never mind.

I understand. Yes, what next?

And give me the commutative diagram, that you claim to exist, for $T \to \mathbb Z$

@PaulPlummer You should prove that a homotopy equivalence is an equivalence relation, and see why the same doesn't work with deformation retraction.

@PaulPlummer it doesn't. as soon as you change your function (i.e. decide to send a to something other than 1), the hom has to change as well, so it doesn't fit.

I think I'm doing a poor job of this, never mind.

yeah @skillpatrol but its not the same see how express ideas on english, IMO. In philosophy language is all... you need to express many very specific things trying, at the same time, not abuse of rare words... it is an art (that I love, ofc :D)

Thanks for trying to help.

I enjoyed doing some multivariable calc from Ted's book, so I wanted him to know... but apparently he is very busy with moving.

@SohamChowdhury The problem is that $a \mapsto \bullet \mapsto 0$, for one direction and the other is $a \mapsto 1$

can't I make $\bullet$ map to 1?

No it has to be a group homomorphism, and homomorphisms map identity to identity

by defining my own $\varphi: T\to G$?

oh.

Z?

@BalarkaSen I will check the equiv relation and the differences. I am having a bit more trouble visualizing the actual contraction from that point directly, I think I had it yesterday, just should double check my intuition

@SohamChowdhury $0$ is the identity in $\mathbb Z$ and $1$ is the generator

a direct contraction can be a bit hard to visualize

it's better to use the transitivity property of htpy equivalences

Yah, pretty sure I had it but I want to make sure I did not actually screw up. I agree that is a better way to prove it, but I feel like "to know to prove it" it is nice to build up a strong geometric intuition

I agree @Masacroso :-)

sure

@PaulPlummer I get it now. Thanks.

No problem. Even in algebra, and abstract nonsense you should work through a relatively concrete example to see what could go wrong

@BalarkaSen harro. why would defining degree w/ abstract homology be difficult?

not difficult, just hopeless to visualize.

as long as we consider homology theories w/ values in $\Bbb{Z}$-Mod

satisfying dimension axiom

oh, yeah

@iwriteonbananas question : consider the collection of all the chain maps from the chain complex of $S^n$ to the chain complex of some nice space $X$.

mod out by chain homotopies between chain maps. this is clearly an abelian group.

are you a native english speaker @skillpatrol??

however, this is larger than homotopy group : not all chain maps are induced from continuous maps $S^n \to X$

yes

so what is this group? it seems like it's something in the middle of homotopy groups and homology groups.

Are you @Masacroso?

seems like we can unify a lot of stuff between homology and homotopy using this group. the similarity between relative homotopy long exact sequence and homology long exact sequence, and mayer vietoris and van kampen, say.

no, Im not @skillpatrol

What is your native language @Masacroso?

I asked cause I want to says something: mathematics (or science in general) books are the easiest thing you can read in a foreign language. Just in the other extreme is poetry and, a bit bottom, philosophy

Im spanish speaking @skillpatrol :)

I see :)