Mathematics - 2018-04-04 (page 5 of 5)

Akiva Weinberger

19:27

@TedShifrin Ohhh… I forgot to multiply the residue by $2\pi i$.

(@GFauxPas)

GFauxPas

That'll do it

anakhronizein

What's the repeated idea of quotients of the for $I/I^2$ from

e.g. like the cotangent space definition

I just saw another construction that used the ideal of nilpotent functions for I and again another thing pops out as this quotient.

Mike Miller

I dunno

anakhronizein

What have you been up to @MikeMiller ?

Still in the writing process?

Mike Miller

19:42

I will never finish

Writing a talk for Friday now

Semiclassical

Graduate time dilation: It doesn't take forever, but it sure as hell feels like it.

anakhronizein

Heh.

@MikeMiller I was wondering if you think Ko Honda would receptive to emails about his notes on contact topology.

I am always wary about emailing professors from different universities about what they write. I don't want to be a pest.

He's on a sabbatical anyways, I hear.

Drag and Drop

Whats the correct way of saying that: 2/3 is twice more favorable outcomes that 1/2? As 1/2 = 1 or 0 and 2/3 is 1 or 1 or 0. My english failed to formulate this tricky sentence

Mike Miller

@anakhronizein Maybe, I don't know. My money is he would be slow to respond.

anakhronizein

19:57

Most professors are.

Daminark

Yo

anakhronizein

Hi Daminark, how are you?

Daminark

I'm doing alright, how about you?

Sha Vuklia

guys

anakhronizein

Good.

Sha Vuklia

20:04

is the underlined trivial?

I need to know quick:p

anakhronizein

If it is not obvious to you that it is trivial, then it is not trivial.

Sha Vuklia

I have to hand in questions about the text

but I don't know if this is trivial

I don't see it now

I don't want to hand in a stupid question:p

Daminark

Lol this reminds of one time in office hours last year for analysis, someone asked why we were allowed to use Besicovitch in a proof from class, and at the time we couldn't figure it out. 2 hours later I was walking down the hall, passed my professor, and she was like "Wait turns out it was trivial!"

In this case it legitimately was, we just had to do it on bounded sets

Balarka Sen

@TedShifrin Only because I have left the chat

I shall return soon

Like Jesus did

Sorry too much Eurocentrism on my part I guess

I take that back

anakhronizein

dat balarka

Daminark

20:22

@Balarka the cure to eurocentrism is characterizing the "big pieces of Lipschitz graph" property using projections

Sha Vuklia

@Dami so you don't see it right away either?

then I'll just include this question:p

Daminark

Well I'm not sure of the notation even

Sha Vuklia

lol bro

that is standard notation I believe

Daminark

But the neighborhood around that sentence doesn't quite imply the underlined bit to me

I'm not sure what $\chi'$ and $\Delta(G)$ are

Sha Vuklia

chi ia colour number, prime means line graph, delta means maximum degree

is*

Daminark

20:29

Never heard of line graph

So gimme a sec

Sha Vuklia

well edge colouring

but you've reassured me:p

oh my project partner just explained it

alright so nvm

Daminark

But the thing is you'd need a lower bound of some kind

Oh huh

Sha Vuklia

haha yea I have to go now, I'm changing trains

Zee

21:02

Can you take a Cartesian product of a set X and an empty set? What’s the result

Just X ?

Mike Miller

The elements of a Cartesian product are pairs (x,y) where x is an element of X and y is an element of Y

If Y is empty there are no such pairs

So the product is the empty set

Zee

It’s seems more like a convention than a logical conclusion but ok

Thanks

Mike Miller

Dunno what there strikes you as convention

Balarka Sen

It's perfectly logical

Zee

I mean the empty set is also an Elena of y

Balarka Sen

21:14

Vacuous truth

In mathematics and logic, a vacuous truth is a statement that asserts that all members of the empty set have a certain property. For example, the statement "all cell phones in the room are turned off" will be true whenever there are no cell phones in the room. In this case, the statement "all cell phones in the room are turned on" would also be vacuously true, as would the conjunction of the two: "all cell phones in the room are turned on and turned off". More formally, a relatively well-defined usage refers to a conditional statement with a false antecedent. One example of such a statement is...

Zee

So you get (x,empty ) = x

Mike Miller

The empty set is not an element of the empty set. It's a subset of the empty set (the only subset)

Balarka Sen

The empty set by definition has no elements

Mike Miller

The empty set is by definition the only set with no elements.

Zee

The empty set is an element of any set

Balarka Sen

21:15

No. Is a subset of any set.

Zee

Fine

Am just annoyed empty X set = empty

I think empty X set = set

Mike Miller

Are you also annoyed that zero times any number is zero?

Zee

No

Balarka Sen

That's what you get when you measure the cardinalities, so you should not be annoyed by this either

Zee

Alright

Although zero times number is about measures not cardinals

Faust

21:43

TACO

How is everyone?

Zee

21:58

Good , How are you

Gtg though

Akiva Weinberger

22:51

Tacocat @Faust

I like that "cat attack" is a palindrome phonetically (even if not orthographically)

Phonemically

Ted Shifrin

rehi DogAteMy ... hi, @Faust

Eric Silva

@Ted how's it going

Ted Shifrin

rehi Eric.

Shaun

Hi everyone!

Ted Shifrin

23:06

hi @Shaun, whoever you be.

Shaun

I'm studying for a PhD in Combinatorial Group Theory and, lately, I'm finding it difficult to stay motivated :/

Ted Shifrin

All Ph.D. students go through waves of frustration, lack of motivation, and excitement and progress.

3

Shaun

It's a beautiful area to work on though.

Ted Shifrin

See? That sounds positive :)

Our resident more algebraic people aren't around at the moment.

Eric Silva

what is combinatorial group theory

Faust

23:08

i like algebra its just that i know nothing

Ted Shifrin

You like most things, @Faust ... well, maybe you hate analysis.

Shaun

Combinatorial group theory studies groups via their presentations.

Faust

@TedShifrin lol you know me so well =)

Eric Silva

o i thought that was like the historical term for geometric group theory

Ted Shifrin

I think geometric group theory is more interaction with topology.

Faust

23:10

@TedShifrin you have any second course in linear algebra exercises or old tests?

Eric Silva

@TedShifrin hence the historical

Ted Shifrin

I've never taught that course, literally, @Faust. I taught a lot of the material in the Artin algebra course, but that was way before LaTeX and I don't have old materials.

Eric Silva

there was a time before LaTeX?

Faust

Alegedly

allegedly?

word

Ted Shifrin

I typed everything on old fashioned typewriters, yup.

Faust

23:12

O.o

yeah i come from the generation that doesnt really understand how to use the mail or cheques

Ted Shifrin

I still remember typing my thesis on a Hermes 3000. I loved that typewriter, but NO math symbols.

Indeed, @Faust, or much else :P

Eric Silva

i know how to use both those things and im p sure im younger than you Faust

Ted Shifrin

LOL, Eric.

Faust

i dont know how to use eithier

not important why learn

Ted Shifrin

I still use both, rarely, but occasionally.

Eric Silva

23:14

it's not so much a thing you learn as when you do it once it's so simple that it's hard to forget how to do it

Ted Shifrin

With dementia, one forgets most things, Eric.

Antonios-Alexandros Robotis

hello

Mike Miller

you'll find a need to use checks soon enough

Faust

i tried to mail a letter once, mailed it to myself

Mike Miller

as soon as you start cursing out your landlord

Ted Shifrin

23:15

Heya @Antonios :)

Antonios-Alexandros Robotis

hows it going

i have a question which perhaps you might be able to help with?

Eric Silva

i concede that it's not really a thing that matters if you have the power of google on your side

Faust

yeah i moved out of my grandparents and bought my first place when i was 18 now i have 5 properties dont think its likely ima ever gunna have a landlord. also i accept email transfers cause its not the the 1800's

Mike Miller

lol ok

Eric Silva

my landlord's dog is really cute

Mike Miller

23:17

congrats on your 5 properties mate the rest of us will be coping with the world around us

Ted Shifrin

@Faust will be our next slumlord.

I haven't met my new landlord.

Faust

@TedShifrin no way i may buy destroyed places but i always renovate them myself to like new condition. if you make a place nice its easier to keep good tenants

Antonios-Alexandros Robotis

Here's what I'm stuck on: I'm reading a proof and the author claims that to construct an isomorphism of locally constant sheaves on $X$ its sufficient to work on an open covering $\{U_i\}$ of $X$ and show the isomorphism on each open.

Ted Shifrin

Sure thing. I think my new landlord is happy to have me, even though I'm making him pay for a new microwave after only a week. :)

Antonios-Alexandros Robotis

Once I have this, the proof is fairly simple.

Leaky Nun

23:19

@Antonios-AlexandrosRobotis sheaf axioms?

Antonios-Alexandros Robotis

its not true for general sheaves

or at least not as far as I can tell

Ted Shifrin

Um ...

Antonios-Alexandros Robotis

sheaves can be locally isomorphic but not globally

Have I made an obvious error ? :P

Faust

@TedShifrin its all a write off, you shouldnt cook too much food with a microwave though

Ted Shifrin

Trust me, @Faust. I know what I'm doing with cooking.

Faust

23:21

you've never invited me over for dinner so i wouldn't know :P

Daminark

Hello nerds

Ted Shifrin

Hi Demonark

Shaun

You're better off asking that on the main site, @Antonios-AlexandrosRobotis

Faust

morning polarbear

Antonios-Alexandros Robotis

yeah probly @Shaun

Eric Silva

23:23

@Daminark yo what did marianna do today my brain hurt so i didnt listen super hard

Faust

1

Q: Find an inner product.

Suppose V is a vector space over $\Bbb C$ (without an inner product), and that $T \in \mathcal L (V )$ is diagonalizable. Prove that there exists an inner product $\langle ·, · \rangle $ on V such that, with respect to this inner product, T is normal. My original thought is well we have $T= U D...

linear-algebra

Ted Shifrin

No, @Shaun, we have people who can handle it here.

But I'm trying to do six things at once.

Faust

@TedShifrin does my argument make sense?

im trying to avoid doing any work...

uniqueness of inverses is ftw

Shaun

Anyway, as I was saying, I'm struggling with my motivation; a couple of supervisor meetings ago my supervisor said I should be studying at least 5 hours a day but I'm only doing about one if I'm lucky :/

Daminark

@EricSilva Damn, sorry. So, we talked about cross ratio, reflections, and classified automorphisms of the unit disk

Faust

23:25

also can someone explain what the difference between and unitary matrix and an isometry is?

Daminark

Specifically, they're all of the form $c\frac{z-z_0}{z\overline{z_0} - 1}$ for some $z_0 \in B(0,1)$ and $|c| = 1$

Eric Silva

ok so i missed good stuff but nothing i havent seen before cool

Ted Shifrin

Yeah, one hour a day won't cut it. I probably averaged 8-10 in grad school.

Faust

@Shaun sounds like the motivation problem im having right now dont want to do anything cause im sick

Ted Shifrin

@Faust: Still sick? Ugh. An isometry of $\Bbb C^n$ that fixes the origin is unitary. But you can have a translation.

Daminark

23:27

There was a homework problem. Show that two points are symmetric about a circle/line iff any other circle/line going through them is orthogonal to the first

Faust

how can i tell when an isometry is a unitary then? @TedShifrin

i didnt know i was working with translations

Ted Shifrin

Does it fix the origin? ... This is a rather important theorem — that any isometry that fixes the origin must be linear.

What's your definition of isometry?

Faust

but if $T\in \mathcal L (V) $ its always fixes the origin

Ted Shifrin

So it's a linear map that's an isometry.

Then it must be unitary, yes. That's a real theorem.

Well, no, it's easy.

Faust

its easy

just me being silly thanks

Ted Shifrin

23:28

Usually, the hard part is deducing linearity.

@Antonios: The crucial thing is why locally-defined things glue to make something global in the first place. So the question needs a bit more precision.

Eric Silva

@Daminark hmmmmmmm

Faust

Diagonalizable is OP

Shaun

I know, @TedShifrin. It's particularly odd because I've been wanting to do a PhD for many years now. The main problem, I guess, is that, a few months ago, my results were superseded by the work of some American mathematician, so I had to change topics (within CGT). This new topic is much more difficult than the last.

Faust

it just gives you everything you want almost always

Antonios-Alexandros Robotis

@TedShifrin actually I may have answered my own question. I'll let you know.

Ted Shifrin

23:30

OK, @Antonios. Happy to chat when it's calmer :)

Antonios-Alexandros Robotis

okay! I'll be tabbed out working on this but ping me if need be.

Ted Shifrin

@Shaun: That's never fun. If you actually had a definitive result, it might still have been publishable even if someone else did it simultaneously.

Shaun

I'm sorry to hear that you're sick, @Faust :/

Faust

I been sick since the end of February nothing new sadly was told to drop all my classes but im still taking a couple feeling really half assed and unmotivated despite loving mathematics :(

Shaun

@TedShifrin Nah, I'd only worked on it for a fee of months - I got a few preliminary lemmas but nothing publishable.

Faust

23:34

Anyway i hope you find your motivation @Shaun

Shaun

Thank you, @Faust.

*few

Damn predictive text . . .

Ted Shifrin

Gotcha Shaun. Well, maybe you can understand that person's work and delve into it a bit tangentially.

Daminark

Is it often that people get sniped in publishing?

Ted Shifrin

In hot fields, it happens, Demonark. One reason I never worked on the most trendy stuff :P

Mike Miller

@TedShifrin Depression is 6x higher in PhD students than the general public, too.

Daminark

23:37

Ouch, that's definitely no fun. Not working on trendy stuff is probably a good idea

Faust

@MikeMiller thats not surprising lots of studies suggest that theirs a correlation between high intelligence and mental illness.

Eric Silva

i think it has more to do with academia being trash than people being smart

2

Faust

@EricSilva life just sucks being a student is wonderful compared to my old job

Ted Shifrin

@MikeM: Is that across all fields?

Shaun

I'll certainly look into it, @TedShifrin; I don't know if I could allude to it in my current topic as it's completely different. (I'm now trying to establish the Tits Alternative for a certain class of cyclically presented groups.)

Eric Silva

23:39

@Faust grad students arent just students

Mike Miller

@Faust Life sucks, says guy with 5 properties

Ted Shifrin

I'm just suggesting that because you already had gotten into that sort of question, @Shaun. But your supervisor would obviously know better than I. When I did research, it was in complex differential geometry and some classical projective algebraic geometry.

@MikeM: No need for that language.

Thank you.

0celo7

@TedShifrin I left a comment on the GMT question you linked that's a little more helpful than the guy who linked Federer's Amazon page.

Faust

@MikeMiller i grew up in a family thats was as dysfunctional as possible whole family has substance abuse and abuse problems, my mother had severe drug problems mental illness she used to beat the living crap outta me just for fun, i have 6 different learning disability including autism and no one gave me anything in my life i had to work for everything i have.

yes life sucks and yes i was lucky enough that my grandparents took me away from my mother but i can defiantly say that it is true that life sucks but its better than not existing so you might as well make the best of the time you have here cause its all you get.

Shaun

I've got to go. (It's late here.) Thank you for listening :)

Faust

23:45

good night and good luck

Transcript for

$Mathematics$ Mathematics