Mathematics - 2014-07-11 (page 2 of 3)

Ted Shifrin

03:00

Well, bedtime for me. Talk to you soon, @Karl.

Karl Kronenfeld

@TedShifrin Good night

Have fun at the doctor's

AndrewG

03:13

@Ted I'm starting to think I'm just too dumb to get these problem sets :|

Tom Cruise

03:52

la la lala la la lala

Karl Kronenfeld

Damnit, I thought the "evil" puzzles at websudoku would be near impossible. After trying one, they don't really seem that challenging.

Anybody have suggestions for other online sudoku puzzles?

is bored :)

Tom Cruise

Tom Cruise don't do sudoku

Balarka Sen

04:13

@Studentmath that's transfinite induction, quite different from the (false) model I showed.

@SanathDevalapurkar Personally I am very much interested in modular curves and stuffs but I never had the fortune to compute the genus of X(N) so I never needed Riemann-Roch or Riemann-Hurwitz. There are small algebraic tricks for computing special cases like X(5) or X(7).

Also, as you don't quite have the background for number theory, I'd suggest you to go through some algebraic number theory textbook before jumping onto modforms, @Sanath. Also a little galois theory should be done -- you need loads of galois theory of covering spaces to understand modular forms.

OK, I gotta run.

Tom Cruise

whoosh

AndrewG

@Ted ex. 3.2 2. c) is just the angle-sum formula for $\tan$, right? (Also, does this problem mean I can view any Mobius transformation as just a rotation/reflection of $S^1$? What about translations? Is that part d?)

blue

07:06

I want to see finite indecomposable algebras classified.

Arthur Fischer

08:37

Hi, all. I have a weird request. A particular troll has come back, again, and I want his account blocked from asking questions post-haste. So if you have the ability, please downvote the following question. Don't vote to delete (I can do that later without any help), but I want to see if I can get this troll blocked from asking questions pretty quickly. Thanks!

-3

Q: Contradiction to assumption of completeness?

The limit of the sequence $(s_n)$ with terms $s_n = \{n\}$ is the empty set. This means, among others, that there is no natural number $n$ that remains in all terms of the sequence. The ordered character of the natural numbers allows us to understand this sequence as a super task, transferring th...

set-theory

2

(One account is already blocked from answering, and if I can get one blocked form asking, then I am in a position to very legitimately start a process to throttle his access to the site.)

skullpatrol

@ArthurFischer have to tried to reason with this troll?

Arthur Fischer

@skullpatrol Personally, no. But Asaf, Michael Greinecker, Brian M. Scott, Andres Caicedo among others have in the past, to no avail. He'll continue to push an "anti-infinity" agenda, which amounts to claiming that infinity is a contradictory concept. He will probably also claim to be able to enumerate the reals, but his enumerations invariably leave out 1/3 (as well as all irrational numbers). There is no reasoning with this individual.

skullpatrol

Sort of like Professor Wildberger on YouTube :-)

who has now started to make videos for year 9 math students in Australia...

Arthur Fischer

@skullpatrol Worse. I think Wildberger might have some coherent thoughts once in a while. This person has none. This might give you an idea of what sort of person he is.

Chris's sis

Greetings

skullpatrol

08:51

Greetings my friend :-)

Chris's sis

@skullpatrol Hey:-) How are you doing?

skullpatrol

@Chris'ssis Fine thank you, how are you?

Chris's sis

@skullpatrol Doing some research, thanks. ;)

skullpatrol

nice

Chris's sis

@robjohn Last evening I came up with this series $$\sum_{k=1}^{\infty}\sum_{n=1}^{\infty} \frac{1}{k^2 n^2 (k+n)^2}$$ that is really beautiful. Did you meet it before?

skullpatrol

08:56

@ArthurFischer thanks for sharing that PDF :-)

blue

holy cow, 275 pages of that crap?

r9m

@Chris'ssis I met an interesting cute problem :D .. are there Polynomials $P,Q \in \mathbb{R}[x]$ for which $\displaystyle \int_{0}^{\log n}\frac{P(x)}{Q(x)}\,\mathrm{d}x=\frac{n}{\pi(n)}\quad \text{ for infinitely many }n\in \mathbb{N}$

robjohn

@Chris'ssis It looks familiar, but I don't know if I've handled those exact exponents yet. The same ideas should work here as in other cases though, especially since things converge absolutely here.

Chris's sis

@r9m Yeap, it's nice. ;)

@robjohn The result of the series is really awesome. :D

robjohn

@Chris'ssis I'll look at it in a while.

r9m

09:00

@Chris'ssis Is it a well known problem ? :O

Chris's sis

@robjohn OK

@r9m hmmm, I'll better look at it after I finish my work here.

(I need to change my keyboard...)

r9m

@Chris'ssis okay :D ...

@Chris'ssis do you have hard keys ? :o

Chris's sis

@r9m Yeah ...

nullgeppetto

09:16

Morning all! May you take a look here? cc @DanielFischer

skullpatrol

@nullgeppetto That is first time I have seen someone put "@" in there question :-)

+1

usukidoll

09:39

anyone know how to use the D operator and method of elimination?

I'm stuck at this one tiny part and it's a critical tiny part so that sucks :(

nullgeppetto

09:50

@skullpatrol, :-) This is the right thing, I believe. @DanielFischer has helped me too many times, and this question is the result of a discussion we had tonigh here, in the chatroom. I just wanted to make it clear and visible to anyone may face a similar problem.

ok, I mean the last night ;)

usukidoll

10:13

0

Q: Find a solution to a linear system using the D operator and method of elimination

This is from Introduction to Differential Equations and its applications by Farlow. Info: The $D$ operator Let $D$ denote differentiation with respect to $t$, and let $D^2$ denote the second derivative with respect to $t$. That is $ D = \frac{d^2}{dt^2}$. In general, we denote the quantity $D^...

differential-equations

dat part gawd

nullgeppetto

11:04

Hi @DanielFischer, I've created a question from our last night's discussion here! What about my last comment in the @daw's answer? Many thanks! :)

Daniel Fischer

@nullgeppetto Unless $A$ is a multiple of the identity, $\mathbf{x}^T A\mathbf{x}$ depends not only on $\lVert\mathbf{x}\rVert$, so you can't write it as a product of a function not depending on $\mathbf{x}$ and a function depending only on $\lVert\mathbf{x}\rVert$.

nullgeppetto

@DanielFischer, so shouldn't I even ask whether we can write it as $\mathbf{x}^TA\mathbf{x}=\phi(\mathbf{x}, \lambda_1,\ldots,\lamba_n)\lVert\mathbf{x}\rVert^2$?

Daniel Fischer

11:22

We can't. The value $\mathbf{x}^TA\mathbf{x}$ depends not only on $\mathbf{x}$ and the eigenvalues of $A$, it depends on how $\mathbf{x}$ lies relative to the eigenspaces of $A$. Since every $\mathbf{x}$ can lie in the eigenspace for the largest as well as in the eigenspace for the smallest eigenvalue of a matrix with eigenvalues $\lambda_1,\dotsc,\lambda_n$, you must know precisely which matrix it is to determine $\mathbf{x}^TA\mathbf{x}$.

nullgeppetto

Thanks @DanielFischer!

Daniel Fischer

You're welcome.

nullgeppetto

@DanielFischer, I hope you don't mind that I added your answer above after my last comment. Just in case someone encounters the same problems with me!

Daniel Fischer

No problem.

nullgeppetto

:

:)

skullpatrol

11:39

@DanielFischer any predictions for Sunday?

Daniel Fischer

@skullpatrol Hot and humid.

skullpatrol

:D

Balarka Sen

Some people just downvotes because they like to

skullpatrol

Welcome to the real world.

blue

@BalarkaSen well, the answer to the question is obviously "no," because otherwise the fact of its undecidability would be well-known, like the continuum hypothesis

Balarka Sen

11:50

@blue "obviously "no"" that's just an overestimation.

It's unlikely, but you have no proof of decidability... yet.

blue

@BalarkaSen you think that if we had a proof right now, that it might not be a well-known fact akin to the continuum hypothesis?

Balarka Sen

also, decidability depends on a certain axiomatic system. i think it should be true that GC is PA-undecidable.

@blue probably.

blue

if someone proved/disproved it or the claim of its undecidibility, the news would blare to the high heavens

Balarka Sen

the same point is made by Git Gud

i was interpreting "is there a proof" as "is it likely?"

blue

@BalarkaSen I think git gud was making the same point as the last paragraph of the OP of the MO question (with strange grammar), not my point.

Balarka Sen

11:58

@blue potato pohtato. i am going to finish this argument by repeating what i said there "i think it's unlikely"

i'd be more than surprised to know that a sieve theoretic argument is unachieveable in ZFC

skullpatrol

I find it strange that he doesn't come here anymore.

Balarka Sen

@skullpatrol Not everyone has self-discipline as a moldy old dish rag.

Daniel Fischer

@skullpatrol Who?

Balarka Sen

@blue breakthrough

skullpatrol

@DanielFischer git gud

Daniel Fischer

12:02

Aha. He was a regular visitor here some long time ago?

skullpatrol

yep

Daniel Fischer

People come and go. Only you and Pedro stay forever.

Balarka Sen

haha

skullpatrol

-_-

Balarka Sen

12:26

I just love xkcd

r9m

12:45

Gigantic SIGH ... I made a silly mistake and no one cares ... no down votes .. no comments ... nothing !!! :( ... looks like no one gives a rats a** :'(

Mats Granvik

@r9m You might get the Tumbleweed badge

nullgeppetto

@r9m, what was the mistake?

Balarka Sen

@r9m #{people who give a rats fart about inequalities} is pretty low.

@r9m you mean this?

r9m

13:00

@BalarkaSen ya .. :(

@nullgeppetto I made a mistake in differentiating :P lol

@MatsGranvik that badge is for Questions :P

sorry guys ... I lost my net connection for a moment :|

Balarka Sen

I kinda knew that it might turn out to be false. It might just be too much to expect that a purely number theoretic problem is resolved by application of basic calculus.

So my idea was not so overkill after all. Indeed, I'd be surprised if its not related to differential galois theory.

r9m

@Balarka .. did you see my edited solution ? :P

Balarka Sen

@r9m nah, but i guess it's wrong too.

you better check it once more.

r9m

@BalarkaSen XD .. you think so ? :P perhaps you are right :)

Balarka Sen

[Psst : Don't take my words too literally. I am ignorant about analysis. A lot]

=)

r9m

13:05

but this time I double checked =)

@DanielFischer if you are not too busy ... can you check if my proof is correct here :D .. Balarka is scaring me with stuff I don't understand :| .. I'm confused !

Balarka Sen

evilgrins

I sometimes scare myself off with stuffs I don't understand. Diff galois theory is one of them.

r9m

@BalarkaSen you wanna apply full power of PNT ?! .. then here's a strong one .. are there rational functions $R(x)$, such that $\displaystyle \int_0^{\log(\log n)} R(x) \,dx = \sum\limits_{k=1}^{n} \frac{1}{p_k}$, for infinitely many $n \in \mathbb{N}$, where $p_m$ is the $m^{th}$ prime number :D

@Chris'ssis see this ^ when you have free time :) .. Its nice too :D !!

Balarka Sen

I am doubt that very much. It's not true, no.

Merten's 1st theorem gives the estimate $\log\log x + M + O(1/\log(x))$ for the sum on the right. While your integral is more or less a polynomial of $n$ and $\log\log(an+b)$.

Asymptotics refutes such an equality for arbitrarily large $n$.

r9m

(grins) You will need sth stronger than Mertene's :D

Its difficult .. and I don't have a solution ^^'

Balarka Sen

It seems Mertens is sufficient.

Chris's sis

13:19

@r9m OK ;) Now, I'm more focused on those problems like the double series you see above (did you know it can be computed elementarily?). They are going to be put in my book.

r9m

@Chris'ssis Awesome :D !!!!!!

2

Chris's sis

@r9m :D

Balarka Sen

@r9m You need polynomials with less roots in the denominator Q(x) of R(x).

Otherwise it may grow like $O(n^k\log\log n)$

r9m

@BalarkaSen if $Q(x)$ has roots .. won't it mean that $R(x)$ will have non-integrable singularities ? :o

Balarka Sen

It depends on where the roots are.

It might just not be in $[0, \log\log n]$ which is plausible as growth of $\log\log n$ is sluggish.

r9m

13:25

oh .. but $\log \log n$ diverges ;) .. we can't have a positive root of $Q(x)$

Balarka Sen

you never said that the equality is true for $n \to \infty$

It's just arbitrarily large.

Formulate the question explicitly first.

I have to run. Bye.

r9m

@BalarkaSen umm ... does the question look inexplicit ? :o

Hippalectryon

13:45

@BalarkaSen Uh I'm not exactly back, but i'm able to come here from times to time ...

Chris's sis

14:21

@Hippalectryon btw, who are you? :-)

Hippalectryon

@Chris'ssis Good question :D

Chris's sis

I know. ;)

r9m

@Chris'ssis You know who Hippa is ? :P

Chris's sis

@r9m My feelings tell me he's somewhat known to me (hard to explain).

Hippalectryon

Gods tend to forget human beings :c

r9m

14:25

@Chris'ssis What kind of a feeling is that ? :P

Chris's sis

@r9m The sixth sense :-)

r9m

@Chris'ssis Crazy movie :P

Chris's sis

@r9m lol, yeah :-)

Daniel Fischer

@r9m Commented. A few glitches, but the argument is sound.

Mats Granvik

Is a matrix power of a nilpotent matrix always nilpotent?

r9m

14:40

@DanielFischer Thanks a lot :D ..

I've been making disastrous silly mistakes :| ...

Huy

@MatsGranvik: What are the eigenvalues of a nilpotent matrix and what are the eigenvalues of any of its matrix power?

r9m

15:02

@Chris'ssis What is the age difference between Chris and Chris's sis ? :D

Chris's sis

@r9m :-)))))))) You may ask anything

@r9m there is a bit of difference ;)

r9m

@Chris'ssis I guess Chris is elder ? :-) (I may be wrong .. could it be that you two are twins :P lol )

Chris's sis

@r9m hahahahaha, you never know. :-)))))

r9m

@Chris'ssis hmm .. I wonder who's replying atm .. Chris or his sis :P

Chris's sis

:D

Balarka Sen

15:12

Dang it

Dang dang dang.

r9m

@BalarkaSen what happened ?

Balarka Sen

@r9m I can't get my code right.

r9m

@BalarkaSen omg haha .. I know how that feels ... brutal :P

moreover I'm poor in CS .. so when I make mistakes in my codes ... It takes out my life just to identify the mistakes :P

Balarka Sen

Also, it seems like that this turned out to be a famous question regardless of 3 initial downvotes by people who just downvotes for the love of it.

Mats Granvik

@Huy Eigenvalues of a nilpotent matrix are zero.

Huy

15:23

@MatsGranvik: And if $A$ is nilpotent, what are the eigenvalues of $A^k, k \in \mathbb{N}$?

Mats Granvik

@Huy Well the trace of a matrix power of a nilpotent matrix is zero, so I guess the eigenvalues of $A^k, k \in \mathbb{N}$ are also zero.

Huy

@MatsGranvik: If $A$ is a matrix with eigenvalues $\lambda_j$, then $A^k$ has eigenvalues $\lambda_j^k$, and in this case 0. And any matrix with the only eigenvalue being 0 is nilpotent.

user105491

15:50

@Balarka Thanks for the advice. Wasn't looking to understanding the book - just looked through it . anyhow, I got alexseev and am studying that now

Balarka Sen

@Sanath Cool!

user105491

Sorry for the bad spelling, etc. I'm on my phone

Balarka Sen

Best of luck!

user105491

Merci!

Balarka Sen

I think Alekseev is really the book you want for now.

user105491

15:51

Ok, got to go, will be back in some time

Balarka Sen

@SanathDevalapurkar OK.

You seem to be a busy boy.

@Sanath If you get stuck on something, feel free to notify me.

user105491

:-) I have to go out for a few minutes, and also thanks!

Balarka Sen

@SanathDevalapurkar I have heard something of motivic galois theory a few days ago.

You familiar with motives?

user105491

Not a lot, but yeah

Balarka Sen

What are they, in short?

I encountered the term in here, btw.

Off-topic, but perhaps you'll like the explanation I gave, @Sanath.

Heya @N3buchadnezzar

user105491

16:00

@Balarka Nice explanation! I'll add what motives are when I come back - 15/20 minutes

Balarka Sen

@SanathDevalapurkar ok! ping me and i'll be there.

ps : the thing i posted is actually galois theory of covering spaces.

glad you liked it.

r9m

@shadow10 hi :D

shadow10

Hi,

You are from Chennai?

@r9m

r9m

@shadow10 Kolkata :) .. I stay in Chennai :)

shadow10

Really? Do you go to CMI?? You must be my senior.... :D

r9m

16:12

@shadow10 :-) .. are you from kolkata ?

shadow10

So is that a yes?

No not exactly, I live close Kolkata, a place called Bally @r9m

r9m

@shadow10 ah .. ic :) .. Bally, Howrah ?

shadow10

Yes!! @r9m

r9m

@shadow10 you are 1st year ?

shadow10

@r9m Yes

Chris's sis

16:19

By the way, it seems the New Zelda is going to be amazing ... (I just saw some pictures).

r9m

@Chris'ssis video games ? :D

Chris's sis

@r9m Yeah. Zelda game is really awesome.

user105491

@Balarka Sorry, its hard to type in my phone. I'll refer you to wikipedia for now (don't see the nlab - it'll just confuse you, as it confused me). If my stupid computer, whose battery is damaged, gets on, I'll tell you some more. Sorry!

Balarka Sen

mach bhath khaoa bangali abar aak koshte kobe theke shuru korlo?

r9m

@Chris'ssis :-) ... I haven't played ... the only game I have played is AOE :D ..

user105491

16:22

@Balarka If you're feeling brave, see encyclopediaofmath.org/index.php/Motives,_theory_of

r9m

@BalarkaSen aak koshte maane ? :P

user105491

Also see www.jmilne.org/math/xnotes/MOT.pdf. Again, I apologize for not being able to type more.

Balarka Sen

@SanathDevalapurkar OK, it's fine. Tell me whenever you have time.

@r9m le mathematique.

user105491

@Balarka Thanks for understanding. Bye!

Balarka Sen

@SanathDevalapurkar What happened to your PC?

r9m

16:25

@BalarkaSen oh :P LOL

Balarka Sen

@Chris'ssis Math and video games don't do togather.

Chris's sis

@r9m The last game I played was Castlevania, the new one, but to be honest I didn't like it that much.

Balarka Sen

I've noticed you'll either get bored of games or be obsessed with it so much you'll forget all your math.

Chris's sis

@BalarkaSen lol, no ;) Well. some games area really nice ...

Balarka Sen

So I have abandoned games completely.

r9m

16:28

@Chris'ssis haven't heard of that :| I'm far far away from the gaming world :P ... but I play AOE sometimes :)

Balarka Sen

@Chris'ssis Most games are stupid.

@r9m AOE is the best.

r9m

:D

Balarka Sen

@r9m How far did you get through in Russian campaign?

Oh, you're talking about AOE

I was thinking of EE. Nevermind.

Chris's sis

@r9m I see. :-)

r9m

AOE I & II .. I haven't played III yet :)

Balarka Sen

16:32

I can't recall the last time I played video games. Must be a few years or so.

Gaming wastes much of your time you could spend thinking of a few math problems.

r9m

The thing I like most about that game is the rubbles and the sound of dying villagers :P lol ... I never convert the enemy .. I kill all and leave no survivors :P

Chris's sis

@r9m lol

@BalarkaSen There are some games that are really amazing. Well, I don't think it's a very good idea to spend all your time in a single area. Life is not consisted of a single colour. And to be honest, I really spend a lot of time doing math.

r9m

thats why my favorite units are the battering rams and the sword men units :P

Chris's sis

@r9m :D

Balarka Sen

@Chris'ssis I think it is better not to waste time on video games. You get addicted to it. I do play games, but that mostly consists of chess and fiddling with Rubik's cube

I am just giving my opinion here.

r9m

16:40

ya .. they are the best for wreaking havoc in the enemy territory ... they break stuff and spill a lot of blood :P .. archers are nice too .. but they die with a pathetic sound (the sound of the dying villagers is exquisite) :P

Chris's sis

@BalarkaSen But how about the addiction to math? :-)))

Balarka Sen

IMO, it is a good idea to spend a lot of your time on a single area.

@Chris'ssis Fair question =)

Chris's sis

:D

Balarka Sen

I think you should get addicted to something you want to get addicted to.

It is better not to draw another addiction to jumble up your whole ideas.

r9m

rum dui saretin =P

Balarka Sen

16:44

@r9m wuzzat?

Chris's sis

@BalarkaSen An American mathematician told me once that even watching a movie is a waste of time. I don't know if it's a good idea to push things so far. I'm obsessed with math, that's clear, but I also like many other things. I cannot be blamed for that. :D

user105491

@Balarka My laptop's battery is messed up, its not getting on. Have to go pick up my brother from swimming now, so see ya later!

Lucio D

17:09

Hello

Balarka Sen

17:33

@Chris'ssis Who're you referring to?

I wouldn't disagree with him though. Watching movie is a waste of time.

@SanathDevalapurkar I'd appreciate it if you can give a short description of motives in elementary terms though.

Tur1ng

18:18

Hi everybody :). I have a quick question about harmonic means, if someone wants to indulge me.

Chris's sis

@r9m @robjohn that double series is precisely $\displaystyle \frac{\zeta(6)}{3}$ :D

r9m

@Chris'ssis :D Awesome :D !!!! .. (I'm eating .. bbl)

robjohn

@Chris'ssis I'll have to look back for the series...

Chris's sis

@robjohn It's a rare beautiful gem.

robjohn

@Chris'ssis Oh, this one

Chris's sis

18:23

@robjohn Yes.

user105491

@Tur1ing What's the question?

Balarka Sen

Heya again @Sanath

is this sirius?!

user105491

@Balarka Hey! Still on my phone, but will try explaining motives.

Balarka Sen

OK @Sanath. I'm ready.

Mario Carneiro

$$\log(1+\frac1{n+1})<\frac1{n+1}<\log(1+\frac1n)$$

Has anyone seen how to derive these inequalities?

the left one comes from $1+x<e^x$, but I don't know what to do about the other

user105491

18:35

@Balarka The category of motives is similar to the category of vector spaces over $\mathbb Q$; specifically hom-sets should be beck$\mathbb Q$ vector spaces.

Balarka Sen

I don't understand what you mean by "Hom-sets should be Q vector spaces"

You mean the morphisms of objects forms a vector spaces over $\Bbb Q$?

user105491

They provide algebraic ways to define topological invariants of topological spaces.

user105491

Yeah, that's what I mean.

Balarka Sen

Aha. Can you give me an example? I can't think of one off the top of my head.

user105491

@Balarka I do not understand what you mean by example - it is a category, whose construction you can see on wikipedia, which, in order to understand, you need to know Chow cycles. Check that out and tell me if you're stuck somewhere (I was stuck there multiple times).

Balarka Sen

18:44

runs and hides You're scaring me off. =P

user105491

For example, to elucidate my point, one cannot give an example of the category of topological spaces, but one can give an example of an (infinity-) category.

Balarka Sen

Oh my god. Objects of a category can be varieties?!

user105491

That's ok, it is a scary topic. Until a few years ago, I don't believe there was a firm foundation for motives.

user105491

@Balarka :-) Objects of a category can be anything sensible!

Balarka Sen

OK. Corr(k) is the category of varieties with morphisms being correspondences. That is all clear.

user105491

18:47

Yep.

Balarka Sen

Correspondences of varieties can be associated with graphs? In what sense?

user105491

You've heard of the Weil conjectures, right? Assuming the standard conjectures hold,there is a simple and elegant proof of the We.il conjecture.

Balarka Sen

Yes, I've heard of them.

But I am not sure how one embeds a corr in a graph.

i think i am reading stuffs way ahead of me.

user105491

Using motives, sorry forgot to add that.

X \times Y is the cartesian product, so the morphisms can be associated to

user105491

Their graphs in X\times Y.

Tur1ng

18:55

@SanathDevalapurkar I was just wondering, if you're taking the harmonic means of a few sets of speeds, for example, the set with the highest value of harmonic mean is still the set with the fastest average, correct?

user105491

Nothing is "way ahead", @Balarka, have faith in yourself.

Balarka Sen

@Sanath But what you've really told me all the way to here is that what is a category of motives (which makes perfect sense). I am asking what are motives.

user105491

Objects of the category of motives.

Balarka Sen

Indeed, trivially.

But there must be a way to define them?

I mean, instead of defining the category first. (I am not even sure if it exists)

user105491

@Balarka one can describe anything by the category of objects; sometimes, things the only method.

user105491

18:59

*this

Balarka Sen

I can't make sense of that. OK, so give me an example of a category that satisfied your definition.

i.e., an example of category of motives.

user105491

@Balarka It is not possible to give an example of something that is already specific, eg., it is like giving "an example of the number 2".

Balarka Sen

But you can't show that such a category exists, can you?

user105491

@Balarka check out the Milne paper I suggested above.

Balarka Sen

I have and found that I can make no sense out of it.

user105491

19:05

@Tur1ing Sorry, I don't know for sure - but I don't think it's true.

user105491

@Balarka check page 6.

user105491

@Tur1ng

Balarka Sen

@Sanath What do they mean by "hX'?

Tur1ng

@Sa

Balarka Sen

X is an algebraic variety, btw.

Tur1ng

19:09

@SanathDevalapurkar thanks

user105491

@Balarka The motive associated to the algebraic variety.

Balarka Sen

Now I am back to where I started : what is a motive? =D

I think hX is rather the object the morphism h is taking X to.

Is that the case?

user105491

@Balarka Ok, interpret hX as the functor taking singular projective varieties to the category of motives.

Balarka Sen

Ah.

OK, OK.

user105491

@Balarka That'd be a good interpretation if you could define h precisely.

Balarka Sen

19:13

Yes, indeed.

That all makes sense!

It's a contravariant functor, right?

user105491

@Balarka You get the beauty of this definition once you see generalized elements, and realize that this is indeed a "generalized element of the category of motives".

user105491

@Balarka No, covariant.

Balarka Sen

What's fun is that $\mathcal{M}_{\sim}(k)$ is much more normal, with one motive associated to each projective varieity and morphisms just correspondences of degree 0.

user105491

Yep, exactly.

Balarka Sen

@SanathDevalapurkar They say that regular map $Y \to X$ induce $hX \to hY$

What do they mean by regular map, anyway?

user105491

19:18

@Balarka Sorry, my mistake.

Balarka Sen

@SanathDevalapurkar Yas

user105491

Sorry, I can't answer that. I have to go. Bye!

Balarka Sen

So I take that the regular map is the canonical map.

@SanathDevalapurkar Yes, I have to leave too.

Chris's sis

19:57

@robjohn I'm also curious about the version in 3 variables ... (it must be fun)

Enjoys Math

20:46

@ArthurFischer are you and @DanielFischer related?

Are you the same person?

^_^

Daniel Fischer

We could tell you, but then we would have to ...

Ted Shifrin

21:05

@DanielF !!

Daniel Fischer

@TedShifrin Double factorial, or factorial applied twice?

Ted Shifrin

you're an odd bird, so it has to be the former

Daniel Fischer

Bird?

Ted Shifrin

that's a British expression, I believe

Daniel Fischer

Yes, but ...

Ted Shifrin

21:12

my slang comes from earlier decades :)

Here you go, @DanielF

Daniel Fischer

Bird = adolescent or young adult female is also fairly old.

Ted Shifrin

Yeah, I concede that, too.

YOu clearly didn't appreciate my humor ... :(

Daniel Fischer

Or I decided to pretend I didn't. The good thing about the internet is that it's really easy to have a deadpan.

Ted Shifrin

Yeah, but one shouldn't subject friends to such appalling behavior :)

Daniel Fischer

We reserve that behaviour for Pedro?

Ted Shifrin

21:20

the appalling behavior?

Daniel Fischer

Yes.

Ted Shifrin

wait ... we subject him to it, or he subjects us to it? I'm confuzled.

Daniel Fischer

We subject him. But in case of any lingering doubt, I wasn't serious. I'd count Pedro as a kind of friend too.

Ted Shifrin

He's actually supposed to be visiting us here in the US soon ...

Daniel Fischer

Giving Tennis lessons and receiving Math lessons is the deal?

Ted Shifrin

21:23

I'm trying to understand the secretary/marriage problem ... totally cool ... I'm gonna have to do this in my probability class.

I think I'm supposed to cook him a happy 21st birthday dinner, too ... I'll get schooled in tennis, for sure ... not sure about who's teaching whom in math :P

Daniel Fischer

@TedShifrin If you manage to keep clear of algebra and stick to analysis or geometry, he's not (not yet, at least) in a position to teach you.

Ted Shifrin

LOL ... won't be long :)

Daniel Fischer

Regarding the secretary problem, it's indeed cool. Just one snag, the candidates don't come in a random order. Fate arranges it that they come in the worst possible order for your strategy, whichever that is.

Ted Shifrin

In my long teaching career, @DanielF, I've had several students who I knew would far exceed me in knowledge and research. It's actually a ton of fun working with them. I won't be surprised if @Pedro ends up in that classification.

LOL @DanielF ... Murphy's law to the aleph null?

Daniel Fischer

@TedShifrin Just plain bloody real-life experience.

Ted Shifrin

21:29

It's still a very cool probability problem :)

Daniel Fischer

Yes.

anorton

Live contest problem: math.stackexchange.com/questions/864375/…

:\

Daniel Fischer

@anorton Have you already flagged?

Ted Shifrin

heya @anorton

Chris's sis

I just noticed I received 2 downvotes again ...

Ted Shifrin

21:34

It's sad that contests (especially "takehome" style at the high school level) really can't exist any more.

Daniel Fischer

I don't understand people cheating in that sort of contest. If you could win money or so, that would be an understandable reason.

Ted Shifrin

We live in sick times.

But one always wants to succeed — it's human nature.

Daniel Fischer

Yeah, but if one comes in first in a Rallye because one's chauffeur drove so fast, what is the joy in that?

Ted Shifrin

We are a generation of politicians: the ends justify the means.

For things like contest/takehome exam problems, we shouldn't be flagging. We should be yanking immediately. This is crazy.

Chris's sis

A really powerful person with a strong character does not need to cheat. Only the weak ones live their lives like that.

Ted Shifrin

21:39

Most of us are mortal, @Chris'ssis.

Charlie

hi guys

and mister

Ted Shifrin

@Charlie!!

Charlie

@TedShifrin hello

Ted Shifrin

it's been a long time, @Charlie

Charlie

@TedShifrin less than it should have been

Ted Shifrin

21:48

You tired of me, too, @Charlie?

Charlie

@TedShifrin no

only professors in my uni

anorton

@DanielFischer I have, yes.

Hi @TedShifrin!

Transcript for

$Mathematics$ Mathematics