Mathematics - 2017-09-01 (page 2 of 5)

skullpatrol

04:01

or a week

or a...

You've presented your idea, and now the "jury" is out.

user84215

@skullpatrol Please tell me first why this question is off-topic.

skullpatrol

You know why.

user84215

I do not know.

skullpatrol

This is a "revolutionary" new idea, right?

user84215

Have you seen my post on the MSE?

skullpatrol

04:14

Yes. I'm following along this whole thing pal :-)

Secret

@MathematicsAminPhysics Then the presence of rooms like linear algebra, alessandro's forcing theorem etc. and how they will be populated occasionally already achieved the notion of workshop you defined?

user84215

It is about the importance of math workshops in learning mathematics.

Wildcard

Random question: does anyone know what happened to the Pacific Tech Graphing Calculator?

I have fond memories of using this beautiful product (the full version) on an OS 9 computer in the heyday of my youth (well, sort of).

And I have Graphing Calculator 4.0, but it hasn't even been updated for Retina displays....

Still beautifully usable, though.

Balarka Sen

@LeakyNun Sphere eversion is a nontrivial theorem that is not easy to understand. I think the basic idea is that any immerson $f : S^2 \to \Bbb R^3$ has a corresponding "1-jet" that is a map $J^1 f: S^2 \to \Bbb R^3 \times \text{Gr}(2, \Bbb R^3)$ which sends each point $p$ to $(f(p), df(p))$ where $df$ is the derivative of $f$, which is of course nothing but a linear injection of tangent spaces $T_p S^2 \to T_p \Bbb R^3 = \Bbb R^3$.

Gr(2, R^3) being the Grassmannian of 2-subspaces in R^3.

Leaky Nun

@BalarkaSen Is it a regular homotopy?

Balarka Sen

04:20

I haven't even said anything about homotopies yet...

Leaky Nun

I mean, I'm not understanding the question.

skullpatrol

Sorry about telling you to "finish high school first" @BalarkaSen

Balarka Sen

@LeakyNun I am not asking a question :P I'm answering to your question, "why is sphere eversion possible?"

Leaky Nun

@BalarkaSen I know. I mean my own question.

I mean, how would I formalize the question?

Wildcard

@MathematicsAminPhysics I'll have a go. Firstly, it's difficult to tell what your question actually is. The title is a statement with a question mark at the end: "Attending math workshops is important?"

micsthepick

04:23

Who knows about sin(18) and sin(-54)?

Balarka Sen

Oh. Well, just that any two immersions of $S^2$ in $\Bbb R^3$ are homotopic through a family of immersions.

That's what sphere eversion says.

Wildcard

@MathematicsAminPhysics The real question seems to be "Is it better to attend math workshops or to read books about math?" This question is entirely opinion based, and is asking for personal advice. Hence it is off-topic according to the defined scope of this site.

But that's really not THE reason it was closed, it's true.

Balarka Sen

Anyhow, the point is if $f, g: S^2 \to \Bbb R^3$ are two such immersions, the second components of $J^1f, J^1g$ are corresponding maps which are elements of $\pi_2(\text{Gr}(2, 3)) = \pi_2(SO(3)) = 0$.

So $J^1 f$ and $J^1 g$ are homotopic.

Leaky Nun

@micsthepick wolframalpha knows

Balarka Sen

If you can boil this homotopy of 1-jets to the level of homotopy of immersions, you're done.

Leaky Nun

04:25

@BalarkaSen homotopic?

Balarka Sen

@LeakyNun ... Oh, you don't know what a homotopy is. Well, maybe try reading some literature.

I don't really have the time to explain right now, but I could do that at a later time.

Just writing down my thoughts on why it's true real quick.

user84215

@Secret They have not been active enough since they have focused on specific subjects and ,therefore, they have not been visited much. However, when we gather all workshops in a room, it will be more active.

Wildcard

@MathematicsAminPhysics The REAL reason it was closed is because you're not asking a question. You have your own answer to the "question" you're asking, and you are using this question-and-answer site as a forum to propagate your opinions.

4

Leaky Nun

@BalarkaSen ok, thanks

Wildcard

I quote the closing lines of your "question": "...because of my opinions about the importance of math workshops I have created the Math Workshops room."

That's emphatically not a question. It's a billboard.

Balarka Sen

04:28

So, uh, a homotopy between $J^1 f$ and $J^1 g$ can pass through stuff which are abstract 1-jets, just maps $S^2 \to \Bbb R^3 \times \text{Gr}(2, 3)$, which do not "integrate" to an actual immersion. These are called formal 1-jets.

I think what Smale did was, he used the holonomy approximation theorem to prove that if you perturb a formal 1-jet sufficiently in a small $\epsilon$-neighborhood of the original, then you can in fact integrate it an actual immersion.

This is why they introduce crinkles in the many sphere eversion videos you see.

Wildcard

@MathematicsAminPhysics so regardless of the quality of your opinions, you will get downvoted for posting those opinions as though they were a question, when in fact they are more like a blog post.

user84215

@Wildcard My question is about the importance of attending math workshops, and after asking the question and bringing the definition, I have stated my attempts in answering the question. Is this bad?

Wildcard

@MathematicsAminPhysics Please acknowledge my answers. You wrote:

Balarka Sen

But I think my understanding of it stops there. I don't really know the details anymore; I should read it at some point.

Wildcard

> Please tell me first why this question is off-topic.

I did so.

You have not acknowledged that communication.

Leaky Nun

04:31

0

A: Find $f'(0)$ for $f(x)=(x^3-\tan^3(x))^{\frac 15}$

The derivative expression is as follows: $$-\dfrac{3\left(\sec^2\left(x\right)\tan^2\left(x\right)-x^2\right)}{5\left(x^3-\tan^3\left(x\right)\right)^\frac{4}{5}}$$ Clearly the derivative at $x=0$ is undefined in $R$. However, using the definition, the limit from the right is: $$\lim_{x \to 0...

argh, people with misconceptions thinking they're right

Secret

@MathematicsAminPhysics The problem is that it will be hard to curate them when you put them all in the same room since unlike an AMA, there are no time stamps that can keep a session in order

Future readers will also have issues trying to figure out what topic had been discussed without some tedious searching

Wildcard

@MathematicsAminPhysics And yes, it is bad to put an answer in the question—especially when it is an opinion-based question in the first place, and your text makes it clear that you are not open to dissenting opinions.

I have on occasion posted a question that I had an answer to already with which I was dissatisfied, and I put the answer as an answer, and mentioned that I had done so in the question. This is entirely different from disguising a rant as a "question."

skullpatrol

::yawn::

Wildcard

@skullpatrol LOL

Secret

@skullpatrol $\emptyset^{\emptyset}$

skullpatrol

04:37

What some popcorn guys?

Wildcard

@MathematicsAminPhysics Have I answered your question? "Please tell me first why this question is off-topic."

Semiclassical

"nothing from nothing means nothing..."

Wildcard

@skullpatrol Sure! How 'bout some grapes, too?

Secret

@Semiclassical ...and there is precisely one way to do so

skullpatrol

you gotta have something...

Semiclassical

04:38

ding

Wildcard

@Semiclassical dang

Semiclassical

dong

Wildcard

:D

skullpatrol

ding

Leaky Nun

dung

eww

skullpatrol

04:38

-_-

Martin Sleziak

@MathematicsAminPhysics It seems that one of the reasons why you posted the question was to advertise your Math Workshops chat room. If you want to do that, why not simply posting an answer with link to the room and a brief description in the List of chatrooms - this post was made precisely for that purpose (=to make people aware of chatrooms which might potentially be useful).

Akiva Weinberger

@LeakyNun What's, uh,

what's brown and sounds like a bell

Leaky Nun

@AkivaWeinberger lol

user84215

@Wildcard Yes. You have answered to my question, but I disagree with your answer.

Wildcard

@MathematicsAminPhysics Thank you for acknowledging. :)

Secret

04:39

@MartinSleziak yeah, that would make the focus clearer

Wildcard

@MathematicsAminPhysics I think @Mart

Oops

@MathematicsAminPhysics I think @MartinSleziak has given a great suggestion. I have a further suggestion:

Semiclassical

Without an audience, a discussion doesn't go anywhere. So one either needs to find an audience or create one.

skullpatrol

Popcorn, peanuts, grapes anybody?

Wildcard

If you want to get some math workshops going, try engaging with the people already here, about math. Not about whether or not math should be this or that, but about actual math.

Semiclassical

And taking that for granted is not going to get anywhere.

Wildcard

04:41

If you get an interesting discussion going, you can then suggest that it be continued over in your chat room (if it seems appropriate to do so).

Martin Sleziak

@Semiclassical Well, I kind of hope that some of the rooms listed there (especially the ones in the subjects I care about) might get noticed by more users eventually.

Secret

calculus will be a good starting point, since it is so ubiqitous

Wildcard

In other words, my suggestion is that if you want to engage with people about math, do it. Don't get all worried about whether the transcript will or will not be easily searchable and blah blah blah. There are people right here in this chat room. All of us like math. Start discussing!

Semiclassical

@MartinSleziak oh, sure. just meaning that one can't take for granted whether the audience is there (not that I take that to be what you were doing)

Wildcard

And taking my own advice:

Martin Sleziak

04:42

BTW @MathematicsAminPhysics' question on the main site just got reopened - revisions/timeline.

Wildcard

I have been playing with a very frustrating combinatorics puzzle for a while (something vaguely similar to Sudoku), and it seems like there should be a solution, but I haven't found one yet.

However! The smaller version of the puzzle is susceptible of solution definitely, and is still interesting:

Start with an empty 7x7 grid

Use two different symbols/counters (I'll call them "A" and "B")

In each row of the grid, place 3 A's and 3 B's (leaving one empty square) such that:

Martin Sleziak

@Wildcard It seems that some of your suggestions are similar to the ones I made in my answer on meta here: Increasing chat use, pros, cons and the tour.

Wildcard

...such that: no rectangle can be drawn on the grid with the same symbol at each corner.

(This refers only to rectangles orthogonally drawn, of course. In line with the grid.)

(...I should say, one empty square in each row.)

@MartinSleziak Yes, agreed and upvoted.

user84215

Thanks for your answers, suggestions, and votes. However, I want to say that I know little math; how can I start a discussion?

Wildcard

@MathematicsAminPhysics Great question! :)

@MathematicsAminPhysics Do you know anything about Combinatorics? (I like combinatorics.) :)

user84215

04:49

little (high school)

Wildcard

@MathematicsAminPhysics For that matter, you might get some paper (or a checkerboard) and give a try at the puzzle I just described. See what you figure out....

Akiva Weinberger

@Wildcard This reminds me of a similar problem of filling a 6x6 grid with integers, not all zero, such that the sum of the corners of any square is zero.

Wildcard

@AkivaWeinberger Oooh...sounds interesting. Is it possible?

Akiva Weinberger

Yes.

Wildcard

@AkivaWeinberger Well then I'll have to try it now. :)

user84215

04:51

I want to encourage other people to start specific workshops.

Wildcard

(Pencil and paper—or pen and lots of paper—is still the very best tool for such puzzles. WAY better than computers, for exploration, at least.)

@MathematicsAminPhysics :D

@MathematicsAminPhysics I admire your persistence.

@MathematicsAminPhysics I recommend you start by reading the questions and answers posted on the main Math SE site in the subjects you're interested in.

@AkivaWeinberger Any interest in trying the puzzle I described? I invented the puzzle myself from an interesting combinatorics chain of research I got onto; it has a relationship to "balanced incomplete block designs."

@MathematicsAminPhysics (Like a workshop in what specifically?)

Akiva Weinberger

Am I interested? Yes. Do I have any idea how to solve it? No. @Wildcard

I definitely will think it over.

user84215

whatever people want

Akiva Weinberger

At some point I should go to sleep, though, and it might as well be now.

Wildcard

@AkivaWeinberger Cool. :)

@AkivaWeinberger G'night.

Secret

04:55

[Random]

Wildcard

@MathematicsAminPhysics Whatever which people want?

user84215

All people

Wildcard

@MathematicsAminPhysics I suggest you start by surveying the people you are interested in contacting.

I think you're ignoring the survey results you already have: downvotes on your proposal, etc.

Secret

I can see there are some people interested in the proposal. You should contact them further

Wildcard

Seconded (@Secret)

@MathematicsAminPhysics I also recommend you watch this video on the fundamentals of public relations. Might clarify some things for you about why your ideas aren't getting very good/broad acceptance on this site.

Leaky Nun

04:59

Knaster–Kuratowski fan

In topology, a branch of mathematics, the Knaster–Kuratowski fan (named after Polish mathematicians Bronisław Knaster and Kazimierz Kuratowski) is a specific connected topological space with the property that the removal of a single point makes it totally disconnected. It is also known as Cantor's leaky tent or Cantor's teepee (after Georg Cantor), depending on the presence or absence of the apex. Let C {\displaystyle C} be the Cantor set, let p {\displaystyle p} be the point ( ...

> Cantor's leaky tent

skullpatrol

:D

user131753

@MathematicsAminPhysics: At this point I would suggest you what others have suggested you multiple times. For the time being try to learn as much as possible the topics of Mathematics which you are interested in and just take a break from proposing ideas about organizing workshops or like that in this site. After a break you give a fresh look to your proposal and see what modifications can be done to it.

4

Wildcard

@LeakyNun I'm missing something. How can the removal of a single point make the entire space disconnected, when it appears that the "legs" of the teepee are connected? (I could see that the "legs" would be disconnected from each other.)

But I didn't read it very close; packing up for the night.

user84215

All my suggestions have been heavily downvoted.

Wildcard

@MathematicsAminPhysics Did you see @user170039's comment?

Leaky Nun

05:03

@MathematicsAminPhysics: in short: the downvotes aren't targeted to you personally. but if you won't quit whining about it, then they will be.

user84215

@user170039 Thanks for your advice.

Leaky Nun

@Wildcard do you know Cantor's set?

Wildcard

@LeakyNun Yes.

skullpatrol

Have you seen my post on Meta MathEd.SE? @MathematicsAminPhysics

user84215

I think many people think that I am a crank troll.

Wildcard

05:04

@MathematicsAminPhysics Yes, they do. (I don't, by the way.)

user84215

@skullpatrol I think so.

Secret

Mar 27 '15 at 11:43, by Chris's sis

Guys, I think it's about prime numbers!!!

Wildcard

I just think you're horrendously lacking a basic knowledge of communication and public relations, which includes good manners as an actual skill.

Secret

So a closed form for the prime numbers finally back in yesterday?

Leaky Nun

@Wildcard I think you missed the part where they kept only the rational points (or the irrational points) on each leg.

Wildcard

05:05

That doesn't make you a crank or a troll. But it DOES mean you're going to go on having your ideas rejected until you repair the faults in your communication and relations to others.

skullpatrol

It isn't down voted, but they don't appear interested as Math Educators.

1

Q: An invitation for volunteers study group coordinators and advisors

This is not an advertisement, but a friendly invitation to share your thoughts and suggestions about this idea. "As a trial, we can find one or two volunteers to 'teach' (better word, anyone?) exactly one course to around ten students..." Here also.

discussion

That^ should tell you something @MathematicsAminPhysics

user84215

Yes.

skullpatrol

Give it some time, pal.

Wildcard

@skullpatrol Again, I recommend you actually watch the video I linked earlier.

Oops

Secret

[Random]
Demonstration of a group using a group of people in a lecture. But the first question is, what makes a good inverse element in a group of people?

Wildcard

05:08

@MathematicsAminPhysics I meant that last comment to be at you.

skullpatrol

Scientology? @Wildcard

Wildcard

@skullpatrol ?

skullpatrol

I'm no Tom Cruz :-)

Martin Sleziak

@skullpatrol Well, Math Educators Meta does have rather low traffic compared to this site's meta. Your post has currently 50 views. Of one of them upvoted and perhaps also looked at link provided there (heather's meta post, chat room), I think you can count it as success.

Wildcard

@skullpatrol I thought this comment was by @MathematicsAminPhysics.

Noticed after my @mention appeared that it wasn't.

skullpatrol

05:10

Ok.

Martin Sleziak

@skullpatrol Do you mean Ted Cruz or Tom Cruise? (Or some kind of mix of both?)

skullpatrol

:-D

Secret

NB the chinese name for field is 體, lit. Object

Wildcard

@skullpatrol (Though, if you do watch the video, I think you'd agree it's the common-sense information that MathematicsAminPhysics is drastically missing.)

Martin Sleziak

Incidentally, I see that WP has a redirect from Tom Cruz to Tom Cruise. Apparently, it's a common misspelling.

Leaky Nun

05:12

@Secret til

Secret

Meanwhile, field as in mathematical objects in every point in space is 场

Wildcard

@MathematicsAminPhysics Anyway, look forward to seeing you back after seeing the video. (Hint, hint.) (I really do think it will help you.)

skullpatrol

I just chose "Cruz" because it has less letters to type @MartinSleziak

Wildcard

@Secret what's with the chinese?

Secret

Just for some reason I am curious on the important property of fields, and then my google search showed me its chinese which I found bizarre because I think 场 is a more literal translation

So the chinese translation means that the algebraic structure known as fields looks nothing like a field in physics structural wise

user131753

05:16

@MathematicsAminPhysics: I believe that you have the passion for Mathematics that you genuinely want to do good for this site. But at this point I think it is better not to take the downvotes personally and think about it in objective terms. It may be the case that some people here had been biased by your earlier comments and posts and that explains some of the downvotes but you need to keep in mind that it may also not be the case.

skullpatrol

"Field" is a Chinese word?

user131753

So, instead of thinking about the motives of people just try to enjoy Mathematics for the time being @MathematicsAminPhysics.

Secret

We tend to use the word 场 to refer to something like a force field, and also in the more restricted sense in physics.

whereas 體 means form or object

e.g. 球體 is ball

lit. round object

skullpatrol

nothing for "sphere"?

Secret

That will be 球面, which means "round surface"

user131753

05:19

After all that's one of the reasons for which you are here. Isn't it @MathematicsAminPhysics?

Secret

So most chinese nouns are like compound words in english

where its meaning is often the bits combined

skullpatrol

Interesting. More "wholistic"? @Secret

user84215

@user170039 Yes. Thanks.

Leaky Nun

@skullpatrol I never distinguished sphere and ball until I came across topology...

Secret

same

skullpatrol

05:25

That's natural.

Secret

@skullpatrol Chinese and most asian culture are also hollistic in nature, emphasise on things like family tradition and to work with nature

whereas most western cultures stemmed from the greeks emphasise on analysis and reductionism

and try to outsmart nature

Nowadays, both views are quite balanced throughout the globe, given that global issues need both worldviews to investigate

skullpatrol

I still get the chills when I hear this.

Oakland Raiders - The Autumn Wind

►

Salt

does "work with nature" mean "infinite CO2 production"?

Leaky Nun

05:41

@Salt lol

Secret and I are both from HK tho

anon

okay, who submitted this?

8

Leaky Nun

@anon thats nice

Salt

i'm dying, my sides @anon

Secret

China has ambitious plans on renewables, and many said it is leading in terms of solar. It however had a lot of issues with the humanities

Salt

still, it should be $\sum_{i}^{\infty} 1/n$

wait, no, it's right

Secret

05:48

It is also quite ambitious in CO2 reduction, while USA risk falling behind due to the trump government's environmental policies

In general, china does ok in the technological sides of things, but poor at humanities

Salt

we got the muskman bringing the future to us soon, it'll all look like the jetsons by this time next year

user84215

06:10

The projective plane is a surface? If yes, why?

Wildcard

@AkivaWeinberger I can solve that one, by the way. It's a more advanced (but very similar) puzzle that I'm having trouble with.

Leaky Nun

@MathematicsAminPhysics how do you define a surface?

user84215

differential geometry

Leaky Nun

how do you differentiate anything around infinity @_@

user84215

It is better to ask this question from those people who consider the projective plane a surface.

Salt

06:53

@TobiasKildetoft i've updated my definition of -G since your comment, if you're interested, at least i think i have

Tobias Kildetoft

@Salt Unfortunately I don't really have time to think about combinatorial games at the moment

Martin Sleziak

Functional analysis room was unfrozen not so long ago and it had some activity recently. If there are some people interested in this area of mathematics, it will be nice if you have a look at the room occasionally.

Salt

that is unfortunate

I submitted a proof that G + (-G) = 0, but I don't think many have looked at it.

Martin Sleziak

Sorry for advertising the room again - if it becomes too much, simply tell me off and I'll try to do this less frequently...

@Salt Is it about this question: Classifying Games by their Groups?

Leaky Nun

@Salt what is G?

Salt

06:56

no, but it's linked in that post

6

Q: Extending Conway Games to $n$ players

Has anyone attempted extending the definition of Conway Games to $n$ players? And if not, what would the definition of $-G$ look like in such a theory? Motivation: Most of the definitions of a game from ONAG seem to have a natural extension to $n$ players. For instance: Let $G = \{G_1|G_2|\ldo...

combinatorial-game-theory

Martin Sleziak

I've had a brief look, but it seems quite far from things I am familiar with.

Salt

I made a lot more progress than I expected, and it led me to the second post

and though the second post is all conjecture, I find it extremely interesting; I probably have a go at trying to solve some or all of it in the next couple of days

i'll*

Tobias Kildetoft

07:09

Does this sentence sound right (especially the very last part)? "The first of these is one of the most fundamental problems in the representation theory of algebraic groups, while the latter has been an open conjecture in small characteristics for more than 25 years and implies the even longer-standing Humphreys-Verma conjecture."

Salt

i think so, assuming "in small characteristics" makes sense, because i have no idea what they are

it is a bit wordy, but easy enough to follow

skullpatrol

Sounds right to me.

Martin Sleziak

I am not a native English speaker so I'm not be of much help. I simply tried google and it seems that formulation "longer standing" is not used very often: "longer standing conjecture" or "longer standing open". But maybe I simply should have chosen a better search query.

Salt

longer-standing seems like a pretty apt description of the conjecture, assuming it's true...I don't know what the conjecture is, but i felt the weight of some long unsolved problem

skullpatrol

> ...in small characteristics for about 25 years and implies the much older Humphreys-Verma conjecture

Salt

07:25

i don't like 'much older'

skullpatrol

That's how I would write the last part @TobiasKildetoft

Martin Sleziak

@Salt As I mentioned, input from native English speakers will probably be more valuable than mine. I simply tried at least Google, to see whether it is commonly used.

Of course, it is possible to ask also in ELU or ELL chatroom.

Salt

everyone knows mathematicians are best linguists

2

skullpatrol

lol

Tobias Kildetoft

@skullpatrol Thanks. Calling it much older might be a slight stretch (it is from somewhere between '72 and '78)

skullpatrol

07:39

Then I'd use just "older."

Tobias Kildetoft

not "the even older"?

skullpatrol

Sure.

Salt

just doesn't have the same weight though

Tobias Kildetoft

@Salt I agree, but I was also not quite happy with how the word longer-standing looked

Salt

fair, l liked it though

skullpatrol

07:43

> in small characteristics for about 25 years and implies the older Humphreys-Verma conjecture

Salt

could you just drop 'about'

skullpatrol

> in small characteristics for 25 years and implies the older Humphreys-Verma conjecture

That's short and sweet :-)

SteamyRoot

Transformational grammar

Transformational grammar (TG) or transformational-generative grammar (TGG) is, in the study of linguistics, part of the theory of generative grammar, especially of naturally evolved languages, that considers grammar to be a system of rules that generate exactly those combinations of words which form grammatical sentences in a given language. TG involves the use of defined operations called transformations to produce new sentences from existing ones. The concept was originated by Noam Chomsky, and much current research in transformational grammar has been inspired by Chomsky's Minimalist Program...

skullpatrol

::runs screaming from the room::

Tobias Kildetoft

I like dropping the "about", but it just feels wrong without the "even"

Salt

07:48

you should just flex your latex "in small characteristics for $> 25$ years and $rightarrow$ the $>> 25$ years hummphrey...

drats

$\rightarrow$

Tobias Kildetoft

@Salt This will be for an abstract that will need to be displayed (hopefully) on a website without MathJax support

Salt

of course i wasn't serious, how about "in small characteristics for 25 years and implies the longer-standing"?

it has a better cadence

hmmm, isn't implies actually $\implies$

"even older" in place of "longer-standing" also sounds good

Tobias Kildetoft

Usually I would probably have just gone with whatever I first came up with, but for these sorts of proposals, I was told it is important to make the best possible first impression.

Salt

you could try "...the long standing"

which, is the usual wording...errr long-standing

skullpatrol

As they say, you never get a second chance to make a first impression :-)

Salt

08:03

and sometimes you don't get a 1st chance to make a 2nd impression

Tobias Kildetoft

Is it generally understood that if I write that someone proved something in 2013 and cite a 2017 paper that the discrepancy is due to publishing times?

Salt

that...is a good question

I might make a mention of it

Tobias Kildetoft

wow, from the timeline on the electronic version, it took the authors about 18 months before they submitted it there. It was probably rejected somewhere else first.

(which is unusual since it was published in JAMS)

Maybe I should just avoid mentioning the year at all

Salt

marketing science?

Tobias Kildetoft

??

user147690

08:08

@TobiasKildetoft What is the fundamental problem you refer to here?

Tobias Kildetoft

@AlexClark determining the characters of the simple modules

user147690

For char p?

Tobias Kildetoft

yeah

user147690

Are you about to publish again? Is there a preprint somewhere?

Tobias Kildetoft

@AlexClark Hopefully soon, as I am preparing a fellowship application, and I have made references to a paper in that which I am still writing

So I should get that done within the next 2 weeks

user147690

08:22

@TobiasKildetoft That's awesome. I imagine it's a stressful time then. What's it about roughly?

Tobias Kildetoft

@AlexClark the paper or the proposal?

user147690

@TobiasKildetoft The paper I meant. The proposal usually contains the conjectures you are proposing to solve right? So normally one keeps that private for some time, or no?

Salt

Just occurred to me that the group of an impartial game is $\mathbb{Z}/n\mathbb{Z}$, for some $n$ which strengthens my conjecture, if that's a thing one can do. I haven't explored impartial $n$-player games yet.

Tobias Kildetoft

@AlexClark Well, the conjecture I propose to solve is Donkin's tilting conjecture, which is well-known

The paper describes an algorithm for how to get the characters of simple modules given that one knows those for the tilting modules and assuming Donkin's tilting conjecture. The main thing is that it works in those characteristics where previous methods fail, due to an example in a previous paper of mine

Secret

08:52

[Random]

(To be done later) illustrating the "trajectory space" for a double pendulum for different parameters such that it spans through all lyapunov exponents

Some elaboration: A "trajectory space" (perhaps there's actually a formal name for that) is a space whose points are continuous curves in $\Bbb{R}^3$

The idea is that for parameters of the double pendulum that result in a lyapunov exponent < 0, the trajectory space should have no chaotic structures, whereas for paramters such that said exponent is > 0, chaos occured.

Rather than picking a set of starting conditions and see how they changes as the lyapunov exponent changes, it seemed to be more informative to be able to plot all possible starting conditions and their evolution (which will trace out a trajectory, or curve in 3 space)

Therefore, it is more like having a multivariable function where the height is the lyapunov coefficient, and each point is a trajectory space, if that makes sense

Salt

like, uh, phase space?

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