Mathematics - 2019-07-14 (page 1 of 3)

Akiva Weinberger

02:43

modular fibration 2

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!!!!!

Also:

mandelmap.com

user76284

Beautiful

user76284

03:04

The imaginary part of the sum of all primes is 2. Still figuring out the real part.

CroCo

05:54

Let a > 0, how can I show -a+sqrt(a^2-4) is always negative?

ABStkokes

Interesting problem - puzzling.stackexchange.com/questions/86147/…

2

Q: Minimize sum of guesses to win lottery

Ten boxes are given with $a_1,a_2,a_3,a_4,a_5 ......a_{10}$ number of balls in them respectively .These boxes are randomly ordered but $a_1,a_2 .....a_{10}$ is told.We can arbitrary select a box and guess number of balls in it.If our guess is greater or equal to number of balls in it then we win ...

Secret

06:18

Here be fractal dragons

Unfolding The Dragon | Fractal Curve |

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bolbteppa

09:26

When does it become important/useful to use a degenerate bilinear form in linear algebra

Tobias Kildetoft

10:02

@bolbteppa Not sure how important it is to "use" one. Knowing whether it is degenerate is quite important though.

bolbteppa

The Killing metric (non LA) is the only place I can remember having to face up to them

1010011010

olleH

I'd like to make an approximation just like equation 6 from this paper

sciencedirect.com/science/article/pii/S0022169499001845

Basically it's an interpolation between two limits

I'd like to do something similar for another function

The authors give no background info so I'm a bit stumped how they did that, and with such accuracy

And I'm quite sure it's not just made up out of thin air

Leaky Nun

11:04

@MatheinBoulomenos why write $\Gamma(U,A)$ when you can write $A(U)$?

s.harp

12:04

@MikeMiller I asked the question on mathoverflow and seem to have gotten two conflicting answers:
https://mathoverflow.net/questions/336073/possible-isometry-groups-of-open-manifolds

although it appears the one providing a counter example is correct

user193319

13:07

Problem: If $g$ is strictly monotone on $\Bbb{R}$, and $f$ is a measurable function on the measurable set $E \subseteq \Bbb{R}$, then $g \circ f$ is measurable.

Proof: Since $g$ is strictly monotone, there is a set $D \subseteq \Bbb{R}$ set of measure $0$ such that $g$ is continuous on $\Bbb{R} \setminus D$ (WLOG, assume that $D \subseteq E$). Since $m(D)=0$, $g \circ f$ is measurable on $D$. Now restrict the functions to $E \setminus D$. Let $U \subseteq \Bbb{R}$ be open. Then $g^{-1}(U)$ is open in $E \setminus D$, since $g$ is continuous on $E \setminus D$.

Hence, $(g \circ f)^{-1}(U) = f^{-1}(g^{-1}(U)$ is measurable, because $f$ is measurable by assumption and $g^{-1}(U)$ is an open set (in $E \setminus D$). Hence, $g \circ f$ is measurable on $E \setminus D$, so it is measurable on $(E \setminus D) \cup D = E$.

How does this sound?

loch

@LeakyNun makes it clearer that this is a functor

Ryan Unger

13:25

@user193319 I didn't read that very closely, but this should mimic the proof that the composition of continuous functions is continuous.

user193319

@RyanUnger I'm not sure I follow. I'm taking the composition of a continuous function with a measurable function.

Ryan Unger

@user193319 Actually you don't need to worry about the discontinuities. Recall that for measurability it suffices to check if $f^{-1}((a,\infty])$ is measurable for all $a\ge -\infty$. But for a monotone (increasing) function, $f^{-1}((a,\infty])$ is always an interval.

So the preimage by $g$ gives an interval, then use the measurability of $f$...

user193319

Ah, nice. Two different solutions. Thanks!

skullpetrol

14:11

@RyanUnger what's this about Princeton admin asking applicants about their criminal record?

Ryan Unger

@skullpetrol what

pretty sure every application asked me if I had a felony

skullpetrol

yeah, I read it on twitter

Ryan Unger

it's a standard question for employers to ask...

s.harp

if you are a student you they arent your employer tho

Ryan Unger

They're paying me...

MatheinBoulomenos

14:13

grad students are often employed (both in the US and Europe)

skullpetrol

I think they got the question removed from grad schools...

Ryan Unger

UT Austin said they'd require a full background check, actually

skullpetrol

what's next? Drug testing :P

Ryan Unger

I have a license for my medical cocaine

Tobias Kildetoft

@skullpetrol Yes, if you don't test positive for caffeine, they won't admit you.

skullpetrol

14:18

:-D

Tobias Kildetoft

I don't even think if my security clearance required me to answer questions about criminal record. But probably there was something in it about allowing them to check that themselves.

Ryan Unger

This is surely not a U.S. TS clearance...for those they come and interview your neighbors, family, etc.

Tobias Kildetoft

TS?

Ryan Unger

top secret

stupid name but that's the official designation

Tobias Kildetoft

you mean Cosmic Top Secret? Or some other level of security?

(or maybe the US has a less stupid naming convention)

Ryan Unger

14:22

Lol, cosmic is a NATO thing, right?

Security clearance

A security clearance is a status granted to individuals allowing them access to classified information (state or organizational secrets) or to restricted areas, after completion of a thorough background check. The term "security clearance" is also sometimes used in private organizations that have a formal process to vet employees for access to sensitive information. A clearance by itself is normally not sufficient to gain access; the organization must also determine that the cleared individual needs to know specific information. No one is supposed to be granted automatic access to classifi...

TS is above "Secret"

the next level is CTS, compartmentalized top secret

that's technically the highest level but it's stratified from within (indicated by compartmentalized)

Tobias Kildetoft

@RyanUnger Probably. The level below it is called NATO secret (I think I have that clearance. At least I applied for it, and they have now given me access to the systems I needed it for, so presumably the clearance went through)

Ryan Unger

CTS is absolutely brutal to get. Lots of interviews, background checks, interviewing acquaintances, lie detector tests

And you have to submit a report on any foreign nationals you come into contact with

Tobias Kildetoft

Well, the lie detector tests would only be in the US

no other nation takes those seriously

Ryan Unger

But the questions they ask are crazy too

They ask about medical history, personal life, habits

skullpetrol

Internet use?

Ryan Unger

14:28

Well they catch people trying to cheat the lie detector test

So why stop using it

Tobias Kildetoft

for NATO secret it was not that bad. But it did require a full list of all current debt, all stays abroad the past 5 years (not counting short vacations) and past 10 years of employment history, including all periods without work

@RyanUnger Because lie detectors have been scientifically proven to not work properly and be beatable

Ryan Unger

No one actually thinks they're foolproof

Tobias Kildetoft

as far as I recall, they are illegal to use in most countries for anything but entertainment purposes

Ryan Unger

The point isn't to have a foolproof system, the point is to just add one more layer of security

What is the purpose of making them illegal?

Tobias Kildetoft

But if that layer potentially says nothing at all, and you have no way of knowing how much it says, it is useless

Ryan Unger

14:31

The word potentially is pretty key there

In some instances it is helpful

Tobias Kildetoft

@RyanUnger In which instances?

Ryan Unger

I'm not in the counterintelligence business and even if I were, I wouldn't be able to answer that question

skullpetrol

Police use them in interrogations, no?

Ryan Unger

I highly doubt that. It would be a violation of the 5th amendment.

Balarka Sen

I prefer the old school lie detector test

Keep pouring boiling water on their face until they crack

:3

or something idk

what times they were, the middle ages

skullpetrol

14:37

the good cop, bad cop routine always works on me :P

@RyanUnger ya, you're in the counterexample business :-)

in The h Bar, Jul 23 '17 at 3:40, by The Raiders of Las Vegas

Bad idea #271: Dropping into the half-pipe on a Segway.

Mike Miller

15:07

@s.harp Yes, Misha's answer is correct. Peter Michor was trying the approach I suggested yesterday, and it doesn't work for reasons I explained then about needing closed orbits.

Misha's answer is very nice.

Érico Melo Silva

@RyanUnger they do in fact use them sometimes, they legally can’t force you to undergo it, but police do things to subtly violate people’s rights during investigations literally constantly

Flintoff

15:59

Hi and hello CHAT

???

So silence

OK bye

MatheinBoulomenos

so silence, much quiet, wow

Ryan Unger

@ÉricoMeloSilva ok doing my CV

which email are we supposed to put

seems really weird to be doing this before the semester starts and we have any of this info

Érico Melo Silva

@RyanUnger im putting my princeton email

Ryan Unger

@ÉricoMeloSilva we don't have the math.princeton.edu email yet

Érico Melo Silva

isn’t that one just supposed to redirect to the ones we already got tho anyway

also yeah when do we get those even

Ryan Unger

16:07

we get them during orientation

I guess it just redirects...

Érico Melo Silva

ok i see

Ryan Unger

there's the grad school orientation and then a math dept orientation

Érico Melo Silva

right

Ryan Unger

what's your netid

I got runger

absolutely based email

Érico Melo Silva

easilva

Balarka Sen

16:09

runger lol

Ryan Unger

whats the a

Érico Melo Silva

my middle name is alexander

Ryan Unger

cool

@BalarkaSen I had runger2 at tennessee

the OG runger is a pediatrician in knoxville

@ÉricoMeloSilva is the title "PhD student" and when (if?) we pass the generals, it becomes "PhD candidate"?

Érico Melo Silva

honestly i have 0 clue but that sounds right

based on what ik of other schools

do u know other ppl in our cohort

Ryan Unger

I only met one other person who got into Princeton at the other schools I visited...not sure if he decided to go there

I know lots of current students

Érico Melo Silva

16:14

lol all the prospies i remember from the open house aren’t coming to pton

Ryan Unger

it's the best place in the world for GA so it wasn't really a choice...

Érico Melo Silva

for the open house they gave us a final list of admits w our chosen fields for the ppl who’d gotten in at that point and only me and 1 other person had GA as their field so there aren’t many of our kind

literally everyone i met at all my open houses was a number theorist

Ryan Unger

LOL blame the fields medals

GA had a rough year, there was also only one NSF award for us

Princeton has a really good number theory program though, doesn't it?

@MatheinBoulomenos do you know

Érico Melo Silva

doesnt stanford too or smth

Ryan Unger

Princeton/IAS has two fields medalists in number theory

plus Langlands, Sarnak

Érico Melo Silva

16:20

presumably also ppl didn’t wanna live in princeton

@RyanUnger my grfp app got such good reviews and i didn’t get it and it was sad

not too sad but sad

Ryan Unger

I had really good reviews too...

Érico Melo Silva

the one person who got it at uchi is way smarter than my dumb ass so it’s ok

Ryan Unger

someone at UTK math got it :P not me

for mathematical biology

Érico Melo Silva

well there u go

bio is a magic spell, the key to unlocking the treasure vault

i think the uchi math person to get t was a number theorist

she’s really very good tho so i get it

Ryan Unger

the guy I met at Austin who also got into Princeton was a PDE guy

Navier Stokes

Will

Alessandro Codenotti

16:25

GA?

Érico Melo Silva

i remember his face but idt i talked to him

@AlessandroCodenotti stands for Good Ass math

Ryan Unger

@AlessandroCodenotti georgia or geometric analysis depending on context

ÍgjøgnumMeg

Evening all

Ryan Unger

hi

Alessandro Codenotti

@ÉricoMeloSilva Ah, I didn't know you applied as a set theorist

Hi @ÍgjøgnumMeg

Balarka Sen

16:26

LOL @Alessandro

ÍgjøgnumMeg

Hey :)

Ryan Unger

ok eric i.gyazo.com/18410c60c2a9be31921a9d4370b2176c.png

Érico Melo Silva

@AlessandroCodenotti u got me there bud

Ryan Unger

GPA is probably not needed right

just put summa

Érico Melo Silva

nah fuck gpa

just put ur latin honors

Balarka Sen

16:27

summa cum laude

Ryan Unger

ya

Érico Melo Silva

we don’t get those at chi

Ryan Unger

wot

bah I need to scrap this format

Érico Melo Silva

chi has no latin honors for some reason

just to seem cool

Ryan Unger

avantgarde

ÍgjøgnumMeg

16:30

When's the start date?

Balarka Sen

what is chi

Ryan Unger

september...9?

Balarka Sen

oh chicago

Ryan Unger

@BalarkaSen Greek letter

Érico Melo Silva

@BalarkaSen no one calls it that i just didn’t want to type

Ryan Unger

16:32

lol

>some quote

Érico Melo Silva

“i got 99 problems”

Balarka Sen

LOL

Ryan Unger

I could cite Thom like Hirsch does

that's always impressive

Balarka Sen

"Singularity, bitches" - Rene Thom

Érico Melo Silva

if the quotes not in french what’s the point

Ryan Unger

16:34

2

Érico Melo Silva

i was always destined for greatness

Balarka Sen

@Ryan what is it with you and i.gyazo

why always that site

Ryan Unger

what else am I supposed to use

Balarka Sen

imgur???

idk fam

Ryan Unger

it captures images and uploads them

automatically

does imgur do that

Balarka Sen

16:35

i guess not

Ryan Unger

yeah I take a screenshot and it gives me the link

Balarka Sen

That's cool

Ryan Unger

@BalarkaSen IAS is doing a special year on h-principles

2021-2022

Balarka Sen

OH

Shit cool

Ryan Unger

you'd better come

Érico Melo Silva

16:37

@BalarkaSen come hang out w us

Ryan Unger

you can apply for funding...normally its only post docs I think but you'll be famous

Balarka Sen

Can I like apply or whatever

Ryan Unger

Tristan Buckmaster is an organizer I think

I think the special years include standard conferences

you can apply for funding for those

there's also year-long funding but that's for researchers

Balarka Sen

idk ill see. seems unlikely i can fund my trip but anyway you two can write notes for me @Eric @Ryan

Ryan Unger

Well Tristan is faculty at Princeton and I aim to learn something about this convex integration business

So I'll be talking to him

Balarka Sen

16:41

Nice! I'll have to learn that as well.

You can teach me maybe

Érico Melo Silva

what is convex integration

Ryan Unger

He solved a big conjecture in fluid mechanics using convex integration

No clue Eric but it was all the rage at the ICM

Érico Melo Silva

oh word

that sounds cool

Ryan Unger

De Lellis has also been working on it recently

Érico Melo Silva

ooo sick he’s cool

excited for his gmt class to fill the holes in my brain that not doing much math for a year has left

Balarka Sen

16:45

@ÉricoMeloSilva It's an h-principle for ample differential relations. I can give you an example which is like the only thing I know

Let me finish my cigarette first lol

Ryan Unger

@BalarkaSen you smoke?

why are the CV templates on overleaf made by indians

Érico Melo Silva

immense brain drain is the basic answer i suspect

Ryan Unger

this is the most Indian thing I have ever seen

Balarka Sen

LOL

@RyanUnger Yeah I do

Ryan Unger

I'm extremely surprised Balarka

Aren't you like 13

Alessandro Codenotti

16:48

@RyanUnger You should watch a bollywood movie

Ryan Unger

Seriously, idk how old you are

@AlessandroCodenotti I have

But putting your JEE percentile on a CV...wow

Érico Melo Silva

smoking is cool and sexy and anyone who says otherwise is a cop nobody @ me for this

Ryan Unger

it's actually a nice template

Érico Melo Silva

this is the template i use actually

Balarka Sen

@ÉricoMeloSilva So look at any smooth path $\gamma : I \to \Bbb R^2$ which is short, in the sense $\|\gamma'\| < 1$. I imagine this as a non-vertical path in $\Bbb R^3$ with it's tangent vector lying inside a fixed cone field along the path

You can also say it's the trajectory of a particle through spacetime idk

Ryan Unger

16:51

@BalarkaSen IAS

Murphy and Eliashberg will be there

hot damn

Balarka Sen

Every such path can be $C^0$-approximated by arclength-parametrized paths, which satisfy $\|\gamma'\| = 1$.

These are always tangent to the boundary of the cone field

A trajectory of a photon maybe

Ryan Unger

Balarka talking about spacetime

Érico Melo Silva

talk physics to me bb

Balarka Sen

Roughly speaking this happens because $\|\gamma'\| < 1$ is a convex differential relation (cones are convex). Gromov proved every ample differential relation satisfies the h-principle; every solution which lies in the differential relation can be approximated by solutions which are tangential to the differential relation (goes along the boundary, of which it's the convex hull of)

Ryan Unger

ugh I forgot how classes work in tex

Balarka Sen

16:55

I think this whole circle of ideas is proved using convex integration but this is where my knowledge stops

Ryan Unger

can I put the .cls in the same folder as the .tex

Érico Melo Silva

@BalarkaSen what does ample mean?

Balarka Sen

@RyanUnger 19. Oh, actually, I graduate undergrad on 2021.

Érico Melo Silva

i love how this man is 3 years younger than me and 300 times smarter than me

Ryan Unger

@BalarkaSen ok so you'll be an Eliashberg or Gromov student already

you won't need our help

Mats Granvik

16:58

Transcript for

$Mathematics$ Mathematics