Mathematics - 2018-08-09 (page 2 of 2)

Akiva Weinberger

18:11

Knot musings

The kinda stuff that happens when you knot surfaces in $\Bbb R^4$ (projected onto $\Bbb R^3$)

http://de.arxiv.org/pdf/1609.09587.pdf

ÍgjøgnumMeg

18:27

@Mathein Hoi! Wie kann ich herausfinden welche Vorlesungen laufen im Semester?

MatheinBoulomenos

@ÍgjøgnumMeg hi!

lsf.uni-heidelberg.de

erstmal rechts oben auf nächstes Semester stellen ;)

ÍgjøgnumMeg

Ahhh nice danke :D

MatheinBoulomenos

@ÍgjøgnumMeg ich hab gar nicht drangedacht, aber ich weiß nicht, wie das mit dem Brexit ist, ehrlich gesagt, hast du das bedacht?

ÍgjøgnumMeg

Ja hab ich, hab aber auch keine Ahnung was da abgeht, hoffentlich darf ich einfach so in Deutschland bleiben hahaha

MatheinBoulomenos

also als EU-Ausländer zahlst du hier keine Studiengebühren, aber für nicht-EU-Ausländer ist es 1500€ im Semester (was wahrscheinlich immer noch ziemlich wenig gegenüber Nottingham ist)

Leaky Nun

18:34

0

A: Galois extension in $\mathbb{C}$

Separability is automatic for fields of characteristic $0$.

@MatheinBoulomenos they flagged my answer :(

ÍgjøgnumMeg

@Mathein hmm stimmt, hab nicht daran gedacht

MatheinBoulomenos

@ÍgjøgnumMeg und evtl. noch Visumsgebühren, das weiß im Moment wahrscheinlich niemand

ÍgjøgnumMeg

jaaa keine Ahnung, ich zieh einfach nach Heidelberg und hoffe mich findet niemand ;)

lol

MatheinBoulomenos

lol

ÍgjøgnumMeg

ich habe noch Hoffnung dass die brexit scheiße gar nicht weitergeht

MatheinBoulomenos

18:41

brexit is really stupid and benefits nobody

ÍgjøgnumMeg

^

Mike Miller

my german is good enough to read "die brexit scheiße"

5

MatheinBoulomenos

@ÍgjøgnumMeg wollte dich nicht verunsichern, aber hab gedacht ich sag dir das mit den Gebühren für nicht-EU-Ausländer

nicht dass das dann als böse Überraschung kommt

Alessandro Codenotti

@ÍgjøgnumMeg So you took a decision?

ÍgjøgnumMeg

@Alessandro Yeah I did but @Mathein has just reminded me that post-Brexit I might have to pay 1500€ per semester in Heidelberg

lol

Alessandro Codenotti

18:48

You'll likely finish your Master before that I think? It looks like brexit will take a long time

ÍgjøgnumMeg

Yeah that's what I was hoping, but I thought that Article 50 meant that we leave in March 2019

Alessandro Codenotti

You have about a year to marry a German then, easy solution

ÍgjøgnumMeg

hahaha

Leaky Nun

@ÍgjøgnumMeg i'm confused, bist du nicht deutsch?

ÍgjøgnumMeg

@Leaky I'm from the UK lol

Leaky Nun

18:50

dann warum sprichst du deutsch?

ÍgjøgnumMeg

@Leaky Irgendwie habe ich die Sprache gelernt

Leaky Nun

:o

ÍgjøgnumMeg

:D

Alessandro Codenotti

Actually you don't even have to marry a German, just a citizen of an EU state that grants citizenship via marriage!

Perturbative

Yo everyone

Alessandro Codenotti

18:52

Hi

ÍgjøgnumMeg

With a face like this and grades like this I'm bound to find a marriage partner immediately after leaving the plane

Perturbative

Hey @AlessandroCodenotti :)

geocalc33

I'm working on working my way into the EU

Alessandro Codenotti

@ÍgjøgnumMeg don't waste time, there will be a lot of Germans on the plane

ÍgjøgnumMeg

hahaha

geocalc33

18:54

in case America goes downhill

MatheinBoulomenos

@ÍgjøgnumMeg I don't want you not to come to Heidelberg :/ but I wasn't sure if you were aware and not reminding you would have felt very wrong and manipluative

ÍgjøgnumMeg

@Mathein haha nooo it was a good thing, I think I'll probably still come and just see what happens

Rudi_Birnbaum

@AlessandroCodenotti Some Irish, eg. (hi to all)

ÍgjøgnumMeg

I have some rich old relatives, maybe they will give me money

Alessandro Codenotti

I guess the UK will negotiate something with the EU for EU students wanting to study in the UK and viceversa as part of the brexit agreements?

MatheinBoulomenos

18:56

@ÍgjøgnumMeg yeah, you don't need to pay for the first semester at the very least (if they are really doing Brexit next march

loch

hey @Adeek

ÍgjøgnumMeg

Yeah most things I've read say that the status of EU students in the UK won't change immediately anyway

hopefully the same is true for UK students in the EU

Rudi_Birnbaum

@AlessandroCodenotti The GB government does not show any sings of negotiating something useful at the moment. Its very sad ...

ÍgjøgnumMeg

How the f*ck did this happen

MatheinBoulomenos

there are so many things that should be negotiated and the negotations are just stalling so if they're really doing the Brexit in March 2019 then nobody knows what will happen.

ÍgjøgnumMeg

18:59

Right, and I haven't seen any sources claiming that it won't happen in March 2019

Rudi_Birnbaum

Yeah its a nightmare. I have some friends working in GB or one from GB working in DE and for all its a total disaster ...

ÍgjøgnumMeg

basically stupid old racist people ruined everything for everyone

MatheinBoulomenos

@ÍgjøgnumMeg yeah that's a nice summary

Rudi_Birnbaum

yes

MatheinBoulomenos

@ÍgjøgnumMeg the easiest thing legally would probably be Alessandro's plan to just marry an EU citizen before Brexit

ÍgjøgnumMeg

19:03

Or change my name to Hans Schmidt, wear Lederhosen everywhere and just hope nobody questions me

MatheinBoulomenos

I think if you marry a German, you even get Bafög

ÍgjøgnumMeg

rofl nice

if we didn't vote to leave the EU I wouldn't have to enter into some sham marriage just to study

MatheinBoulomenos

@ÍgjøgnumMeg as long as you only live on beer, sausages and kraut, it should work out

ÍgjøgnumMeg

hahaha

Rudi_Birnbaum

he'll have to learn to make bad jokes as well

ÍgjøgnumMeg

19:05

How many Germans does it take to change a lightbulb?

MatheinBoulomenos

one. We are efficient and don't have any humour

ÍgjøgnumMeg

One; Germans are efficient and unfunny.

Rudi_Birnbaum

thats a start ...

ÍgjøgnumMeg

HA

sniped

Rudi_Birnbaum

lol

geocalc33

19:09

@Rudi_Birnbaum I'm looking for a family of functions that is symeetric about $y=x$ and $y=1-x$ and has a smoothly varying parameter that transitions the function from itself to it's inverse

in the unit square

the line $y=x$ is the crossing point at which the function either transitions from itself to its inverse or vice versa

the family $f_n(x)=x^n$ does not suffice because all the functions in this space are not symmetric about $y=1-x$

Rudi_Birnbaum

@geocalc33 maybe ellipses rotated around 45° (and only take one half).

geocalc33

thanks

Rudi_Birnbaum

np!

geocalc33

super ellipses also might work

Adeek

good @loch your here

I was wondering do you know why we need those very general points ?

they say that from those very general points we get the family

but it seems that given any variety we can always construct the spread in the way I explained earlier.

Are germans really rude @MatheinBoulomenos ?

I heard rumours that they are super rude.

Semiclassical

19:23

I’m dubious that you’ll be able to find functions such that this works. (Finding curves which fulfill this is easy enough, eg a small circle at the center of the unit square. But such a curve is not the graph of a function.)

Adam

why did they change the formatting it automatically implements a bar slidey thing after a certain amount of characters I don't want one put it back the way it was

Rudi_Birnbaum

@Adeek Yeah :-)

Adam

sorry not a huge fan of change

Adeek

I think that is related to the comment you made earlier that I didn't go through 100 %

that we get a family from the $\alpha$ @loch

MatheinBoulomenos

@Adeek lol

Adeek

19:28

lol

do you know why do we need this very general point notion it doesn't seem to be useful @loch

ÍgjøgnumMeg

@Mathein hey nice Analytic Number Theory is running this semester then?

geocalc33

@MatheinBoulomenos how do you make the infinity symbol in latex?

MatheinBoulomenos

\infty

@ÍgjøgnumMeg yeah. Also "Galois cohomology and Galois representations" and Algebraic Geometry

ÍgjøgnumMeg

yeah I saw this, I don't know if Galois Cohomology and Galois representations will be very useful for me though

MatheinBoulomenos

and the seminar "Darstellungstheorie von GL(2)" is actually about a special case of Langlands

@ÍgjøgnumMeg depends on what you want to do. I think it's a bit like an unofficial "Algebraic Number Theory 3"

ÍgjøgnumMeg

19:35

Idk how many things you have to pick tbh, it's a lot different from the English system lol

yeah but I mean, I don't think I'll have the background for it

MatheinBoulomenos

ah yeah it would be difficult probably

ÍgjøgnumMeg

lol

should I choose like 3 Vorlesungen or what?

Soz for spamming questions

geocalc33

@Rudi_Birnbaum

I figured it out

MatheinBoulomenos

@ÍgjøgnumMeg maybe we should talk those things not here, since it doesn't intersest anyone else probably

Rudi_Birnbaum

@geocalc33 good!

@geocalc33 But its true. those two symmetry operations combined give a third one which copies a point $(x,y)$ to $(x,y')$ with $y\ne y'$, so those are not functions from $[0,1]$ to $[0,1]$, but you could call them relations.

geocalc33

19:50

ah yes

Adeek

Loch here ?

geocalc33

@Rudi_Birnbaum is it possible to solve the equation $(1-x)^n+y^n=1 $ for n?

Rudi_Birnbaum

Freshman's dream

The freshman's dream is a name sometimes given to the erroneous equation (x + y)n = xn + yn, where n is a real number (usually a positive integer greater than 1). Beginning students commonly make this error in computing the power of a sum of real numbers. When n = 2, it is easy to see why this is incorrect: (x + y)2 can be correctly computed as x2 + 2xy + y2 using distributivity (commonly known as the FOIL method). For larger positive integer values of n, the correct result is given by the binomial theorem. The name "freshman's dream" also sometimes refers to the theorem that says that for a prime...

geocalc33

so it's not possible

I need the binomial theorem

and for the record i did not make the freshmans dream mistkae

so idk why you put that there

Rudi_Birnbaum

@geocalc33 To say that it depends on over which field you work ;-) But over $\Bbb R$ not to my knowledge. Cannot prove it either ...

geocalc33

19:56

which fields can I work over? how about the reals

that's not a field though

okay

Rudi_Birnbaum

it is

geocalc33

oh the reals are a field?

cool

Rudi_Birnbaum

so are the rationals

geocalc33

I learned something new today

Rudi_Birnbaum

When the "common" laws of addition and muliplication holds its a "field".

The "binaries" $\{0,1\}$ are another example.

the integers are no field because you do not have "division" (which I summarized by "common" laws ...).

$\frac{1}{2}$ is no integer, hence $\Bbb Z$ is no field.

Alessandro Codenotti

20:04

wtf happened to the layout of MSE?

Rudi_Birnbaum

@geocalc33 So when you work over the "binaries" freshmans dream is reality and you can solve your equation for n. :)

Perturbative

It got rekt

KeJie

20:19

Did they change the design of the site? Looks terrible.

Alessandro Codenotti

yeah

KeJie

It was perfect but now they ruined it.

The design looks very cheap now tbh

geocalc33

@Rudi_Birnbaum can you help walk me through the solution over the binaries

?

Rudi_Birnbaum

@KeJie This is like in evolution "perfect" is no stable property ...

Or maybe better to say in sexual reproduction

@geocalc33 It will be mostly pointless for you, I guess. $x$ and $y$ will be only allowed to be either $0$ or $1$. ...

geocalc33

oh yeah

Rudi_Birnbaum

20:32

@geocalc33 that means our "universe" consists of exactly four points: $(0,0),(0,1),(1,0),(1,1)$ and some of those will be our curve.

For larger of such "finite fields" it will get more interesting and the general case $\Bbb F_p$ such a field of any prime order, this is something you might learn about in university.

G. Ünther

Funny, are there so many people from Germany here? Or do I just think that because there was a lot of talk in this chat about it lately?
Ich meine, ich bin ja selber auch aus Deutschland, deswegen frage ich mich das gerade. Könnte auch confirmation bias sein, also naja.

Alessandro Codenotti

There a few Germans and a few people who speak German but are not from Germany

ÍgjøgnumMeg

20:48

I identify as zeroth generation Austrian

Alessandro Codenotti

I can understand German fairly well but I need some serious exercising to get my spoken/written German to an acceptable level again

MatheinBoulomenos

@G.Ünther two people in this chat will move to Germany next semester for their masters

Faust

21:25

@MatheinBoulomenos @TedShifrin i need a resoucre for Banach algerbras please?

MatheinBoulomenos

@Faust hi! long time no see

Faust

im not dead!

just been really sick but seems the specialist figured out whats wrong with me

cot me a grand to get in and see him but was well worth it

im doing some stuff on c* algebras and was wondering if you had anything good for banach spaces and or hilbert spaces

MatheinBoulomenos

oh that's good to hear!

Faust

yeah will be back on regularly till septem,ber need to get caught up

Maximus

hello, is there something wrong with my calculation:

$(m+2)^n-(m-2)^n = 2 {n \choose 1}m^{n-1}+ \dots + {n \choose n-1}m2^{n-1}-{n \choose n-1}m(-2)^{n-1}+{n \choose n}2^n - {n \choose n}(-2)^n$

and how to write this in summation notation?

MatheinBoulomenos

21:30

I don't know much about this analytical stuff, but hilbert spaces are treated in every functional analysis text, so picking an intro func analysis text will suffice for those

for Banach algebras, I'd recommend Rickart - General Theory of Banach Algebras

I haven't read it in any detail, more skimmed it, but what I saw seemed nice

Faust

ok any other pre reqs for C* algebras you could recomend i read?

MatheinBoulomenos

this book looks like quite a good fit for what you need, but I haven't read it myself: springer.com/us/book/9783319067278

the last chapter is on C* algebras!

Faust

i have

MatheinBoulomenos

is it good?

Faust

amazon.ca/Functional-Analysis-Walter-Rudin/dp/0070542368

this one

sorry like half a thought

MatheinBoulomenos

21:34

ah okay

Faust

its supposed to be good but doesnt have a specfic section for banach spaces

MatheinBoulomenos

that's strange

I took a class on functional analysis, but we didn't use any book, so I can't really recommend anything

the book I linked has chapters on Banach spaces, Hilbert spaces, Banach algebras and C*-algebras, so it seems as close to the topics you want as it gets

but that doesn't say anything about the quality of the exposition of course

Alessandro Codenotti

I really liked the first 5 or 6 chapters of Brezis for the "standard" functional analysis stuff and I used it very little but Conway's functional analysis book seemed good for some more advanced stuff (including Banach algebras and C*-algebras)

MatheinBoulomenos

ah, I wanted to have a look at Conway's functional analysis book, anyway

haven't got around to it

Faust

ok thanks alot :)

i got a friend over to study so i should gte back toit ill see youte

later*

Alessandro Codenotti

21:41

I remember I read from Conway's book how to use the Stone-Cech compactification to construct the dual of $\mathcal C_b(X)$ (with some assumptions on $X$) which is pretty neat in my opinion

Here comes the analyst! Hi @Eric, you probably have better suggestions for functional analysis books

Rithaniel

22:02

Hey, does anyone know a good place to start reading up on the most efficient ways to pack 3D objects? I'm trying to find a good pattern for tetartoids.

jackbenimbo

I just wanted to reach out and thank mathexchange as without your help, I would have been in very bad shape for Calc II. Today I take my final, and although I have MUCH MUCH to review prior to calc III, the community has helped me so much in my learnings.

loch

22:18

@Adeek unfortunately i'm not quite sure too! i suspect that things might be easier if the original thing was written in the language of schemes... (or maybe not)

anyway - I think the idea is that, say you have a variety defined over $k \isom \mathbb{Q}(T)$ (e.g. if it is defined over $\mathbb{Q}(\pi)$, then if you think about the transcendental points on $\mathbb{P}^1$, these would correspond to different embeddings of $\mathbb{Q}(T)$ to $\mathbb{C}$,

so if you're only thinking of the transcendental points, then at least it seems "right" to me that thinking this way gives you some notion …

i haven't quite reconciled this with what i suggested with the elliptic curves / other examples yet -- but this is what i think the author intended when he wrote that paragraph

Eric Silva

@AlessandroCodenotti its been a long time since i read functional but i like brezis and i have a copy of kreyzig i use sometimes

i havent read many others that i can summon from my brain hole

loch

so maybe the main point is that when you were thinking about elliptic curves $y^2=x(x-1)(x-t)$, where $t$ is transcendental, when we look at this sitting in $\mathbb{P}^2 \times \mathbb{P}^1 \rightarrow \mathbb{P}^1$ (what you suggested earlier)

the fibre over non-transcendental points (non-very general points) are going to give you an elliptic curve which is "algebraically distinguishable" from the original elliptic curve that you started with

and the fibre over transcendental points (very general points) are going to give you elliptic curves which are "algebraically indistinguishable" f…

Adeek

back @loch

1 sec let me see your discussion above

ohh

okay I see

then using analytic methods we can kinda detect things

which aren't algebraically indistinguishable

I have a trivial algebra question

on page 4 we have a filtration $F^m \Omega_{X(k)/Q}^{\bullet} = Im( \Omega_{k/Q}^m \otimes \Omega_{X(k)/Q}^{\bullet -m} \rightarrow \Omega_{X(k)/k}^{\bullet} )$

I don't understand why does this make sense

is it because the tensor product is defined over K ?

so elements live inside of $\Omega_{X(k)/k}^{\bullet}$?

manooooh

22:38

Hello guys! Quick question: we know that if $\vec u\parallel\vec v\Rightarrow\vec u\times\vec v=\vec0$. My question is to know if the reciprocal is true. I take the vectors $\vec u=(1,1,2)$ and $\vec v=(0,0,0)$. It verifies $\vec u\times\vec v=\vec0$ but $\vec u\not\parallel\vec v$. Is my counterexample correct?

loch

I think the map is just the wedge product

Adeek

oh so it is not the tensor product

yeah tensor product doesn't make sense

loch

oh the indices are confusing though

*the subscripts

Adeek

no I understand the undices so what is happening with this -m

is that we shift things to the right

by -m and if it goes below zero then the complexes are automatically 0

I think that is how it works

and elements of $\Omega_{k / Q}^m$ are automatically elements of $\Omega_{X(k)/Q}$

loch

yeah i think youre right

Adeek

22:42

on what ?

the tensor product ?

loch

i meant the indices

Adeek

yeah

I think your right though on the wedge product

the tensor doesn't make sense

loch

yeah

Adeek

do you understand the SES ?

this is my last question sorry to bug you like that

I just don't understand the surjectivity

loch

I think you should read the middle things as $F^0/F^2$

then the surjection is $F^0/F^2 \rightarrow F^0/F^1$

(note that $F^2\subset F^1$, so this makes sense)

Adeek

22:48

ohh

loch

and of course your kernel is $F^1/F^2 = Gr^1$

Adeek

yeah makes perfect sense

awesome thanks so much

I understand the rest of the paper

you should discuss with me your research as well btw

@loch have you had a chance to look at my pdf ?

loch

not yet! I'll have a look at it at some point..
I'd also be happy to rant about some of the stuff I'm interested in! but maybe not now

Adeek

okay @loch

I will add mirror symmetry soon just give me a year :D

then I can pretend to do actually things that are applicable

haha

@loch I solved first two chapter of Hartshorne I would like to finish 3,4 during the fall

and maybe upload my solutions online

loch

good job!

it gets more fun/less dry when you do some stuff with curves/surfaces

Adeek

23:03

Yeah I am excited to do that I love more geometrical stuff

loch

also when you said you solved first two chapters of Hartshorne - did you actually mean you finished every exercise in ch2? that's a lot!

Adeek

yeah

I literally spent this last year doing math 12 hrs a day

haha

I was very productive but then in July I got burnt out and didn't do math for almost 3 weeks doing it but not as much

during my PhD though I will change things I think I will work hardcore for 2 weeks and take 2 days off

loch

23:19

its also important to also spend time on things that arent math :)

2

But being productive is good!

Adeek

yeah

geocalc33

0

Q: Solving system of static symmetric super-ellipse equations

How does one solve this system of static symmetric super-ellipse equations for $s=1,2,3,...?$ $ x^s+y^s=1 $ $ 1-((1-x)^s+(1-y)^s)=0 $ $ (1-x)^s+y^s=1 $ $ 1-((x^s+(1-y)^s)=0 $ Thanks.

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$Mathematics$ Mathematics