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

6:27 PM

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

@ÍgjøgnumMeg hi!

lsf.uni-heidelberg.de

erstmal rechts oben auf nächstes Semester stellen ;)

Ahhh nice danke :D

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

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

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)

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

6:34 PM

0

Separability is automatic for fields of characteristic $0$.

@MatheinBoulomenos they flagged my answer :(

@Mathein hmm stimmt, hab nicht daran gedacht

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

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

lol

lol

ich habe noch Hoffnung dass die brexit scheiße gar nicht weitergeht

6:41 PM

brexit is really stupid and benefits nobody

^

Mike Miller

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

5

@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

@ÍgjøgnumMeg So you took a decision?

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

lol

6:48 PM

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

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

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

hahaha

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

@Leaky I'm from the UK lol

6:50 PM

dann warum sprichst du deutsch?

@Leaky Irgendwie habe ich die Sprache gelernt

:o

:D

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

6:52 PM

Hi

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 :)

I'm working on working my way into the EU

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

hahaha

6:54 PM

in case America goes downhill

@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

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

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

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

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?

6:56 PM

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

hey @Adeek

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

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

How the f*ck did this happen

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.

6:59 PM

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

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 ...

basically stupid old racist people ruined everything for everyone

@ÍgjøgnumMeg yeah that's a nice summary

yes

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

7:03 PM

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

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

rofl nice

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

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

hahaha

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

7:05 PM

How many Germans does it take to change a lightbulb?

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

One; Germans are efficient and unfunny.

thats a start ...

HA

sniped

lol

7:09 PM

@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 $y=1-x$

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

thanks

np!

super ellipses also might work

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

7:23 PM

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

@Adeek Yeah :-)

Adam

sorry not a huge fan of change

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

@Adeek lol

7:28 PM

lol

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

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

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

\infty

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

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

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"

7:35 PM

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

ah yeah it would be difficult probably

lol

should I choose like 3 Vorlesungen or what?

Soz for spamming questions

@Rudi_Birnbaum

I figured it out

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

@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.

7:50 PM

ah yes

Loch here ?

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

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...

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

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

7:56 PM

which fields can I work over? how about the reals

that's not a field though

okay

it is

oh the reals are a field?

cool

so are the rationals

I learned something new today

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.

8:04 PM

wtf happened to the layout of MSE?

@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

8:19 PM

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

yeah

KeJie

It was perfect but now they ruined it.

The design looks very cheap now tbh

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

?

@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 $1$. ...

oh yeah

8:32 PM

@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.

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

8:48 PM

I identify as zeroth generation Austrian

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

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

9:25 PM

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

@Faust hi! long time no see

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

oh that's good to hear!

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?

9:30 PM

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

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

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!

i have

is it good?

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

this one

sorry like half a thought

9:34 PM

ah okay

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

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

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)

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

haven't got around to it

ok thanks alot :)

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

later*

9:41 PM

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

10:02 PM

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.

10:18 PM

@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

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…

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

10:38 PM

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?

I think the map is just the wedge product

oh so it is not the tensor product

yeah tensor product doesn't make sense

oh the indices are confusing though

*the subscripts

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 $\Omega_{X(k)/Q}$

yeah i think youre right

10:42 PM

on what ?

the tensor product ?

i meant the indices

yeah

I think your right though on the wedge product

the tensor doesn't make sense

yeah

do you understand the SES ?

this is my last question sorry to bug you like that

I just don't understand the surjectivity

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)

10:48 PM

ohh

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

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 ?

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

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

good job!

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

11:03 PM

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

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!

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

11:19 PM

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

2

But being productive is good!

yeah