@Mathein hmm deutschlandstipendium gibts anscheinend noch

lol

Hey everyone!

Hi @Daminark

How's it going? Any idea what you'll do regarding Heidelberg?

@Daminark I think I'm gonna go, there is a buddy programme and Mathein said he will see if he can get me as his buddy so he can help me hahaha

and there is a scholarship which I am applying for now

Hi @Dami

How far is Bonn from Heidelberg?

@Alessandro 235km according to google maps

lol

Hey is algebraist around atm ?

hey @Daminark are you around ?

Near chaos in the logistic map, the trajectories have became so unstable that it spills over to neightbouring equilibria, producing chaos

@ÍgjøgnumMeg hmmm, I could come say hi :P

@Alessandro that would be cool!

first conference of the people who spend too much time in mathchat

Hey @Alessandro and @Adeek!

hey

just have a simple question

And yeah that makes sense @ÍgjøgnumMeg

I am not algebraist type yet

so I am not sure why this is true

do you know why this is true @Daminark ?

@ÍgjøgnumMeg lol

What's your current definition of finitely generated?

I'll wait for a cool model theory talk to be held in Heidelberg and I'll use that an excuse to come and have a beer together

you live in Germany @AlessandroCodenotti ?

Sounds cool :)

@Adeek Not yet, but I'll move to Germany for my master in October

cool

what are you planning to work on ?

@Daminark I am not sure

Is it just finitely generated as an algebra? If so presumably the point is that you can just list a generating set, some are transcendental and others are algebraic

Set theory and related areas (model theory, logic etc.)

why not geometry ?

And if you have an algebraic element, it'll generate a finite extension, so if you have finitely many such elements, still gonna generate a finite extension

Lmao Adeek people are interested in different things, some folk just like subjects more than they do geometry

Yeah I was just kidding :d

@Daminark I see

:d

This is a new one

One of my favorite ones that I've discovered recently is this :V

@Daminark so the $\beta_i$ are the algebraic elements

@Adeek Geometry and Topology will be my secondary area (I have to pick more than one), but I think I'll do algebraic topology

geometry is for loser nerds

^

and the $\alpha_i$ are the algebraic ones ?

I looked at the analysis courses offered in Bonn but I don't like them :/

@Alessandro so no algebra/number theory?!

Well, the $\alpha_i$ are independent transcendental elements over $\mathbb{Q}$

you are uninvited from the heidelberg meeting

So basically you have an algorithm for doing that. You have a generating set. Let $\alpha_1$ be some transcendental guy over $\mathbb{Q}$, let $\alpha_2$ be transcendental over $\mathbb{Q}(\alpha_1)$, keep going

Since it's finitely generated that terminates at some $\alpha_T$

I see until you don't have any transcendental elements

and you run into algebraic

@ÍgjøgnumMeg algebra, number theory and logic are in the same area so the more courses I take in one of the three the less credits I have left for the others, but I can probably do one or two courses in algebraic geometry or something

Now, the rest of the guys are gonna be algebraic, not necessarily over $\mathbb{Q}$, but over $\mathbb{Q}(\alpha_1,\ldots,\alpha_T)$

@Alessandro Faaair, I'm actually really excited to do some alg. geo

okay I see

@ÍgjøgnumMeg alg.geom is cool

@Alessandro wait so there's a bound on how many classes you can take in one area?

@Daminark can you explain more about what finitely generated field extension means

so it is finitely generated as an algebra over $k$ ?

Yeah

@Adeek I hope so!

@ÍgjøgnumMeg which road are you planning to take for it ? Analytic or algebraic ?

are there any ANT regulars in this chat?

@Adeek Algebraic :)

A for analytic btw

@Daminark well you have a mandatory minimum number of credits in each of the three areas you pick, plus 30 credits for the thesis, so this is also an upper bound unless you want to do 12000 courses and graduate with more than 120 credits

Oh yeah AG seems fun, gonna take it this fall with a professor who's... quite something

@Daminark can you tell me more why we can write it in the other form

Which part is still hazy?

that is as polynomial in $Q(x_1,\ldots,x_T)$ mod out

Alternatively

part

Ah, well you can just think of one algebraic element

AG is usually thaught by Scholze in Bonn, this and the course notes available online scare me a bit

So if $\alpha$ is algebraic over $k$, then $k(\alpha)$ is isomorphic to $k[x]/(p)$ where $p$ is the minimal polynomial of $\alpha$

sure

So this is just doing this for a bunch of them simultaneously

oh alright

okkk

The $\beta_i$ are algebraic over $\mathbb{Q}(\alpha_1,\ldots,\alpha_n)$, so you induct

My geometry is getting really good but I do need to work a lot on my algebra skills

yeah I see @Daminark

That makes sense, yeah, probably helps to have both down to a degree. On the other side I should probably learn some geometry. At least AG, not knowing it made dealing with elliptic curves mildly tricky

why don't we just prove noether normalization

Because the proof is annoying

well it's important

Where else is the idea of the proof used?

"predicting" chaos = need less noisy data

(Basically I wonder whether the theorem is important in the way that Sard is important or not, extremely useful statement that gets applied everywhere the proof is a one-shot)

is Sard the one about critical value being nowhere dense?

or a null set?

Null set

brb

Is uniform convergence invariant under reparametrization?

Whoa @Secret is that the logistic map? Why does it look so fuzzy?

Here is an animated Lyapunov map

oO

@Rudi_Birnbaum no but yesterday we heard some so as I was getting surrounded by thunderstorms I had to turn back even though I was 5 minutes away from the goal and then for the next 2 hours we ran / slipped aaaall the way down and once there it turned out the bridge had been destroyed and we had to be rescued by the firefighters, it was a rough day

there was an article in the local news too but it's behind a paywall

I shouldn't have stopped at the lake

@mercio O..o Oh dear! Good to hear that you are doing fine, after all!!

my legs have been hurting all day

imagine climbing 1100 meters up and down and then being told "oh now you have to climb this hill and someone will be waiting for you on the other side"

How can I write sup with two sub indices as two rows?

@mercio oof

When will our @balarka return

I am not sure if that can be plotted without going fuzzy. If that can be done, it will definitely show the structure within the chaotic region more clearly