i really want to visit portugal at some point

Me too.

André told me many very exciting things about lisbon

You'll have lots of opportunities to go to conferences in Spain and Portugal, I'm sure. I just went to France :P

where in france?

Paris and Lyon.

@Daminark how is smartyboi

(For math, that is.)

oh nice :)

I hurt Demonark's feelings, Eric.

:(

Worse than telling him that his humor is humorless.

@Eric I like him quite a lot, though I will say he's very bad at giving psets

lol i agree with this assessment

The one he gave us this week was our first one in like, over 2 weeks

i love him as a human

It drives me nuts when talented lecturers totally blow teaching by not assigning regular homework or being available for office hours.

Not that I'm naming names ...

@EricSilva human-zoned?

I mean I like his lectures for the most part, he gets flubbed every now and then but then we get back on our feet, unlike when Soug fucks up and the rest of the class is lost

But yeah the week building up to the midterm he didn't give a pset on purpose, like yeah that's fair

I feel like a failure ... I never fucked up badly enough to waste more than a minute.

what has he covered

@TedShifrin there's always time

Nope. I'm done.

aww

So, Soug had already done stuff like Hahn-Banach, open mapping, etc so we just started off with weak/weak* topologies and Banach-Alaoglu, Krein-Milman, Eberlein-Smulyan

With some ergodic theory interspersed throughout

interesting

is eberlein smulyan the one about characterizing weak compactness

Then we switched to spectral theory, first for compact operators and then the functional calculus business so we could write a general symmetric operator as an integral wrt a projection-valued measure

that's good stuff imo

spectral theory is l i t

Eberlein-Smulyan says that the unit ball in a space is weakly compact iff it's weakly sequentially compact iff the space is reflexive

Hyo

so yes is the answer to my question

@AkivaWeinberger syup

As you have inferred, and yeah the spectral theory bit has been a whole lot of fun

@Akiva hai

my reading course was just spectral theory

basically

But yeah so now we're doing the Sobolev inequalities (we also showed it was equivalent to the isoperimetric inequality up to black boxing all the relevant geometric measure theory)

my fav

I just reread an old horror screenplay and it's still real good

what screenplay

After this we're gonna use it to talk about the wave equation, then do a bit of semigroup theory and Hille-Yosida which has something to do with the heat equation somehow, and if we have time, more ergodic theory

Deeper by Max Landis, I don't know if it's getting made but a draft got leaked a while ago

Guy descends to the ocean floor in a submersible

@Daminark evolution equations (heat, wave) are what semigroup theory and the like are allllllll about

What is there other than topology and algebra

I guess analysis is a thing

but that's kinda topology

not really

loluwotm8

Lol, I find that point-set topology has come up way more in analysis than in actual topology

OK, maybe I have it backwards

Analysis isn't topology, point-set topology is analysis

@Daminark in some sense htis is why point set exists

But like, if someone says "I'm a topologist", they probably mean algebraic/differential topology

And that has a different feel to it

when someone says they are a topologist, they usually mean they are a geometric topologist

I'm way too tired to think rationally at the moment

which is neither of those things

algebraic topologists say "hello im Peter May"

lol

Kek, he's the only one here (I mean I guess there's also Dylan and Akhil) that I know of tbf

Is there a subject which puts together analysis and algebra? Is that what Lie theory is?

Operator algebras are a thing

Hm yeah

I have no idea what those are

a lot of analysis uses algebra to lesser or greater degrees

very rarely is it anything uber advanced idt

research mathematics is not organized in a way to correspond to the names of courses in your undergraduate curriculum.

@AkivaWeinberger Study D-modules

See, there are two times when the name of a subject is absolutely useless in telling you what it's about

@PVAL-inactive i think there's a prof here who says "subjects exist but boundaries between them dont" which your comment reminds me of

One is when it's named after a person, one is when it's named after a goddamned variable

@AkivaWeinberger Well you know it's about D-modules

Right, so they're modules that we've decided to call D for some reason

D is for differential

^

that's not all D is for

could be Dirichlet

perhaps :P

but at least in this case

D is for dope

if you know what I mean

dope-modules

wink wink

I guess it's a little better than, like, "K theory" 'cause it's got the word "module"; K theory is just, uh, the study of Ks I guess

(I'm making an innuendo!)

Do you have any @EricSilva

The K on K-theory is for Klasse (German for Class as you'd expect)

Right, so these are differential modules. And modules are like vector spaces but shittier.

K is for GrothendiecK

That actually sounds cool though

@AkivaWeinberger Not shittier, just less structured.

K theory is a hip hop group

K is for Korean isn't it?

It is, I use their cover pic on discord :P

And then you've got J theory across the sea

@AkivaWeinberger "K-theory is like kpop but with theory instead of pop"

Yeah

Exactly

K-pop, on the other hand, we what we call K-soda in this part of the country

@PVAL-inactive is it actually

Oh I didn't even think of incorrect term for soda, pretend like I was saying "Pop" to mean dad

or K-coke in the south

@EricSilva no probably not

@EricSilva No, it's for Klasse which is class in German (Source: Rosenberg K-theory text)

but it is in K_0

apparently

mmk

Well that's true :P

For some reason do Carmo used $K^n$ to refer to a cube

For bocKs

Like was $K$ supposed to be an interval or something like that? What

well, cube starts with K

@XanderHenderson I lived in Texas for a few years and have heard this happen on occasion but like... 0_0

for kompact prolly

or kube

I mean, K is both silent and invisible

kubus

Coke is /way/ more specific than soda

I'm pretty sure they don't even use Ks in Portuguese

cubo

in portuguese

and compacta

Like if someone talks about sprite as coke they're making two mistakes. First is thinking about sprite, and second is calling it coke

arg!

when you get older all sodas will feel like mistakes

@AkivaWeinberger sometimes we do

mostly in loan words i guess

NEVER F'ING MIND!

@Daminark people actually call sprite coke?

yes

in some places coke is a generic term for soda

and Pepsi, too

yeah but not sprite!

sprite, 7up, ginger ale

yes

I mean I haven't heard people refer to it specifically as coke, but like

all coke

i have heard it

Some people might say hey can I have some coke?

In Atlanta I'm pretty sure referring to drinks other than Coke is a crime

coke = pepsi, sprite = 7up = ginger ale = ...

And someone's like sure do you want Pepsi, Sprite, etc?

these are two equivalence classes

Thinking about drinks other than Coke is a thoughtcrime

@Daminark wot if you want cocaine

@0celo7 people will use coke or cola for any of these

Er, Colombian snow

Lol it has been some time since I've had soda since my first year and a half I was ridiculously unhealthy and I sorta want to at least begin to deal with that

@EricSilva I've lived in America for a while and can't say I've heard anyone actually do that

If I asked for ginger ale and recieved a sprite, I'd be in prison.

But Pepsi is the best, followed by Coke, followed by whatever nonsense other types of soda there are

@0celo7 It's a South thing

I live in the South!!!!

i have heard people do it but not in a restaurant where youre asking a server for one

Where do you live?

Tennessee

Arright

I've never been to the South

@0celo7 If someone asked me for cocaine I'd probably back away slowly... and then much more quickly

ive been over friends places and heard them ask for a coke and get handed fuckin orange soda

Tennessee isn't really the south

Georgia and Mississippi, on the other hand

ESSPECIALLY Georgia

and just not bat an eye

Alabama is the true south

we should ask Dr. Shifrin, when he shows up again

oh, yes! Alabama!

@Daminark do u have any idea how many people here do cocaine

that, too

I've never been south of DC

it's a lot

@EricSilva if that happened to me... I wouldn't go to prison like PVAL since tbh I'd have a good enough case to be acquitted

@AkivaWeinberger havent u been to argentina

@AkivaWeinberger my parents are in DC

Self-defense or something like that

Well I mean I've been to Argentina

which is the south according to some metrics

Argentina isn't the south

GOD DAMN Yyes I have @EricSilva

Texas is its own thing I think.

get rekt @Akiva

I lived in Texas too

can we please give Texas back to Mexico?

i sniped u on your own life

or, like, let them have their independence or something?

I don't remember what people said there

@XanderHenderson what did texas do to you

I did do some horse riding in Argentina though

@0celo7 George Bush Sr

George Bush Jr

I don't think the USA wants to give up that many natural resources.

The Dallas Cowboys

(I don't even like concussion ball, and I can't fucking stand the Cowboys)

The Dallas Cowboys are a blessing to the rest of America

@Daminark tbh i was super shook when its happened

Because the other teams get to not be last place

best bush

the god-awful high school concussion ball culture

What sport do they play

No idea

But I know they're supposed to be utter garbage at that sport

sportball

Tex-Mex food

Oh, football

by Xander's description

Are you actually serious

@Daminark

hello fellow humans, are we going to the sport game?

The one that doesn't involve feet and only sort of involves a ball

I remember I was walking with a friend once and we saw a shirt that said "Win, tie, or lose, I will always support the Cowboys" and he was like "Yeah we should retitle it "Lose, lose, or lose""

That one

I sure do hope that the home team wins!

@0celo7 I do not give one about competitive sportsball

@AkivaWeinberger you kick the ball like 10 times in the game

The only sport I care about is HvZ

that's not a sport it's a larp

OK so you only sort of use feet and it's only sort of a ball

I used to fence, but then my knees died :\

@Daminark I don't "care" either but I know which sport the Cowboys play

Now, basketball teams...yeesh

mimes placing a fence

No clue

Our head coach probably makes more than the entire mathematics faculty

@PVAL-inactive Ours got paid 6 mil to leave

I still don't quite know all the rules to baseball, despite technically having played in several times in gym class

ours got paid way more than that

@EricSilva Take that back right now or I will get you with my nerf gun

go for it my man

@PVAL-inactive Big 10?

l a r p

HvZ?

…Humans versus Zombies?

nerds vs mondo nerdz

@AkivaWeinberger There are a lot of technical rules in baseball

I actually really, really like the game, but more as a quantitative exercise than anything else

Yeah it's humans versus zombies

I honestly never have as much fun as I do in this game

and, perhaps, as an excuse to get drunk in public with friends

are you a human or a zombie rn

$10.4 million

Zombies Are Were People Too

apparently

Reno had a really fun AAA team, and a great stadium

Still human, got all the points possible so far

@PVAL-inactive If your school is like mine, the athletics department had to fork that over from ticket sales and donations

@AkivaWeinberger hot take the zombies are the people and the people were the zombies all along

Here, they don't get any school funding

I'm a zombie right now, I'm staring at my phone and not moving

@Daminark they should add a third faction

(not moving anything other than my thumbs, which are typing)

That's good, tbh I don't believe in these sorts of things getting school funding, that should be focused on academic and research business

@EricSilva Plants!

perfect

@EricSilva Nonono! The People are zombies, the zombies are soylent green, and soylent green is PEOPLE!

Plants vs zombies, humans vs zombies... What about humans vs plants?

lol

Looks to the rainforests

The people are leading! The people are rioting!

@Daminark i guess the humans are winning and its sad

i guess even if we win we lose

@Daminark It's called PvE

:thonk:

If we win human vs plants, we die, if we lose, we also die

That's what global warming is, really

@EricSilva I have a question for you

global warming is: No matter who or what you are, you will be roasted

@EricSilva If $u\in W^{1,p}_0$, is $u^+\in W^{1,p}_0$? No hypothesis on the boundary.

Global Warming is the true meaning of "PvE"

it is, the common enemy of all earth existence

and once again, something big is expected to happen in 2020 (US election besides)

Hm, there's PvP, there's PvE… Is there EvE?

Nature documentaries

@AkivaWeinberger pve is also eve i guess

> When a skeleton's arrow hits another hostile mob (with the exception of creepers and with the aid of a player to distract the skeleton), the other mob will attack the skeleton, and neither mob will attack a player until one of

EvE

Ah yeah

That's how you get disks

I used to make this weird trap involving pistons to make it easier

and then I stopped playing Minecraft

@0celo7 hmm

@Secret To be clear, I was using E for environment, not enemy

Player versus environment

Ah I see

@EricSilva I think the key is to show that if $u_k\in C^\infty_c$ such that $\lim u_k=u$, then $\lim u_k^+=u^+$. Then surely $u_k^+$ can be approximated by $C^\infty_c$ functions.

I had an argument but then I realized the operator $u\mapsto u^+$ is not linear.

im sure you can do this

I'm sure too, but I'm currently in a hell of obvious things I can't prove :(

I guess $u^{+} = \frac{|u| + u}{2}$

@EricSilva Maybe one needs to reprove an analogue of lemma 7.5 in GT

Okay, I'm blanking on a good fourth question for a test. So far I've got (a) prove that angle of parallelism increases with decreasing distance in hyperbolic geom; (b) prove whether the summit or base is longer in a Khayyam (Saccheri) quadrilateral; (c) does the Pythagoran Theorem hold in elliptic geometry, explain your reasoning; and (d)...?

Would prefer something elliptic to hyperbolic, to balance. These are high-schoolers, and they've got 45 minutes.

The division algorithm says if $a,b$ are integers and $b$ nonzero then there exist unique $q,r$ such that $a=qb+r$ and $0\le r<|b|$. I can't find $q,r$ when $a=5,b=7$

you want to use the larger of the two on the LHS @Silent

at least for this formulation of the algorithm

@Silent (0, 5) isn't working for you?

hmm!

thank you

I suppose the alternative is the trivial factorization

hi @MatheinBoulomenos

hi

what are you doing up haha

dunno, can't sleep

I know the feeling

Last night I was repeatedly dreaming of some curve thing then waking up LOL

Oh I had a dream recently and when I woke up my first thought was "damn, I confused hereditary and semi-hereditary rings in that dream, that was useless"

LOL

I need to finish writing some notes for the classes tomorrow

just finished the "ring theory" notes

Hello, I need some help showing that (3n choose 2n) is less than 7^n.

I'm trying to prove through induction, but I'm stuck at (3(n+1) choose 2(n+1))

I can't think of any good ways to handle it.

@Antonios-AlexandrosRobotis nice, what are they about?

they have a midterm next week

so its just solutions for their practice test

I see

which is just proving irreducibility of polynomials PID UFD, Euclid. Domain stuff

I find this material a bit dry, honestly, but oh well

yeah, that was the ring theory stuff which we did as part of our LA course or in the "algebra 1" course. Ring theory really got serious in the "algebra 2" course

what did you guys do in the LA course

well, we proved the implications Euclidean => PID => UFD and Noetherian and we proved the structure theorem for f.g. modules over a PID

oh nice

and did some stuff on domains, like gcds and lcms etc.

that gave a really nice theortical approach to minimal polynomials and canonical forms

we had exercises like "Prove that in a domain $R$ $\operatorname{lcm}(a,b)$ exists iff $\gcd(ra,rb)$ exists for all $r \in R$" or "Prove that $\Bbb{Z}[\sqrt{2}]$ is a Euclidean domain"

was that a first year course?

yeah

students often don't get to that here until grad school it seems

in the exam we just had to do some random commutative algebra stuff

among other things

I think it was something like we were given definition of localization (we had seen fraction fields) for an integral domain and we had to figure out the correspondence between prime ideals in $S^{-1}R$ and prime ideals in $R$ which don't meet $S$

lol nice, what year are you now?

third year right now

interested in PhD in de?

I want to do my masters in Germany for sure

as for PhD I have to see then

1 or 2 year masters?

We only have 2 year masters

gotcha

w/ thesis I imagine?

but many people need 3 years if they have an ambitious master thesis

yeah, everything is with thesis here, bachelor and masters

I wish I had done a thesis during undergrad

would have been nice

what will you do undergrad thesis on?

Galois representations attached to cuspidal Hecke eigenforms

one of my friends knows a good bit about galois reps

I mean to learn about them this summer

I haven't learned that much myself

I'm going to take a course on modular forms next semester

oh cool!

and one on more algebraic number theory

and I think it makes more sense to try to read up on Galois reps after that

I'd like to properly learn some algebraic NT soon, but we'll see. I have enough on my plate :p

I think I might maybe to try go somewhere else for a PhD, dunno. Being a PhD student here in Germany is very different. You don't have classes other than research seminars and conferences or a lot of others who are on the same level than you, you just start working in a research group and write your thesis while you do so

We have maybe 2 or 3 actual "grad schools" which are more like in america probably, but that's how it is at most schools

yeah it's a bit different here, though it seems to depend heavily on the university

Also, if I'd manage to get in somewhere prestigious, that could help with the career in Germany even. One of my profs went to Princeton for his PhD and then came back to Germany

yeah there are definitely some big name schools in the US

one of my friends recently got in to princeton

@nitsua60 derive the angle defect = area formula for spherical triangles?

time for me to sleep

night

night! @Antonios

Wondering about something in statistics: So, correlations of X to Y are common plots which is useful to see whether two variables X or Y in some data set are proportional or inversely proportional, but is it make sense to talk about a correlation plot of X,Y to Z, thus showing how Z depends as a function of X,Y in terms of +ve or -ve correlation, or it is much better to do this separately in pairs?

[Random]

In my PhD data stuff, I use the ordering a < b to mean 'b is more negative than a" since we are more interested in how much more stable something is

and I have to add those footnote to ensure nobody gets confused

you could use |a| < |b|

good point

uh wait, actually no, because we do have positive values, and we are really talking about stuff is more stable when more negative

so our ordering is literally the reverse of what < used to mean

[Random]

Scatter plots, even if there are no correlations, sometimes the distribution of data points are localised, that is itself also a useful trend

I need a clarification: every permutation can be written as product of disjoint cycles; and; every permutation can be written as product of transpositions; but there exist permutations such that they can't be written as product of disjoint transpositions, otherwise every permutation would be of order 2. Am i right?

a permutation is a product of disjoint transpositions iff it is of order 1 or 2

Evening.

@Secret thank u

It works

ok now to go back to business...