I will be content if suffering leads to mild amusement

I have no expectation I'm just here to memorize the Math symbols and how you guys are using them :). I am very much a noob.

@BalarkaSen I don't actually remember how that computation goes

Oh, maybe Serre

Yeah, using local coefficients

The action of $\Bbb Z_2$ on $\Bbb Z_3$ translates to the action of base on fiber

So the $E^2$-page is $H^p(\Bbb Z_2, H^q K(\Bbb Z_3, 1))$ where $H^q K(\Bbb Z_3, 1)$ is the $\Bbb Z_2$-module described by this action. In dimension $0$, just standard cohomology of $\Bbb Z_2$. In odd dimensions, $H^p(\Bbb Z_2, \Bbb Z_3)$, where $\Bbb Z_3$ is with this action making it a $\Bbb Z_2$-module. In even dimensions, zero.

I am taking BZ/3 -> BS_3 -> BZ/2: is that going to be problematic?

Boo a @Balarka @MikeM

spooked

Is it weird that I'm here too?

Oh no. @CaptainAmerica is here.

Hi @Ted

Hehe

Hi, demonic @Alessandro

Hi @Ted @Alessandro

Hi @Mathei

Hi @Mathein

Can we use the dominated convergence theorem for $L^p$ functions?

I've been making really big truth tables today.

yes

Really? The theorem only mentions $L^1$ functions.

The one I just did was for this: $(P \wedge R) \lor \lnot(Q \wedge S)$

Saying $f$ is in $L^p$ is the same as saying $|f|^p$ is in $L^1$, so

You get convergence in the $\|\cdot\|_1$ norm, but you can apply it to functions in $L^p$ or over any other measure space

Depends how you're going to state/apply it, I think, @LogarithmicDerivative.

Yuck @CaptainAmerica

>:C

I am having a hard time understanding Vizing's theorem. Wikipedia states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than the maximum degree Δ of the graph. If I am looking at an undirected graph and determining if it is bipartite wouldn't I just need 2 colors no matter the max digree of the graph?

@Ted See my question to Tobias above

Why yuck

Do math papers mostly have one reviewer

@Rick Sure, the theorem doesn't always give you the smallest number of colours

@LogarithmicDerivative The general version is that $f_n$ can be any measurable functions over $(X,\mathcal A,\mu)$ and $g$ is in $L^1$ of that measure space

Yeah, @MikeM. Most. They have enough trouble finding reviewers as it is.

@AlessandroCodenotti: Is the conclusion then "Then $f\in L^p$ and $\|f_n-f\|_p\to0$"?

Are there any theorems that will

Oh! I found it further down on Wikipedia.

@Rick Not without involving much more information about the graph itself

what are some exceptions?

things like annals?

@LogarithmicDerivative I think you need $g\in L^p$ too if you want to get convergence in $L^p$

I actually am sufficiently far removed from this, Mike, that I don't know.

hey chat

is there anyone familiar with the sylvester decomposition of a binary form?

sure, don't worry about it

vaguely curious was all

I'm sure you can ask most faculty at your institution and they'll know, Mike.

i suspect so

But that requires talking with people in real life

@BalarkaSen No, it seems ok to me, I don't know why I got paranoid

well, I know the number of vertices and all their connected vertices. But it's undirected.

I think my action of $\Bbb Z_2$ on $H^*(K(\Bbb Z_3, 1))$ is not correct

You have made an error in your calculation of that cohomology group I think

Remember the coefficients

@Alessandro: Mike knows how to talk to people.

If $H$ and $K$ are open subgroups of a topological group $G$, is $HK$ open?

Walk up to them and press A

yes

@Mathein That's a union of translates of H, no?

@MatheinBoulomenos Isn't that $\bigcup hK$?

$G \times G \to G \times G$ given by $(g,h) \mapsto (g,gh)$ is a homeomorphism, and then the projection to the second factor is an open map because projections always are

now stick $H \times K$ in there

thanks

Don't say anything Balarka...

fine or you can do it by hand like a normal person

Sniped y'all

Say $\Bbb Z_3 = \{1, x, x^2\}$. The action of $\Bbb Z_2$ on $H^1(K(\Bbb Z_3, 1); \Bbb Z) \cong \Bbb Z_3$ is by switching $x$ and $x^2$.

Stop

Actually do you even need both of them to be open?

Stop stop stop

What are the coefficients

<--- runs away

I'm a garbage person

$H^1(K(\Bbb Z_3, 1); \Bbb Z)$ is zero

So I found that the only graphs that can be 1 colored are edgeless graphs. So to look for a graph with edges, you would only ever need two colors.

@BalarkaSen Those are not the coefficients we have been talking about

@AlessandroCodenotti Right, just one needs to be open, and neither needs to be a subgroup.

We are trying to understand how $H^*(G;\Bbb F_p)$ relates to the cohomology of a p-Sylow

@MikeMiller I am using the spectral sequence of $K(\Bbb Z_3, 1) \to K(S_3, 1) \to K(\Bbb Z_2, 1)$. First I want to identify the action of the base on the cohomology of the fiber (both with $\Bbb Z$ coefficients) properly.

We want the answer with $\Bbb F_2$ coefficients so that seems unwise

Hmm, I see. You're right.

I am way ahead of myself. I have to put a whole day's effort into this.

I should sleep

I am also not in the right place to do this math seriously right now

Only to post Kyle Hyde gifs

@Rick If you're saying that any graph with edges is $2$-colorable,then that's wrong

@MikeMiller what would a quantum topology class by a knot theorist entail?

I find it kinda strange that there are no homeomorphic copies of $S^n$ lying in $\mathbb{R}^n$

ask the knot theorist who is teaching the quantum topology class

i am neither

I know...

@Perturbative: How can you find that surprising? How can you fit the circle into $\Bbb R$?

@Perturbative no, I am saying if you are only looking if an edge exists you only need two colors

@Zee My guess would be something to do with quantum invariants of knots and $3$-manifolds

Ohh whoops for some reason I was thinking of $S^{n-1}$ @TedShifrin

Sorry

Well, then there are tons of 'em, @Perturb!!

@TobiasKildetoft that was my guess too, thx

"Hmm, what would this very complicated mathematics class by a very complicated mathematician entail, I wonder? Does anyone know the answer? Seems hard"

Gives answer

"That was actually exactly my guess"

Yeah I made a huge error @TedShifrin

@BalarkaSen Idk what your saying . I didn’t even say half of this stuff

just pullin thy leg

@MikeMiller I had a question......

.....

Good luck

It's not exactly math.

Wow then I know even less

Oh god

Heh

statement of purpose/letter of intent for Ph.D.: should it be basically about my research interests and why I'd be a good pick, not why I love math?

I am getting mixed signals. So I need yet another mixed signal.

So far it seems to be biased towards talking about research interests and why you are a good pick ("i have done research")

@anakhro "I enjoy both math and not starving so please take me. No seriously, do take me"

That balogna probably doesn't matter very much

Heh

I wrote something about how I like number theory, what my background was, and how I wanted to work with professors X Y and Z because I liked their work on W

I got into one school out of twelve

And I don't remember the rest of the statement

Wait but you're not doing number theory

@anakhro Look through academia.stackexchange.com where this has been asked several times. There are a couple of math professors who are quite active there and will have provided good answers to this

@AlessandroCodenotti Quite true

Yeah I was looking for Mike in particular.

I can try to find the statement but I'm not sure how much luck I will have

So how did you end up doing topology?

It's fine, I just wanted to know your thoughts.

Found an early draft

Let me find your emailk

how much do they give a math PHD candidate to live on?

2 loaves and a fish.

@Rick Who are "they"?

@anakhro just tell me when you're here and I'll post the link then delete.

@MikeMiller I am here, or I can send you an email

they being your average University. what kind of fish because if it's salmon sounds like a good deal

si

that's an early draft, much was changed and I have some emails from people suggesting reorderings etc.

but it might help for context, since broadstrokes didn't change.

Ah, I see. Thanks!

@AlessandroCodenotti "And you may find yourself / in another part of math / and you may find yourself / doing instanton homology / and you may find yourself / behind the cover of Krohneimer-Mrowka / and you may ask yourself / How did I get here???" - Mike

sure

@Rick there is not really any useful such thing as an "average university"

Ok lets just say UCLA

somewhere on the order of 23-26k/yr (in a city with a relatively high cost of living)

O, wow. but you get subsidised housing

no

the graduate housing is actually unduly expensive and i intentionally moved out early on.

I didn't even know places offered graduate housing.

23-26 in westwood is like renting out a box next to a trash can

yep

i guess you're a ugrad here

i moved to around pico/robertson

I was, graduated in 2008

aha, i see

in general UCLA math is on the slightly better side of things

math phd programs are an opportunity cost. you are taking a monetary hit and accepting a more difficult time w/ expenses than you otherwise would

with the implicit understanding that a phd gives you opportunities on the job market that you wouldn't have without it

well, you def will have opportunities, silicon valley is sucking you guys up.

sure, and wall street. those are the two most common exits

up to the individual whether either/each of those are good for them

ugh, Wall Street / finance

But actually @Mike (and all the other people doing or already with a phd), at which point did you know what field you wanted to work in? How did you choose?

you would probably dude just as well without a phd, a masters would suffice.

I magine there are versions of a finance career where you get to keep your soul, but they seem like the exception

@AlessandroCodenotti I knew I wanted to do some sort of algebra since the first course I took in algebra back in my first year of university. The precise topic I ended up in was determined more by who I ended up with as advisor than anything else

@AlessandroCodenotti By the time I made it to grad school I had already moved away from number theory since I really enjoyed the algebraic topology class I took

no they all take your soul. one group are just hipsters and the others are your traditional oligarchs

I was at that point going to either do topology or algebraic geometry

Lol. I’m just covering my bases: whether there exist ethical jobs in finance is a very different question than their typicality

And Ciprian offered a class called "the equations of gauge theory" when I was in my second year

That's when he got me.

I see

I think ultimately I really wanted to study diophantine equations and nobody at UCLA did stuff like rational points on varieties

Everything was too Lamglands

I can’t rule out the former, but the latter seems self-evident

I already have an idea of the general area I'd like to get in, but nothing too specific

Let's not pretend there are many ways to keep your soul

@loch And i think that AG is the really hard one

I’d say “work in the public sector” but I’m not that naive

(I mean, it depends what state you work in)

geom rep theory and arith. geom people have to know AG too - but they have to know rep theory / NT equally well - so it's like double the work!

Is geometric representation theory either geometric or representation theory

That seem to be pretty big here in Bonn. It's definitely not my cup of tea though

@loch "my undergrad place was pretty good at algebraic geometry" says nobody ever

That's pretty cool

I was just being mean

@LeakyNun the faculty is definitely strong in alg.geom!

What is a langlands dual

Something about eoot syatems ?

oh no perverse sheaves

hides

yeah i think you just consider the dual root system

Don't worry, @BalarkaSen, they're neither perverse nor sheaves

Kinky.

@Alessandro hasn't it already been established that you'll be doing ergodic theory?

Alessandro will do chaos theory over spectrum of a ring

That'll eventually settle the Collatz conjecture and yield him a Fields medal

chaotic spectral theory

He will prove the Birkhoff ergodic theorem over $\text{Spec} \, \Bbb Z$ using mixed motives

are you guys talking about perverse sheaves

No

go away

>"My experience with these lectures suggests that motives are like onions; they are complicated, multi-layered objects, and any attempt to cut too quickly to the heart of the matter can leave the audience in tears."

- Spencer Bloch

ive got some derived categories here if you want em, 40 dollars

Bloch always writes weird shit

What else has he written?

btw I realised today that most of the stuff by "Cartan" that I thought was modern and hip was by the father. I also realised I had thought "Elie" was the son and "Henri" the father, but it was the other way around

@Daminark Apparently there is a thing called the logic action which is an action of a permutation group on the set of models of a theory (thought of as a topological space) which allows to use tools from descriptive set theory, so maybe one can fit a bit of ergodic theory in there too with a big enough hammer

@LogarithmicDerivative I can't remember the article

But it was definitely creepy

Are you talking about the one where he said the math was sexy?

@BalarkaSen: Yikes. I couldn't find much on Google.

Because that wasn't that creepy.

Found it

projecteuclid.org/download/pdf_1/euclid.bams/1183548011

@anakhro nooooot the precise wording

He is weird.

Can someone help me with this? I'm dealing with truncated functions.

I don't see why we get $k^{p-q}$.

This is the definition of a truncated function. We just have $k$ instead of $n$ and $f$ instead of $r$.

@MikeMiller any book suggestions lately? Geometry or topology.

i haven't read any books in a long time

of any kind

Oh no.

@MikeMiller gotta get on that audible my friend

need to finish writing and then do whatever i want tbh

audiobooks are great

I have been listening to lots of radio realizations lately

What are the seminal papers in geometry? @BalarkaSen maybe you know of a few?

I know of a few for symplectic geometry.

Gromov, "Hyperbolic Groups"

@BalarkaSen may want to look at stronger conditions like abnormality if you're looking for more infinite examples

Gromov, "Partial Differential Relations"

Gromov - I am sorry

Gromov, "

Let's find a different author

Heh

Oddly enough, the paper I had in mind for symplectic geometry was also Gromov. :P

@Alexander Hmm, OK

I will think about it for infinite groups

Thurston-Eliashberg's Confoliations is probably good for you

Well yeah, I have read it.

Oh nice dude

Teach me

Heh

Not right now though, it's 3:30 AM. Definitely teach me at some point!

I will teach you when I think of something I find cool to teach you.

Confoliations is cool!

I want to understand it

I want to understand it, too.

We can understand it togather then

When it comes to the algebraic topology stuff it starts slipping away from me.

What is the best way to learn algebraic topology?

In your opinion, of course, @BalarkaSen

I've seen homology theories, the first fundamental group, covering spaces, deck transformations, etc.

But it's just a bunch of concepts to me.

And not something I feel like I have learned right.

@BalarkaSen do you want to hear a joke?

@anakhro I think the best way to learn something is to start seeing (and doing) applications

I just powered through exercises in Hatcher and answered a lot of question in MSE and I think that made is stronger.

-best +only

But eg I am weak at cohomology theory (computing the ring structure, etc etc) because I haven't actually used it much

So flail with exercises a bit and then call it a day?