point-set-topology

[honest narwhal]

I was checking [REDACTED] and noticed someone got in there

[rugged swan]

lol

[honest narwhal]

And I'm like

[tough imp]

Love it that Shamrock says "very long shot"

[honest narwhal]

How tf do I not have a Rutgers acceptance yet?

[tough imp]

have you no faith in me?

[rugged swan]

cursed story

[honest narwhal]

I should've gotten in there day 1 after applying\

[cedar pebble]

I have faith in Chmonkey

[honest narwhal]

So I email them like yo I heard people are getting answers what's up on my end?

[tough imp]

[honest narwhal]

And they're like yeah we only sent a few, you're in line to get in but

[sleek thicket]

I do not have faith in chmonkey

That's why I was telling others to send good vibes

[honest narwhal]

Your GPA is 3.5ish and we don't have your transcript so we don't know what your math GPA is

[sleek thicket]

Because I can't

[honest narwhal]

So you're in line but not top of the top, send us your transcript and we'll waitlist since you expressed interest, expect an answer in April

[tough imp]

Wow

thanks Shamrock

[sleek thicket]

[honest narwhal]

But yeah the day after the tragedy of my grad apps I emailed the 4 schools being like yoooo whaddup

Duke it was too late for, Wisconsin ended up taking me, and I pulled out of Penn and Minnesota because lol

But yeah January 28th is when I found that out, February 6th is when I got Notre Dame

[cedar pebble]

And you seem reasonably happy at Wisconsin so you won in the end

(as happy as one can be during this shit show of a time to go to grad school lmfaooo)

[honest narwhal]

Yeah Wisconsin's p good for sure

[frigid patrol]

Wiw

Wow

[honest narwhal]

Lol yeah, at least I def am not upset in any way that could likely be resolved by being at another grad school

[frigid patrol]

Wow

How did you fuck up that badly Dami XD

[cedar pebble]

I'm pretty happy with where I ended up too

[honest narwhal]

I mean def there are some places that would've been a better fit, Michigan likely, tbh not UCLA

[cedar pebble]

would have liked the higher stipend from Duke though

[honest narwhal]

Stanford/MIT would've been coo

Harvard/Chicago have the name but if I'm being honest with myself in a way neither would be a great choice

Harvard because not too many home run advisor choices (Gaitsgory's a dick, Lurie left, Gross/Mazur retired, Harris works on nerd shit, etc)

Chicago because it's prob not a good idea generically to stay at the same place for undergrad/grad

[cedar pebble]

Harris works on nerd shit

hahahaha

hey I know a Harris student she's quite happy

[honest narwhal]

Lmao yeah I'm sure he's solid just that like

[cedar pebble]

very classical AG though

[honest narwhal]

Idk when I hear the phrase birational geometry I wanna give someone a wedgie

Maybe a birational wedgie

[cedar pebble]

I declined to take the birational AG course offered this semester from like, one of the top birational people out there

I mean there was an unavoidable time conflict

but more importantly

if you miss like

ONE (1) class

you're basically dead to him from that point forward

😰

[sleek thicket]

oof

[honest narwhal]

I mean you had perfect attendance last semester right?

[cedar pebble]

[honest narwhal]

Idk if that info is public lol but yeah

[cedar pebble]

nah I've definitely posted about it on twitter

[honest narwhal]

Tru

[cedar pebble]

also not horribly embarrassed about it, it is what it is

[honest narwhal]

Oh no I meant like

The fact that your guy is as litt as he is

[cedar pebble]

😛

I'm pretty sure most people know who I am at this point, for better or for worse

(a lot for the worse aaa)

[honest narwhal]

Fair fair, after AGS doxxing no longer exists

Nobody can dox you if you preemptively dox yourself

[cedar pebble]

yea this birational prof I'm good friends with his single student

[honest narwhal]

It's foolproof

[cedar pebble]

I left the office really late one night

and ran into his student in the elevator

who just got out of a 5 hour advisor meeting

[honest narwhal]

Dayum

[cedar pebble]

he was all sweaty

and he goes

"I'm going to get drunk :("

[sleek thicket]

😬

[honest narwhal]

That's exhausting but also wow having an advisor who is down to meet that much is probably good

Simon met with me so much the week of the NSF to help figure out my research statement

[cedar pebble]

yea I mean I scheduled a meeting with that professor once and it ended up being 3 hours

it was a lot

he asked me if I read such and such a book on toric geometry and I said no and he looked at me like I was a moron

[honest narwhal]

3 or 4 extra hours on top of our weekly meeting and the reading group he organized

[cedar pebble]

really nice guy lol

[honest narwhal]

Lmao

I don't think I know too many such characters here offhand?

[cedar pebble]

he's kinda infamous here

[honest narwhal]

I wish we had a Benson but so it goes

[cedar pebble]

I mean he has a LOT of clout so people kinda put up with him

[honest narwhal]

"Oh my God you're so dense I could literally define a rational map on you"

[cedar pebble]

Daniel has less clout so people put up with him less

[honest narwhal]

Is he the type of person that requires being put up with?

[cedar pebble]

sometimes yea lol

[obtuse meteor]

how did #point-set-topology transform into #grad-school

[cedar pebble]

yea I have no idea

(should we move?)

[obtuse meteor]

no i'm just messing

[cedar pebble]

😛

less interruptions than the other channels

he always asks a million good questions during seminars, sometimes in a way that's a little

[coral pawn]

What server is that?

[honest narwhal]

So what do you guys think about char classes?

[cedar pebble]

speaker introduces definition
Daniel has already though of some very specific question about a very nontrivial example within the next minute

[obtuse meteor]

we do not mention the forbidden name

[honest narwhal]

It's dead now and for good reason

[frigid patrol]

👁️

[cedar pebble]

yea anyways that's a bit of drama I would like to avoid

[chrome dew]

are you like a born again christian

[coral pawn]

Is it like a discord server?

[sleek thicket]

Did you know that S^1 acts on all odd dimensional spheres?

Embedding an odd dim sphere in C^n

[sleek thicket]

And multiplying S^1 with C^n by thinking of points on the circle as complex numbers

anyways, if you consider the action of the circle on S^3

[obtuse meteor]

big nozoomi

[sleek thicket]

you obtain a quotient map S^3 -> S^3/S^1

[cedar pebble]

BIG nozomi

[sleek thicket]

And one can show S^3/S^1 ≈ S^2

[frigid patrol]

unit sphere in C^n is S^2n-1 ?

[sleek thicket]

Contemplating this group action reveals the server

[cedar pebble]

I mean anyone can DM me and I can tell them what the deal is 😛

[obtuse meteor]

Negi moment

[sleek thicket]

idk why you need dms I just told them what the server was

[cedar pebble]

my association with that place is not something I'm proud of but it is whatever aaa

[honest narwhal]

Lol

[obtuse meteor]

I don't have a born again emote

then again I was also associated at one point

[sleek thicket]

[honest narwhal]

Good lol

It was... Toxic

[tacit stratus]

this is a surprising amount of tea for a math discord server

[honest narwhal]

Higher level math mostly yeah. Anyway I won't discuss much more now

So what's your favorite homotopy group?

[cedar pebble]

Was it like this server minus middle schoolers
in mathematical content yes, in moral character no

[sleek thicket]

My favorite homotopy group is probably π1(S^1)

Just a really cool thing to learn for the first time

[tough imp]

The server was called Da Jungle

Oh wait that’s my server

[sleek thicket]

Toxic

[honest narwhal]

Just the n=1 case of Hopf degree theorem right?

[tough imp]

Hahaha I forgot about that

23 notifications

The toxic one here is you Sham

[tacit stratus]

i like the homotopy groups of the infinite symmetric product

[sleek thicket]

Oh that was the person with the dog pfp

Explaining dold kan

And monoid stuff

[honest narwhal]

Actually I saw Hopf degree theorem before the ordinary covering spaces proof of pi_1(S^1)

[sleek thicket]

It's just one dm

[tough imp]

Oh

Dami moment

[honest narwhal]

Since I took difftop first lol

[tough imp]

If there were two guys on S^1 and one killed the other with a rock would that be fucked up or what?

[sleek thicket]

How do you do it with diff top?

[frigid patrol]

Dami moment

[sleek thicket]

Oh nvm I see

You can choose a smooth map homotopic to it

[honest narwhal]

Yup smooth approximation is based

[sleek thicket]

To prove degree classifies homotopy class

That's cool

This is how my class did it [with degrees], it just developed degree theory on S^1 along with covering spaces

So I was like

"aren't those the same proof?"

[honest narwhal]

Yeah, there are proofs of Hopf degree that don't go through smooth stuff

I don't remember the deets of the smooth proof tbh

It's been quite a long time

[sleek thicket]

Does anyone want to sanity check some category memery for me?

it's about vector bundles and thus is geometry

[honest narwhal]

I probably don't know this but take a shot

[sleek thicket]

Fix a topological space $X$

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

define $\mathscr{C}$ to be the sub-2-category of $\mathsf{Cat}$ whose objects are the categories of finite dimensional real and complex vector spaces

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

and whose $1$-morphisms are all the functors $F$ such that the induced map $\mathsf{Hom}(V, W) \to \mathsf{Hom}(F(V), F(W))$ is continuous for any $V, W$

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

this makes sense since hom sets in the category of finite dimensional R vector spaces/C vector spaces are themselves finite dimensional vector spaces, and thus have a natural topology

and whose $2$-morphisms are all possible natural transformations between two functors of this kind

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

let $\mathscr{D}$ be the sub-2-category of $\mathsf{Cat}$ whose objects are ${\mathsf{Bun}\C^X, \mathsf{Bun}\R^X}$, where we include all possible functors and natural transformations

does that all make sense?

[gentle osprey]

shamroc$\overline{k}$

[cedar pebble]

Bun^X_C and Bun^X_R are the categories of complex and real vector bundles on X respectively?

[sleek thicket]

yup, sorry

[cedar pebble]

cool cool I'm following

[honest narwhal]

"The full-sub-2-category" how many hyphens will it go?

[sleek thicket]

lol

there's a so there's a way of turning continuous functors (in the sense above, not in the sense of preserving limits) between these categories of finite dimensional vector spaces into functors between the corresponding categories of bundles

you just apply it on fibers

if you have a system of trivializations of $E$ and these have transition functions $\tau_{\alpha\beta} : U_{\alpha} \cap U_{\beta} \to GL(V)$, we can compose with the map $GL(V) \to GL(F(V))$ to get new transition functions

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

does that make sense?

[honest narwhal]

I buy it

How does this play with the 2-categorical business?

[cedar pebble]

Yea, you're applying F fiber-wise and gluing?

hmm let's see

[sleek thicket]

Pretty much, yeah

functorality means the cocylce condition is preserved

is a way to think about it

I think

[cedar pebble]

Yes!

[sleek thicket]

I *think* this should be a (weak) 2-functor $\mathscr{C} \to \mathscr{D}$ (weak in that it's only associative up to 2-cells)

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

does that seems plausible?

[honest narwhal]

Not sure if that was well-stated but basically does anything funky happen with natural transformations?

[sleek thicket]

and like, does all of this make sense?

well that's my question lol

[cedar pebble]

Yea I think this more or less checks out

[honest narwhal]

Lmao

Fair

[sleek thicket]

okay cool

[cedar pebble]

although I'm curious why you're trying to treat real and complex vector bundles in the same picture

[sleek thicket]

this should make my homework much easier, but also be annoying to prove

that's how Lee does it in his book

and my problem is about realification and complexification

together

[cedar pebble]

I think the picture is a little clearer (and can be reduced to some facts about delooping) if you're doing one thing at a time

oh I see

[sleek thicket]

(I don't have just one problem where I want this lemma, but one is about those two)

[cedar pebble]

okay yea if you want to think about complexification then sure you need both items in the picture

[sleek thicket]

I mean you could look at all possible topological fields

I think

[honest narwhal]

Which problems? I'm curious

[sleek thicket]

but it's going to be ugly unless you stick to these two

[cedar pebble]

p-adic vector bundles

[sleek thicket]

lol

this is the first one dami

[tough imp]

Did you figure out why you get the -bar for realificarion and then complexificarion?

[sleek thicket]

there is a lot of bookeeping here, and my instinct with bookkeeping is to throw category theory at it

[gritty widget]

lee's bundles book looks hard

[honest narwhal]

Oh so are you basically just trying to say smth like

[sleek thicket]

hahaha ttera

i am

[honest narwhal]

Okay it's true on vector spaces

[sleek thicket]

this is not lee

[honest narwhal]

gg

[sleek thicket]

this is my brain worms

yes exactly dami!

[tough imp]

Okay sham but

That’s how I do it too lol

[sleek thicket]

well yeah, im not saying they're unique brain worms

[tough imp]

Either that or I say, eh, sheaf you take care of it

It’s not brain worms it’s just

Brain butterflies

[sleek thicket]

okay so the second part is basically $V \otimes_\R \C \cong_{\C} V \otimes V^*$, I think?

if you know the functor business

[cedar pebble]

lmfao this gives me a similar feeling to sitting in on Negi's research meetings with his advisor, occasionally I will bring up some idea and immediately they both start trying to CATEGORY THEORY the whole thing, like even if doing so is extremely inappropriate and doesn't solve anything

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

omegalul

[cedar pebble]

And yes, for both parts you're noting that this happens at the level of vector spaces and then you're gluing

[sleek thicket]

i sometimes need to curtail this impulse

[cedar pebble]

everything you're doing glues really nicely

[honest narwhal]

Wait so is his definition of complexification and realification just doing it fiberwise?

[sleek thicket]

yeah that's essentially it

but like

yes dami

he has a general construction of lifting functors

to define tensor/hom/realification/complexification

exterior powers

etc

[honest narwhal]

Somehow I feel like phrasing it categorically is... How to put it

[sleek thicket]

just all the bundles he defines this way lol

[honest narwhal]

Morally it's the correct way to think about it

[tough imp]

Remember to sheafify after you tensor

[honest narwhal]

But actually formalizing it as a 2-category is taking too long

[cedar pebble]

yea I mean you can do these constructions globally without necessarily doing it fiber-wise and checking that it glues

[honest narwhal]

Like you literally have a map

[sleek thicket]

well he is not doing this

i am doing this

[honest narwhal]

I know, I'm telling you this lol

[cedar pebble]

I know one cute way to do this is to thinking of these vector bundles as O_M-modules and then just doing the whole construction globally in one step

[tough imp]

O_M the sheaf of smooth functions?

[cedar pebble]

although there may or may not be some things you still need to check

yea

[honest narwhal]

Like I buy what you're doing makes sense and is morally what's happening but, and perhaps this is because I don't know enough category stuff to be category-minded yet (sorry Peter), my inclination is to just say

Okay write the map

It should commute with projections because duh

And probably continuity is gonna go nicely as well

gg

[sleek thicket]

yeah but writing the map is also annoying lol

[cedar pebble]

say O_M the sheaf of real valued smooth functions, and its complexification the sheaf of complex valued smooth functions

[sleek thicket]

I have to define it locally

because my definition of the complexification is on fibers

or hmm

I guess I don't

I can define it on each fiber

[honest narwhal]

Yeah

[sleek thicket]

and then check continuity in a cover

[cedar pebble]

alternatively you can use Serre-Swan and then just do this whole thing globally that way

[honest narwhal]

lmofa

[sleek thicket]

i cannot use serre swan

[cedar pebble]

yea fair you will lose points

[sleek thicket]

although I think he said he was gonna add it as an exercise

because I asked for it

and he was like

"good idea!"

[cedar pebble]

but sometimes you need to lose points just to stick it to the man

[tough imp]

What is serre swan

[sleek thicket]

based

modulepilled

[tough imp]

Pog

[sleek thicket]

okay alex

I answer your qustion with a question

[tough imp]

DOx

[honest narwhal]

Projective modules = vector bundles

[tough imp]

Lol

[honest narwhal]

Under hypotheses

[sleek thicket]

what is a projective module?

lol or not

[honest narwhal]

It's a vector bundle

I just said

[tough imp]

...

[sleek thicket]

i didn't ask you???????

[honest narwhal]

You did you just don't know it

[tough imp]

This is true for schemes tho

I think withh like

Noetherian hypotheses

Or something

[cedar pebble]

Serre Swan says that if M is a smooth manifold and E is a smooth vector bundle over M then you can take the space \Gamma(E) of smooth sections of E and this is a finitely generated projective C^\infty(M)-module

[sleek thicket]

also this doesn't apply here lol

[cedar pebble]

when M is connected every finitely generated projective C^\infty(M)-module arises in this way

[honest narwhal]

I think Serre did it for varieties and Swan for manifolds

[sleek thicket]

i am working with an arbitrary topological space at this point

[cedar pebble]

oh

[sleek thicket]

not CHaus

[cedar pebble]

very well then

okay yea then this doesn't apply 😦

in that case you would REALLY lose points

[sleek thicket]

lmfao

I think I will do the abstract nonsense

but I have a good reason

[cedar pebble]

anyways I think you have the right idea

[sleek thicket]

I don't actually know the formal definition of a weak 2-functor and this will teach it to me

[cedar pebble]

omg

[sleek thicket]

well cmon

it's not like ive had reason to before

but now

there's one in the wild

i don't want to scare it away

[honest narwhal]

"I'm gonna do what's called a pro-gamer move"

[cedar pebble]

(although I implore you to think about how to do this in the most reasonable way possible)

😛

but yea I think your approach works and I like it

[sleek thicket]

yeah I thought it was a cool way to frame things

also, related

here is a question for you

[tough imp]

Joe papa

[sleek thicket]

we can do this for smooth functors/bundles too yeah?

are there nonsmooth but continuous functors?

[frigid patrol]

Guys

How do I learn ag

[sleek thicket]

you simply

[tough imp]

Cry

[sleek thicket]

intuit

@mossy ermine

[tough imp]

No intuit

[sleek thicket]

intuit

[honest narwhal]

Yeah PTY I've been wondering the same thing

Tbh I wish I attended Dima's classes

[tough imp]

Intuit is fake

It doesn’t exist

[cedar pebble]

just do what Chmonkey did and PUNISH YOURSELF

[honest narwhal]

I would probably be good at AG by now

[tough imp]

Yeah

[sleek thicket]

guys how do I shove my private parts in a wood chipper

I really need to do this yall

it's important

please tell me

[tough imp]

Try Hartshorne sham

[sleek thicket]

> This is what you sound like

[tough imp]

Okay do I need to recover the screenshot?

[sleek thicket]

oh no

[tough imp]

first year of grad school

...

[sleek thicket]

lmfao

[honest narwhal]

Eventually the answer is that I should stop being a wuss and just read Matsumura -> Hartshorne

[sleek thicket]

matsumura is good

[tough imp]

Matsumura is based

Also Dami

[cedar pebble]

@frigid patrol actually how much AG do you have exposure to? Do you know the basic story but just need to drag your balls through the broken glass that is Hartshorne exercises or would you benefit from a proper introduction first?

[tough imp]

Look at Algebraic Geometry I by Goertz and Wedhorn

[sleek thicket]

wait I just thought of a meme. everyone head to #groups-rings-fields so I can post my meme

[tough imp]

This books is based

[placid thorn]

hello all I've got meself a baby metrics question

[sleek thicket]

shoot!

[placid thorn]

so, say I've got a metric like $d$

[gentle osprey]

An Orc

[placid thorn]

and I want to prove that uhhh $d(x,y)/(1+d(x,y)) \le d(x,z)/(1+d(x,z)) + d(z,y)/(1+d(z,y))$.

[gentle osprey]

An Orc

[frigid patrol]

@cedar pebble I read Miles Reid undergraduate algebraic geometry

[placid thorn]

right? Triangle inequality stuff for functions of this metric here

I'm not quite sure of how to attack this inequality here

[cedar pebble]

ah okay @frigid patrol something like Hartshorne or Vakil or Liu might be appropriate at this point then

The exposition in Vakil is much better it's just stupidly long for what it accomplishes

[tough imp]

I feel like this is more analysis tbh but we’re already here

[sleek thicket]

I don't think the metric is important here

[placid thorn]

we have the property that $d(x,y) \le d(x,z) + d(z,y)$

[gentle osprey]

An Orc

[cedar pebble]

I like the exposition in Liu better (with the exception of sheaf cohomology, where Hartshorne is unquestionably better) and then the exercises in Hartshorne are definitely the best out there

[honest narwhal]

Lee does not want to know your location

[placid thorn]

but I'm not seeing how we can leverage that here

[sleek thicket]

I think you can forget about the metric? let $r,s,t$ be nonnegative reals such that $r \leq s + t$ and prove $r/(1+r) \leq s/(1+s) + t/(1+t)$

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

this implies your statement by what you said, right?

basically I'm saying forget about $d$ lol

[gentle osprey]

shamroc$\overline{k}$

[placid thorn]

does it?

yea

we can say that $d(x,y)$ returns r

[gentle osprey]

An Orc

[sleek thicket]

right exactly

[tough imp]

Yeh

[sleek thicket]

so this is a little more friendly, I think

[honest narwhal]

Lol nG in that case I should probably read Liu since at this rate AG isn't likely the main focus of my stuff

And slogging through Hartshorne exercises feels intimidating

[cedar pebble]

yea I like Liu a lot especially because of the arithmetic stuff treated at the end

[tough imp]

Nah do every exercise in Hartshorne unless you do that you won’t know any AG

[placid thorn]

"we must prove that $a/(1+a) \le b/(1+b) + c/(1+c)$ for any arbitrary nonnegative values of $a,b,c$."

[gentle osprey]

An Orc

[sleek thicket]

yeah

[tough imp]

You won’t be able to do anything, people say scheme and you go “ab”

[honest narwhal]

I'm just tryna learn AG in a week or two is that so much to ask?

[cedar pebble]

do every exercise in Hartshorne
end up forgetting all of it years later

[placid thorn]

not arbitrary

[tough imp]

That’s why you TeX solutions to every one...

[placid thorn]

that's obviously untrue

[tough imp]

Not like I’d know about that...

[cedar pebble]

Me, reaping: haha this is sick
Me sowing: oh fuck no this is terrible

[sleek thicket]

oh sorry I misread

yes

[placid thorn]

a = 1, b = 0, c = 0

[sleek thicket]

you need a <= b + c

[honest narwhal]

Lol I remember making a joke to Daniel Litt where someone asked about AG books and he recommended Hartshorne

And I was like yeah should take about 4 months or so

[cedar pebble]

excuse me what

[placid thorn]

theeere we go yeah

[honest narwhal]

And he was like wellllllllllllll not quite before he realized I was joking

[sleek thicket]

so if we just multiply everything out we get the equivalent equality $r + rs + rt + rst = r(1+t)(1+s) \leq s(1+r)(1+t) + t(1+r)(1+s) = s + sr + st + srt + t + ts + tr + trs$

yeah?

[gentle osprey]

shamroc$\overline{k}$

[cedar pebble]

actually lmfao I asked for a good book to self study complex analysis for the qual

Daniel sent me uhhh

[sleek thicket]

now we can cancel stuff

[cedar pebble]

a 400 page book

[tough imp]

Was it

[honest narwhal]

SCHLAG

[sleek thicket]

lmfao

[cedar pebble]

YEA

SCHLAG

[tough imp]

Lmfao

[sleek thicket]

oh how did quals go?

[honest narwhal]

YES

BASED SCHLAG

[cedar pebble]

said it should take maybe a month tops

[sleek thicket]

i need to read schlag

:/

[tough imp]

That book was oof

[honest narwhal]

I wish Schlag used his own book in the bootcamp when we did complex analysis

Instead of fucking

[tough imp]

I don’t know anything about riemann surfaces

[honest narwhal]

Titchmarsh

[tough imp]

And I took a course on it pog

[frigid patrol]

1 month for 400 pages

Sheesh

[sleek thicket]

so @placid thorn your inequality is equivalent $r + rs + rt + rst \leq s + sr + st + srt + t + ts + tr + trs$, and we can cancel repeated terms to get $r \leq s + t + 2st + srt$, I believe

[frigid patrol]

My pace is 1 page per week

[cedar pebble]

I mean if epo can do it anyone can

[tough imp]

Max told me to just read a concise course in algebraic topology

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

oh yeah lmfao

[tough imp]

Over winter break

[sleek thicket]

that was

[cedar pebble]

oh god

[sleek thicket]

hilarious

[cedar pebble]

don't read concise

[tough imp]

When I was going to japan

[cedar pebble]

[sleek thicket]

and anyways @placid thorn this last equality is obvious

since r <= s + t

[cedar pebble]

May literally got banned from teaching intro AT for a bit because of that book

[sleek thicket]

tfw this poor person tried to get help with metric spaces

and the chat was flooded with ag hell

lmfaooooo

[honest narwhal]

When he taught undergrad complex at Chicago though he used some "Basic Complex Analysis" book by Silverman

But he apparently at times referenced his book?

Idk

[sleek thicket]

i feel like chmonkey whined to me about proving this inequality for the hyperbolic metric

but it's actually easy lol

[tough imp]

Shamrock

[sleek thicket]

ive owned you

[tough imp]

No I didn’t

[honest narwhal]

His book is the main one used by the people who teach grad complex in Chicago geometrically

[tough imp]

And if I did

[sleek thicket]

hmmmm

[tough imp]

It was harder

[sleek thicket]

i remember whining

oh right it has like cosh or smth

[tough imp]

And if it wasn’t harder

Fuck you

[sleek thicket]

lmfao

[honest narwhal]

Half the time it's Schlag's book and the other half of the time Lawler co-opts the class as probability lol

[cedar pebble]

Oh here's a slightly scary problem: let \mu be the (normalized) volume form on H/SL_2(Z). Construct a 1-form \psi on H/SL_2(Z) such that d\psi=\mu

I cannot find a non-pretentious way to do this

[sleek thicket]

hmm

i will think about it

[tough imp]

H being the upper half plane?

Oh and SL_2 acts like yeh

[cedar pebble]

yea, SL_2(Z) acts on it by linear fractional transformations

👍

[sleek thicket]

so the space is volume forms is 1 dim

yeah?

[cedar pebble]

Yup!

[tough imp]

I used FTOFGMOAPID for my Riemann surface course

[sleek thicket]

and SL acts by isometries, right?

like via mobious transforms

[tough imp]

[cedar pebble]

Yup!

[sleek thicket]

it's been a while since complex lol

okay so we get a metric on this quotient

and we can pick an orientation

and get a canonical volume form

[cedar pebble]

If you want to do this concretely the volume form in the usual upper half plane model is dx dy/y^2 and you pass this to the quotient

[sleek thicket]

this is my first instinct

[frigid patrol]

What an acronym

[sleek thicket]

right exactly

[cedar pebble]

so a natural thing to try is like

[sleek thicket]

right

so this gives a canonical volume form to start with

[cedar pebble]

start with x dy/y^2 and try to average over SL_2(Z)-orbits

but I didn't end up getting incredibly far with this

[sleek thicket]

for defining the volume form?

[cedar pebble]

for defining \psi

[sleek thicket]

oh right

makes sense

actually wait

[cedar pebble]

I mean x dy/y^2 solves the cobounding problem on H, you just need to force it to be SL_2(Z)-invariant

[sleek thicket]

topologically what is $H/SL_2(Z)$?

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

like it's some surface, right?

[cedar pebble]

topologically it's C

[sleek thicket]

isn't this question purely about the smooth structure?

unless im missing something

[cedar pebble]

(in grey is the fundamental domain for the action of SL_2(Z) on H)

[sleek thicket]

oh i misread initially

you want it for the specific volume form

not an arbitrary one

[frigid patrol]

Cute triangle

[cedar pebble]

Yes, exactly

[sleek thicket]

alright seems more tractable, mb

so it's C with some weird metric

[cedar pebble]

sure, if you like

although I do think it's easier to think of this as like

[placid thorn]

lol I thought that trying to multiply it out would get really ugly

[cedar pebble]

doing things on H/SL_2(Z) is the same as doing things SL_2(Z)-equivariantly on H

[sleek thicket]

sure

[placid thorn]

I was mistaken

thank you shamroc!

also good taste in albums!!!

[sleek thicket]

thank you!

[frigid patrol]

What does it mean when you say a map between two G-sets is G-equivariant?

[sleek thicket]

it commutes with the group action

f(g x) = g f(x)

[tough imp]

It means that the map is good

[sleek thicket]

okay so NG here is my thought now

$H^2_{dR}(\C) = 0$ and $\Omega^3(\C) = 0$, so all top dim forms are exact

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

I imght be missing something

[honest narwhal]

Well idk if you can auto extend forms on H to those on C no?

Or really SL(2,Z)\H

Unless you're saying take a diffeo?

[sleek thicket]

I thought NG wanted a form on H/SL(2, Z), which he said was diffeo to C?

I know very little complex analysis so Im treating this as a diff top/geo problem lol

[cedar pebble]

yea I think it's clear that these things exist for abstract reasons by what Shamrock is saying, but it's not at all clear that the things produced this way will yield SL_2(Z)-invariant things on H

[honest narwhal]

Yeah the problem said construct so I imagine it's more like

Gib formula

[sleek thicket]

hmm okay

[cedar pebble]

yea it's kinda tricky

[sleek thicket]

well this is constructive as long as you have an explicit diffeo $H/SL_2(\Z) \to \C$

[cedar pebble]

idk I might be able to unwind the proof I have to get something reasonably concrete?

[gentle osprey]

shamroc$\overline{k}$

[sleek thicket]

because exact = closed is a calc 3 problem for C

[cedar pebble]

actually Dami I forgot if I showed you the really pretentious proof of this that I wrote up somewhat recently

[sleek thicket]

like my argument is basically, push your form forward, do calculus to show it's exact, pull it back

I think

[cedar pebble]

It uses (g,K) cohomology and Eisenstein intertwiners between principal series representations

it's completely stupid

[honest narwhal]

Wait hold up

Why is SL(2,Z)\H diffeomorphic to C?

[sleek thicket]

idk lol Im just going off of what NG said

[cedar pebble]

I mean one has to be careful here

such a map certainly does not preserve the complex structure

[sleek thicket]

sure

is that important? do you need like a holomorphic form?

as I said, I'm thinking of this purely in terms of diff top

[cedar pebble]

You should definitely be able to get a holomorphic 1-form out of this iirc

[sleek thicket]

hmm

[honest narwhal]

Wait so I didn't get a lot of sleep last night so I might be being a dumbass here

But SL(2,Z) is discrete and acts by hyperbolic isometries so isn't that a covering space action?

[sleek thicket]

alright im gonna go 2-pill myself now

[honest narwhal]

So I'd think that SL(2,Z)\H has non-trivial pi_1

[cedar pebble]

you have to be careful about how you define \pi_1 and how you're thinking about the quotient here

if you're thinking about this quotient as an orbifold then it has \pi_1=SL_2(Z), appropriately defined

but if you're forgetting the orbifold structure you're just getting a genus 0 surface with one puncture (at infinity)

[honest narwhal]

Oh and in that case it's C huh

[cedar pebble]

mhm!

But again you have to be careful if you're trying to do this holomorphically

again I think it's easier to avoid that mess and just try to work on H itself and then try to force things to be SL_2(Z)-equivariant

[wanton timber]

Note that SL_2(Z) does not act freely on H, so it is not a covering space action (i and the sixth root of 1 both have nontrivial stabilizers)

[cedar pebble]

which is usually done by orbit-averaging as in Eisenstein series

[honest narwhal]

Right okay so I did have a brain fart

[cedar pebble]

Dami as you can see the proof I have in mind is uhhh

yea

[honest narwhal]

Yeah lmao it's quite something

[astral cedar]

Hello people

I was trying to study coherent sheaves

I wondered, is it possibile to somehow define them categorically

[tough imp]

Wait wut

[astral cedar]

Wait

Should have finished the phrase before hitting send lol

I meant, defining them as some sort of abelian closure of Vect(X) in the category Sheaves(X)

(Supposing that such a thing as an abelian closure even exists)

[tough imp]

I don’t know if coherence can follow categorically. You can define O_X-modules as a module object over a ring object in the category of sheaves on X

There’s a guy who was explaining that to me earlier

But I feel like the coherence bit of that is hard to really describe categorically but maybe??

[astral cedar]

I thing there might be some issues with the morphisms, but I am really not sure

What I would want to do is to take the full subcategory Vect(X) of vector bundles of the abelian category of O_X modules

And then adding to it kernels and cokernels

[sleek thicket]

I think you should have a notion of abelian closure of a subcategory (maybe you need full?)

actually after thinking about it for 1 more second I'm not sure anymore lol

I wanted to take the intersection of all larger subcategories which are abelian, but subcategories of abelian categories might have different kernels/cokernels

so maybe you want the smallest exact subcategory containing it?

[astral cedar]

Isn’t Vect(X) already exact by itself?

Oh you mean containing a ker

[sleek thicket]

By exact subcategory I mean an abelian subcategory where the inclusion functor is exact, i.e. preserves kernels and cokernels

[astral cedar]

Oh thanks

Yeah thats seems a good notion

[sleek thicket]

this should be preserved under intersections

unlike arbitrary abelian subcategories

(I don't see any reason those should be closed under intersections, I mean)

[astral cedar]

Yeah

[sleek thicket]

it also seems like what you were originally thinking

with "add in the kernels and cokernels"

[astral cedar]

Precisely

[sleek thicket]

since we want those measured from the larger category

[astral cedar]

So I guess if this construction makes sense it would actually produce the subcategory of coherent sheaves right?

[sleek thicket]

I'm not familiar enough with AG/sheaves of modules to say, sorry

[astral cedar]

Np

[sleek thicket]

but if every coherent sheaf is a kernel/cokernel of a map between locally free sheaves then yeah

oh yeah isn't coherent like, locally finitely presented? or something?

[astral cedar]

Yeah but I guess that comes by coming from vect(X)

[sleek thicket]

so every sheaf is locally the cokernel of a map in Vect(U) for some open U of X, yeah?

but it's not clear to me that this subcategory generated by Vect(X) globally contains all of them (once again, not familiar with this stuff lol)

[astral cedar]

Yep

I am honestly not sure

I would be quite surprised if existed an intermediate notion between vector bundles and coherent sheaves, though

[sleek thicket]

so here's my concern like

consider taking Vect(X)

and adding in all kernels a cokernels

to get a new category C1

then doing this to C1 to get a category C2

and so on

we can take the union to get a subcategory C of the category of coherent sheaves

yeah?

and this will be closed under taking kernels and cokernels

it *should* be abelian

I think

but to be in there you have to globally be a kernel of kernels of cokernels of kernels of.... between locally free sheaves

whereas coherent sheaves are about local, topological behavior

idk if this makes sense lol

[astral cedar]

I’m honestly not sure I’m traumatized by the borel hierarchy

[sleek thicket]

hahaha

I love the borel hierarchy!

feels so sick to reduce a problem about all measurable sets to something dumb about F sigma deltas or whatever

[astral cedar]

Yeah cool stuff

[honest narwhal]

Wait did someone say borel hierarchy

[placid thorn]

how do open metric spaces work?

I'm still having trouble grasping those

[ivory dragon]

i havent heard that terminology before; how is it defined?

[placid thorn]

"A subset U of a metric space (M, d) is called open if, given any point x in U, there exists a real number ε > 0 such that, given any point y in M with d(x, y) < ε, y also belongs to U. Equivalently, U is open if every point in U has a neighborhood contained in U."

[ivory dragon]

oh, you mean open subsets of a metric space

have you been exposed to any analysis?

[river granite]

not sure what you mean by how they "work", one defines open sets b/c they sometimes have interesting properties or allow you to define more stuff

[ivory dragon]

intuitively you can think of open sets as sets such that every "point" has points "all around" it

[river granite]

e.g. you can show that a function between metric spaces is continuous (in the epsilon/delta sense) iff the preimage of any open set is open

[ivory dragon]

a good source of examples here is R under the standard topology

for example, the interval (0, 1) is an open set in R

[placid thorn]

ahhh

[ivory dragon]

if you name any number in this interval, i can find an epsilon such that every point within that distance is also in the set

[placid thorn]

but (0,1] isn't

[ivory dragon]

so if you named, for example, 0.999

[placid thorn]

cause we could pick 1, for example

[ivory dragon]

i might choose epsilon = 0.00001

and then 0.99901 is in this set, as is 0.99899

but yeah, (0, 1] is not open

because if we take 1, 1 doesnt have points "all around it"

[astral cedar]

Yeah, to be precise when you talk about a set being open or closed you have to specify the ambient space

[ivory dragon]

now R is just one example, examples of this are numerous in topology and often in more esoteric sets/metric structures on those sets

but it's the motivating example

[astral cedar]

For example, (0,1] is not open when considered as a subset of R, but is open if you see it as a subset of (-inf, 1]

[ivory dragon]

another example would be R^2, i.e. the 2-dimensional coordinate plane, under the standard metric structure

if we consider, say, a disc in this space

a disc is open if it doesnt contain its "edge"

and not open if it does

so say, ${(x, y) \mid x^2 + y^2 < 1}$ is open, but ${(x, y) \mid x^2 + y^2 \leq 1}$ is not open (and is closed)

[gentle osprey]

Namington

[ivory dragon]

in fact, if we add ANYpoint on the "edge" (circumference) of the circle to the open disc, we no longer have an open set

note: in R^n, "open" and "closed" are mutually exclusive except for R^n and the empty set (which are both open and closed); however, in other structures, it's possible for other sets to be both open and closed as well

"closed" just means "complement of an open set"

anyway, the way to topologically think about "open" is that we have no "sharp" behaviour

because we can always take neighbourhoods, we dont have to worry about "weird edge cases" unless we're at the edge of the metric space itself

this makes them fairly well-behaved, especially with respect to continuous functions

[obtuse meteor]

Closed sets are also nice. Because it means you understand limiting behavior,,,

Topologists constantly privileging opens

[placid thorn]

okay, I ask this because I'm trying to reason about the backwards of this proof

d1 and d2 are metrics on the same set with constants C, C

' such that C*d1 \le d2 \le C'*d1

for any points x and y that you plug into d1 and 2, ofc

and I'm trying to prove that if a subset is open on U for d1, it's equivalent to that subset being open on d2

I've proven the forward, but I dunno how to prove the backward

"We begin by proving the forward. Suppose that $U$ is open with respect to $d_1$. this implies the existence of a positive value $\epsilon$ where for any $d_1(x,y) < \epsilon$, for any $x$ in $U$ and any element of $y\in X$, $y$ is also contained in $U$. If we can prove, then, that there exists an $\epsilon'$ where for any $x\in U$, $d_1(x,y) < \epsilon'$ implies that $y \in U'$, we will have found that $d_2$ is open over $U$. Consider $\epsilon' = C'*\epsilon$. Then we know via the linearity of multiplication that for any $y\in U$, $C'*d_1(x,y) < \epsilon'$ (substition for $\epsilon'$), this implies that $y$ is in $U$. Therefore, since $d_2(x,y) \le C'*d_1(x,y)$, if $d_2(x,y) < \epsilon'$, $y$ is contained in $U$. Thus, we have found an $\epsilon'$ which proves that $d_2$ is an open metric with respect to $U$. \"

[tight agate]

there's some symmetry to your condition

[gentle osprey]

An Orc

[tight agate]

now that you've done the hard work of proving it for one, try to use the symmetry

[placid thorn]

I tried using that symmetry, but I got stumped by C maybe being a decimal

cause in that case, d_1 might not necessarily be less than d_1*C

[tight agate]

sure, C can be less than one

[placid thorn]

so I try to go, "okay, suppose that d_2 is open

that means that d_2(x,y) < epsilon implies that y is in U

so, we want to prove that d_1(x,y) < epsilon' implies that y is in U for some epsilon'

[tight agate]

no I mean try to find another inequality

that sandwiches d1 between some constants times d2

and then your old proof works (assuming it is correct)

I mean find ? and ?? such that ?d_2 < d_1 < ??d_2

[sleek thicket]

hey everyone who was telling me I was overcomplicating things get this

it's actually a strict 2 functor!

Bet you feel silly now :^)

[obtuse meteor]

when did you decide to wake up and choose violence?

[thorny flame]

question can I get away with learning about topological manifolds without knowing anything about algrebreic topology? Like I'm thinking of picking up "Lee's INTRODUCTION TO
SMOOTH MANIFOLDS" but only have gone through like the first 3 chapters of Munkres Topology (up to countability and seperation axioms)

[sleek thicket]

well if you're interested in topological manifolds Lee has a different book for that

ISM will use the fundamental group and covering spaces at times

[thorny flame]

oh wait hm

[obtuse meteor]

I have ISM downloaded, but I refuse to read it

[thorny flame]

I'm mostly interested from like a GR perspective

what is ISM?

oh intro to smooth mani

gotcha

eh fukkit i'll learn the fundamental group as I go along can't be that bad right

[sleek thicket]

this is bad vibes Faye

also I would not recommend it but ultimately it's up to you

ISM > category memeing which is why I'm forcing Lee to read several pages of cateogry memery

[obtuse meteor]

is this to me?

[sleek thicket]

No sorry it's too slim

[obtuse meteor]

ah

[thorny flame]

see like I just don't wanna learn the Tychenoff theorem and like all those general theorems

[sleek thicket]

I strongly recommend ISM lol

But you don't need to read it

I'm just kidding around

[obtuse meteor]

I should read it. but geometry

[sleek thicket]

That book has very little geometry, only topology 😌

[thorny flame]

wait is ISM not just differential geom?

[sleek thicket]

it is not

If you want GR applications you'll need IRM (introduction to riemannian manifolds)

Which is the successor to ISM

Accept smooth structures into your heart faye

[thorny flame]

ugh ok well one step at a time i guess

[obtuse meteor]

,,,no

[gentle osprey]

Cohomologay

[sleek thicket]

IRM covers those!!

[obtuse meteor]

fucking texit is homophobic

[sleek thicket]

you are being homophobic because you don't want to learn de rham cohomology

[obtuse meteor]

(if you don't parse this as a joke I'm sorry that you're dumb)

[sleek thicket]

A disgrace to you're name

[gritty widget]

IRM

[thorny flame]

cancel texit

[obtuse meteor]

I know enough about de rham cohomology

just don't ask me to compute it

:)

[gritty widget]

the relativity in IRM is, to my understanding, purely garbage computations

[thorny flame]

tru but I mostly just want a math counterpart to supplement my actual GR studies ya feel

[gritty widget]

O'Neill's Semi-Riemannian Geometry with Applications to Relativity

one moment i think i posted it in the server before

nvm i don't think i did

do carmo RG?

he uses confusing and unclear notation

and spares a lot of details in places

[peak wraith]

Frankel's "geometry of physics" (https://fedika.com/wp-content/uploads/2019/02/The-Geometry-of-Physics.pdf) is a pretty good mathematical physics primer for a lot of broad modern topics

including a quick n' dirty intro to the diff geo you need for special relativity (getting used to the weird "geometry"of pseudo-riemannian metrics/the minkowski metric on euclidean space), then more generally tensors/connections for manifolds

[sleek thicket]

just to be clear, I do not recommend IRM with your current background

[peak wraith]

do carmo is...ok. if want good easy fast, Lee's smooth manifolds is great. skim the first chapter or two, then you've got plenty of topics to bite into

[sleek thicket]

not saying all books are bad at your level

[thorny flame]

ah ok

I think maybe I'll speed through ITM since there seem to be some things I've learned in there, then do ISM then IRM. I'm not studying it for class or anything just to prepare for grad school so I got time

[obtuse meteor]

@sleek thicket do you think ISM without ITM is a bad idea btw

ITM seems hella dry

from what I've seen

[sleek thicket]

ISM without general topology is a bad idea

[obtuse meteor]

well yeah lmao

[sleek thicket]

but you don't need the classification of surfaces or w/e

[obtuse meteor]

aight

[sleek thicket]

I said it because the person asking the question said "topological manifolds"

[obtuse meteor]

mhm

[sleek thicket]

👀

[tidal cedar]

From looking at the contents and index of ITM it seemed pretty interchangeable with other general topology books

[sleek thicket]

yup

it just also does the classification of surfaces essentially

and like, focuses more on topological manifolds

rather than caring too much about pathological weirdness

[tidal cedar]

Yeah NGL ITM seems better in that regard

[sleek thicket]

ITM is written as "everything my students needed to read ISM"

[tidal cedar]

Counterexamples are nice but I don't wanna do a ton of them for the main reference

[obtuse meteor]

I don't believe in classification of surfaces

[frigid patrol]

WHat is ITM

[tidal cedar]

Lee Introduction to Topological Manifolds

Prerequisite for the smooth manifolds book as Sham mentioned

[frigid patrol]

No

Why would it be prereq

[tidal cedar]

You don't literally need to have read that exact book, but it's meant to teach one the stuff you need to then do ISM

[tidal cedar]

[sleek thicket]

faye that's super cringe

the classification of surfaces is a really beautiful result

wait let me see if I can galaxy brain this up for you

"homotopy equivalent and homemorphic coincide for connected compact surfaces"

"the first integral homology group classifies connected compact surfaces"

i mean the classification is even cooler than this because it tells you what you get

but still it's based

right of course, but I'm trying to put it into language that someone who has category brain worms will appreciate

also yeah I love polygonal presentations

and playing with them

(i also have categorical brain worms, I am currently writing an exposition on 2-categories and 2-functors for my bundles course's homework)

yeah!

I love it lol

and then later when you do like, cohomology or w/e

it gives you really simple models

like I had to draw pictures of RP^2 # ... # RP^2 and whatever

to really understand cocycles

and how the cup product works

which part lol?

we have conclusively proven

classification of surfaces = based

because they have the same euler characteristic and are both orientable

I should learn alg top

I joined a hatcher reading group in the second quarter

so i like

speedran homology in 2 weeks

and then spent 10 weeks on cohomology

it was a cool supplement to de rham stuff in my manifolds course tho

lmfaoooo

that is

awful

that's like

lmfao

cohomology is infinitely more confusing than homology

otoh I would like to learn morse theory...

[tidal cedar]

Flippy flippy the chains and then add a commalg thingy on top, cohomology = ez

[sleek thicket]

wow, hank you fiona

cohomology easy now

hahahahahahahha

that is so fucking based

[tidal cedar]

I don't know this prereq

[sleek thicket]

"what's the problem just do a general construction in homological algebra"
> me before getting absolutely destroyed by cohomology

turns out the topology of the situation matters

[tidal cedar]

okay, but if you pretend you do

[sleek thicket]

lmfao

thats so incredibly cool

that's like

all of my courses lmfao

well not grad algebra or ITM-the-course

but that's because I had already done algebra and topology

2nd courses are great lol

I would retake my courses on varieties, schemes, smooth manifolds, riemannian manifolds, and algebraic topology if it cost me no time

at least this quarter Im taking a second pass through homological algebra

[obtuse meteor]

Classification of surfaces is based

I am just allergic to simplices and triangulation

[sleek thicket]

oh yeah lmfao

i have not read a proof of it

also I am going to have to simplicialpill myself this quarter

but it's simplicial sets so I get to keep my memer street cred

[tidal cedar]

Yes omg

Then you can do infty cats

[sleek thicket]

lol

maybe in a distant future

right now I just want to understand dold-kan

[tight agate]

simp sets are a model for infinity cats, so you're already doing them

or really quasicats

[sleek thicket]

i am going to block people who attempt to infinity pill me in the next 10 weeks while I simplicially shitpost

you have been warned

$\mathsf{Shitpost}^{\Delta^{op}}$

[gentle osprey]

shamroc$\overline{k}$

[tight agate]

dold kan looks cool

[sleek thicket]

I might give a talk on it On Here 🙂

[tight agate]

cool

[sleek thicket]

chm and I are doing it for our homological algebra class

there's a presentation component

[tidal cedar]

https://tenor.com/view/do-it-star-wars-gif-4928619

[tight agate]

do you know what some of the other presentation topics are?

there's so many cool homological algebra topics

algebraic de-rham cohomology

group cohomology and chow rings

verdier duality

[sleek thicket]

Yeah I'm really excited for them, lemme find my screenshot

This is what we have so far

Other projects might be added

group coho is covered in class

Okay yeah there's at least one more group but with no project choice so far, and the question marks have been removed from DGAs

[elder yew]

dox

[sleek thicket]

lol

I was gonna post this on Twitter so I didn't censor my/Alex's name

I am really hyped for these presentations tho

[elder yew]

Should be fun!

[tough imp]

Wow you name drop my name

bfut don't name drop your own?

wtf?!

smh my head

[sleek thicket]

process of elimination!!!

My name is....

Dold Kan

[tough imp]

Dold

[sleek thicket]

My project partner is Mr. Simplicial Groups

That's right, chmonkeys real name is simp

[tough imp]

[elder yew]

Good luck on your presentation chmonkey

[sleek thicket]

we still have 9 weeks to go thankfully

[tough imp]

Hahaha he didn’t say good luck to you Sham

Yeah haha

[sleek thicket]

lmfao I've been owned

Jonathan didn't reply to my email asking for meeting times...

[tough imp]

So...

[sleek thicket]

But did respond to reu stuff

[tough imp]

Well

Max hasn’t yet done my recc

So...

[sleek thicket]

Better than radio silence

[tough imp]

Tomorrow...

I’m gonna dm him on twitter

[sleek thicket]

Lol do you remember our first interaction with max?

Like

[tough imp]

Yeah

I know

[sleek thicket]

This is not surprising lmfao

[tough imp]

I’ve emailed him before as well

Anyway I didn’t want to have to go to twitter dm but

I feel like when it’s 2 days before it’s due it’s permissible

[sleek thicket]

Yeah true

[tough imp]

Like...

[sleek thicket]

Could you ambush him at a seminar?

[elder yew]

Is the letter a hard deadline

[tough imp]

Idk what seminars he goes to lol

[elder yew]

or are they just kinda like

[tough imp]

I think so... I mean idk

[elder yew]

🤷

[tough imp]

I would rather not play around with the deadline tho

[elder yew]

Most of my letters were late and nobody cared

REU might be different

[tough imp]

Nah this is for Columbia

[elder yew]

I emailed one prof asking if he was still taking students - he informed me that he was retiring this term. Then told me (1 month after the deadline) that if I hadn't applied just email him all the materials

He'll look at it

[tough imp]

Also lol at ambushing him at a seminar

[tight agate]

ah REUs...

hopefully I can just convince someone over here to supervise an REU

[elder yew]

Goes to physics department shamefully

[tight agate]

ye but I don't see a point in doing an REU in another school

if stuff wasnt online I mightve considered doing one

[elder yew]

The main point is to get a letter outside of your home school

[tight agate]

so that I can visit and stuff

[elder yew]

Seems to strengthen your application

[tight agate]

does it?

I would rather just improve whatever connections I have

[elder yew]

It's hard to say for sure

But what seems to make sense is this

[sleek thicket]

it looks good on an app, that's enough for me lol

[elder yew]

"You went to another institution other than your home school and showed that you can be productive there. This gives credence to the idea that you will be productive outside of your home school"

Which is exactly what you will be doing

[sleek thicket]

the grad-school-application-optimizer has logged on

[tight agate]

I mean sure, doing an REU looks good. But does it have to be at another school?

[elder yew]

No it doesn't. Isn't Gangbo et al. running one in something?

[sleek thicket]

sure but my school's one closed

sorry for misunderstanding

also you gotta actually get into your school's program...

I wouldn't be comfortable applying to just 1 school even if it was my school's

[elder yew]

I think it's good if it's at LA. I mean who is gonna snub their nose at that?

Also might prove your ability to do research at LA, improving your chances of getting in

[tight agate]

lots of them offered projects last year

usually ~7 different projects

[elder yew]

They seemed to have started that in summer 2018

[tight agate]

that you can apply for

[elder yew]

Right when I left lol

[sleek thicket]

o im applying to ucla