Homotopy Theory

Jon Beardsley

2:01 AM

@EvanJenkins good to know. did i say they were? I don't really know about such things.

Will

@Evan you should star the incriminating reply for posterity, I heard Jon loves that

Jon Beardsley

@LoganM no I'm not. my officemate Vitaly is

Logan M

@JonBeardsley I know Vitaly. Who are you working with then?

(btw I'm a physics grad at JHU, but the only math professors I know are Nitu and Jack)

Jon Beardsley

oh! cool. I'm working with Jack

do you know Kevin Grizzard? he's a pretty good friend of mine.

Evan Jenkins

@JonBeardsley Click the little arrow on my post.

Jon Beardsley

2:05 AM

oh thanks! close one

Logan M

@JonBeardsley Yeah I know him also.

Jon Beardsley

oh cool. oh yeah! were you in Nitu's class? I was there for part of that.

do you have a big beard? I may know who you are.

Logan M

Yeah I was there occasionally. If you were there you probably saw me. I'm the one with the obscene amount of hair on my face.

Matthew Pancia

jon "no beard" beardsley

Jon Beardsley

yeah, no beard for me

Evan Jenkins

2:07 AM

Jon Beardless

Jon Beardsley

and yeah, I saw you there, and in Jack's class I'm pretty sure. I'm the jerk that showed up to his class and hi-jacked him as soon he was done teaching you guys

Matthew Pancia

Jon not-so-Beardsley

Logan M

Oh yeah I remember you now. It's hard to recognize people just based on internet photos though.

Jon Beardsley

yeah totally

and yeah. i'm Beardfree Beardsley

kind of like butterfree

but, more about beards, less about butter

Matthew Pancia

hmm

Logan M

2:10 AM

This seems like an opportune moment to make a shameless plug for my ridiculous Facial Hair Area51 proposal

Matthew Pancia

during SXSW i saw a novelty band called The Beards

they only sing about beards

they have like 3 full length albums

Evan Jenkins

This reminds me, I should update my gravatar.

This one is missing a beard.

Jon Beardsley

that's a lot of music about beards

i like that really the only math that has been discussed in this room so far is type theory and algebraic geometry

Will

come on

it was HOMOTOPY type theory

not completely irrelevant

Jon Beardsley

well

yeah

but still, it makes my joke less funny

and besides, it was barely homotopy type theory

Will

2:13 AM

and it was barely a joke

Jon Beardsley

it was basically type theory with an infinitesimal arrow pointing at homotopy theory

that's true. more of an ironic observation

Matthew Pancia

explain more jokes to me JB

Jon Beardsley

do you know what the B is Benoit B. Mandelbrot stands for?

*in

Matthew Pancia

Beardsley

Jon Beardsley

It stands for Benoit B. Mandelbrot

Matthew Pancia

2:16 AM

oh that's pretty funny

ZING

now explain it

hahah

yes I thought that was the point

Jon Beardsley

i'm feeling cyberbullied

please stop cyberbullying me

so Will, who are you anyway?

Will

2:18 AM

please stop cyberbullying me

Jon Beardsley

are you a grad student? an undergrad? a boy genius?

no, i'm the room owner, I'm allowed to cyberbully

Will

sorry master

Jon Beardsley

lol

okay. time to go listen to Bossa Nova and do math

have a lovely evening all

Question

if an elliptic curve is given by some equation

y^2=x^3+Ax+B

or something

i mean......

isn't this an affine abelian variety?

Evan Jenkins

No

Jon Beardsley

oh

Will

2:25 AM

the origin is not contained in that set of solutions

Evan Jenkins

You want the projective closure.

Will

it's at infinity in that representation

Evan Jenkins

You're taking y^2z = x^3 + Axz^2 + Bz^3

In projective 2-space

Jon Beardsley

aha

Evan Jenkins

Yes, the additional point at infinity is the marked point.

Jon Beardsley

2:25 AM

so, we can get an affine variety, but it's not a group

Evan Jenkins

Right

Jon Beardsley

super!

Evan Jenkins

Actually, you can take any point as the marked point.

Jon Beardsley

i see, but..... if it's not projectificated, it's not a group?

even if i take some other point as the identity

Evan Jenkins

Right

Because there will be some pairs of points that add to the point at infinity.

Jon Beardsley

2:27 AM

yes, right, kewl

Evan Jenkins

The group operation is take two points, and find the third point that intersects the line they form.

Jon Beardsley

yeah

okay, now, when i want to get the formal group law, i take the taylor expansion of the group structure at.... the marked point?

well.... "taylor expansion"

Will

I'm not sure I agree with taking any point as the marked point

obviously youu can translate everything

but if you are doing chord-tangent you want to take a flex right

Jon Beardsley

obviously

oh i see what you're saying, chord tangent, yeah

Evan Jenkins

Oh, yes.

Jon Beardsley

2:29 AM

genuinely.

Evan Jenkins

With that definition of the group law.

Jon Beardsley

what is a flex right

btw

Will

a flex is a point at which the tangent intersects the curve with multiplicity at least 3

Evan Jenkins

Inflection point

Jon Beardsley

aha

Evan Jenkins

2:31 AM

Do I have a beard yet?

Will

you want that for your point to be able to be an identity for the chord-tangent grop laaw

Evan Jenkins

Maybe I need to log back in.

Will

yes you do

Jon Beardsley

you have a beard

Will

everyone was too intimated by it to comment on it

Jon Beardsley

2:31 AM

when i click on your name

David Roberts

@EvanJenkins Also make three comments in a row so your picture gets bigger

Evan Jenkins

Ah, wunderbar.

David Roberts

so we can read

like this

Evan Jenkins

Candyman

David Roberts

a

d

Jon Beardsley

2:32 AM

lol nice try!

David Roberts

we

Bigger

Jon Beardsley

o

okay sorry i'll stop

no i wont

huge photo!

Will

we have a winner

David Roberts

Sorry, tried to make a bunch of quick lines and the system wouldn't let me.

sdaer

Evan Jenkins

Can
I
Just
Do
This?

Jon Beardsley

2:33 AM

yes

Evan Jenkins

Well that worked.

David Roberts

Yes

But I see no beard

Jon Beardsley

except ur little picture is still your old one

Will

I see the new one

David Roberts

And the big picture

Jon Beardsley

2:33 AM

nah i'm seein that beard

David Roberts

I see the beard when I click

Jon Beardsley

and that bow-tie. super choette

(sic)

David Roberts

Bow ties are cool

Jon Beardsley

yeah, it's kind of all i wear now

David Roberts

Sorry, couldn't help myself

Jon Beardsley

2:34 AM

except people keep saying to me "oh now you really look like a professor!"

Evan Jenkins

Just a bow tie? How risqué.

Jon Beardsley

but i never see professors wearing them

David Roberts

:S

Evan Jenkins

!

David Roberts

Well, I tried to convince my wife I didn't need to dress fancy to give a talk at a conference, citing Mike Hopkins as an example...

Jon Beardsley

2:35 AM

hahah

i'd like to give a talk at a conference

i'd wear a bow-tie

David Roberts

Shorts and a T-shirt

Jon Beardsley

you better believe it

David Roberts

But it's winter here, and it was Singapore then

Jon Beardsley

that reads as if Singapore is a season

David Roberts

Singapore only has one season

Jon Beardsley

2:36 AM

to e

Evan Jenkins

It is.

David Roberts

Bang on the equator

Jon Beardsley

i see

how sad

Will

well it's not due just to that

David Roberts

Nice and warm all year around

Will

2:36 AM

it's a lot of climate regulation from the ocean also

David Roberts

True

Jon Beardsley

listen guys, please take this to the climatology.stackexchange chatroom

Evan Jenkins

insert John Baez joke

David Roberts

Sorry, but I was talking about Mike Hopkins and his talk about E_\infty stuff

Jon Beardsley

what if i made this room and just kept kicking everyone out, and just sat here talking to myself

David Roberts

2:37 AM

You are talking to yourself, we are all bots

Evan Jenkins

You already did. We're just your sockpuppets.

Will

it'd be like Arnav's room

Jon Beardsley

what if that IS what I'm doing, I just don't know it

whoa, we all had the same thought

David Roberts

Re: Lem's Peace on Earth

Evan Jenkins

That's because we're all you.

Jon Beardsley

2:38 AM

yeah, Arnav's AG room

hahaha, excellent.

i'm glad i know some stuff about elliptic curves

David Roberts

Hey, it's a great way to think out loud and keep a transcript

Jon Beardsley

well, that's the only way i worked out that what i really wanted was a cogroup scheme

David Roberts

Good on you, Jon

Don't listen to those other nasty voices

Jon Beardsley

indeed

Evan Jenkins

Are you sure you didn't want a group coscheme?

Jon Beardsley

2:39 AM

absolutely

though i like to think about cosheaves. by which i do not mean covariant functors satisfying descent

Evan Jenkins

Codescent, you mean.

Jon Beardsley

yeah sorry

David Roberts

Like Lawvere's quantity and quality

Evan Jenkins

Also known as ascent!

Jon Beardsley

that's not what i don't mean

David Roberts

2:40 AM

Intensive and extensive

Jon Beardsley

yeah, totally. insensitive

David Roberts

Wow, now the system is being cranky and not letting me post comments quickly

as well

These are real mathematical things, you know.

All about topos-theoretic approaches to classical physics

Jon Beardsley

no i mean a category fibered in grothendieck topologis

David Roberts

??

Jon Beardsley

that is not a "real" thing

David Roberts

2:41 AM

No, no it's not

Jon Beardsley

but it'd be cool if it were. also, sheaves of sheaves of sheaves of sheaves of....

Evan Jenkins

A textbook example of toPoe's law: made-up topos-theoretic terminology is indistinguishable from the real thing.

Jon Beardsley

so those are $\infty$-sheaves, right

Will

don't pretend you wrote sheaves infinitely many times there

Jon Beardsley

$\aleph_3$-sheaves

i did, the internet just couldn't handle it

i'm particular interested in $(\aleph_3,\aleph_2)$-categories

Will

2:44 AM

I thought you were interested in large cardinals

those don't seem very large to me

Jon Beardsley

i'm not actually

Will

that's a relief

Jon Beardsley

interested in anything

i don't know any big cardinals

Evan Jenkins

Not even the Pope?

Jon Beardsley

except the Reinhardt cardinal

which I'm pretty sure can't exist

or something

does mathematica solve systems of equations? it seems like it should really do that

Will

2:46 AM

of course

Jon Beardsley

because that's what i need to happen right now

but like, everything is symbolic, systems of equations in terms of just a whole bunch of constants

David Roberts

In the absence of AC we know of no reason why Reinhardt shouldn't exist.

Jon Beardsley

oh that's right

and i'm not really down with AC anyway

David Roberts

mathematica.se, please

Jon Beardsley

is that a thing

Will

2:47 AM

ref/Solve in the mathematica documentation gives examples

Jon Beardsley

cool

David Roberts

I saw. But with homotopy type theory, you shouldn't need it.

Jon Beardsley

holy shit, it WILL NOT let me post even remotely fast enought

David Roberts

Yes, was doing that to me too

Jon Beardsley

can homotopy type theory fix my clogged kitchen sink?

Will

2:48 AM

only if the clogging is simply connected

Jon Beardsley

most likely not the case

David Roberts

Only if the clogging is nilpotent

Evan Jenkins

Don't try to fix clogged sink with Coq.

Jon Beardsley

hahhahaha

i already learned that the hard way.

David Roberts

Just use Require Import Sink

Jon Beardsley

2:50 AM

my sister asked me what i do, and i was trying to explain to her the notion of contractibility, and she got really frustrated, because you just can't shrink anything that small

or at least, you'd need some kind of hydraulics or something

Will

are we still talking about Coq?

Jon Beardsley

ZING

and also: ew. that's my sister bro.

David Roberts

Sorry, Require Import Sink. (missing full stop)

Jon Beardsley

Yeah, I didn't notice your mistake, my Coq is pretty rusty.

this is out of control. we're never going to get any grown up mathematicians in here

David Roberts