Alex

Google doesn't really give me anything relevant for 'raw geometry'

I think I've listened to all of riverside (and the pineapple thief, porcupine tree)

@BalarkaSen How do you know? I'm interested in most mathematics these days (although pdes haven't got a place in my heart yet)

Any music recommendations btw? I'm kinda dry

@BalarkaSen What is raw geometry?

I'm thinking about tensor triangular geometry, and the classification of t-structures on triangulated categories. Do you care about any tensor triangulated categories by any chance? (Maybe the stable homotopy category of finite spectra?)

What are you working on these days @BalarkaSen?

Some of my irl circle of friends have been vanishing due to graduation, moving countries etc, so I'm back to chat rooms haha

Hi there :D

@BalarkaSen I read it :P

@TedShifrin Not enough high quality content anymore? :P

@AMDG But once you fix an f and g those numbers are not arbitrary. Also n,m are not variables? They are natural numbers

So why are you saying 'an arbitrary number of inputs'

For a fixed f,g, there are only n and m inputs, right (respectively)?

But sure, you can consider $\Bbb C^n\times \Bbb C^m \to \Bbb C$ if you want

@AMDG I don't know what you mean by that. I just mean that normally you would want to consider $f(x_0,\dots, x_n)/g(x_0,\dots,x_n):\Bbb C^n\to \Bbb C$ where $g:\Bbb C^n\to \Bbb C-\{0\}$

@AMDG I mean it would be more reasonable if $n=m$ for example

Also it's kinda weird for $f,g$ not to be taken values from a common space, unless there's something specific you have in mind

Don't you mean $f:\Bbb C^n\to \Bbb C$ and $g:\Bbb C^m\to \Bbb C\backslash\{0\}$ at least?

@AMDG Where f and g are maps from what n+1 and m+1 dimensional spaces, to what space?

This theme continues en.wikipedia.org/wiki/…).

@AMDG It's because its the side length of the triangles, much like square numbers

@AMDG What do you mean by quotients in general? Quotient groups, quotient spaces, quotients of types of spaces under types of actions?

@AMDG triangular numbers

Well that goes without saying :')

Do you have a specific paper/notes in mind?

This maybe? swc.math.arizona.edu/aws/2019/2019WickelgrenNotes.pdf

I think it's sections 2,4,10, and 11 that I mainly want from this paper, but I'll ask my adviser tomorrow about it

The first section is definitely rather technical :')

To understand the second section, I've gone off to read Paul Balmer's paper on Witt groups

@loch Maybe I can ask you about the content some time, depending on how much you got through

I better get to reading this Levine paper, I'll be back later :D

See page 27 bottom to page 30

got it

Looks like I've never emailed you before

It's all elementary, but long

@BalarkaSen I can send them to you now if you want :D

Bloody kids these days with their valuation rings

He hated those young new found contraptions in ANT

Well Serre and someone else gave their reasons they're confident about

lmao, I'm sure you're joking, but I don't know the reference

He even abandoned them like a true chad

he's a massive player

Grothendieck had a bunch of children

Well, he also actually defined the Brauer group of a scheme, whose definition I recalled above (In his three paper series le groupe de brauer)

Actually upgrading to gerbes is reasonable, and Grothendieck tried that (for solving the period-index problem)

We've strayed too far from god

In Tannaka Duality for Geometric Stacks the definition of the analytification of a (geometric) algebraic stack of finite type over C is seemingly not given. Does anyone know a reference with a definition?