talk was fine, but not great

wrong crowd to be prattling on about brown-gitler spectra to

what's up with you being redacted all the time, @ArnavTripathy

@Eric I wonder what crowd is right to prattle on about Brown-Gitler spectra...

glad talk went well :)

i'm having computer troubles lately

hey Tyler

Hey, @JonBeardsley I just want to make an addendum to my bundle gerbe crash course

I know you're not here right now, but you'll read this when you get back

Recall that I said we had a groupoid X_1 => X_0 such that X_1 -> X_0 \times_M X_0 is a principal A-bundle (M:= X_0/X_1).

Well, that is a bit unmotivated.

One can instead take the bundle of groups Lambda X_1 -> X_0, where \Lambda X_1 is the pullback of X_1 -> X_0 \times_M X_0 along the diagonal X_0 -> X_0\times_M X_0

(in the above we don't a priori assume that we have an A-bundle)

This bundle of groups is essentially all the automorphism groups Aut(x) glued together for all objects x\in X_0, parameterised by X_0

We then can say X -> M is an A-bundle gerbe if \Lambda X_1 -> X_0 is isomorphic to the trivial bundle of groups A \times X_0 -pr-> X_0

That's all :-)

yo

interesting

thanks

i'm afraid i still find the whole construction rather unmotivated

oh, there was more coming, but you left :(

i was just going to ask about where we find ourselves used bundle gerbes, feel free to reply later if you'd like.

hey jon. sorry, I'm mostly just lurking at this point.

oh no worries

:)

some interesting convos have happened here recently

it's sort of neat that it's all recorded

so here's something that might be a neat topic for discussion, if anyone ever comes around and wants to talk: recall the spectra $X(k)$, which are the Thom spectra of the maps $\Omega SU(k)\to \Omega SU\simeq BU$. This is pretty much all I talk about these days... sorry.

Well, here's a neat fact, if $E$ is complex oriented then $E^\ast(\mathbb{C}P^k)\cong E_\ast[x]/(x^{k+1})$ and $E_\ast[b_1,\ldots,b_{k-1}]$, sooooo part of me is wondering whether or not one might compare $X(k)$ to $\mathbb{A}^k$, and the notion of an $n$-orientation is sort of similar to the cogroup structures I described above.

whoops, that should say $E_\ast(X(k))\cong E_\ast[b_1,\ldots,b_{k-1}]$

in other words, one notes that $\pi_\ast(HR\wedge X(k))$ is the affine $R$-line, so one might hope that $\pi_ast(X(k))$ is something like.... the affine $\mathbb{S}$-line. LOL

erm, affine $R$-$k-1$-space, or whatever

and erm, affine $\mathbb{S}-(k-1)$-space

what's up with your chats, arnav

they are straight Messed Up, brother

well you know how it is

@SeanTilson bob bruner, audience of 1

was Bob in here?

oh i get it. he wants to hear you go on and on about Brown-Gitler spectra

yeah

yeah pretty much

Welcome @FernandoMura

oops

(sic)

Arnav, how are you doing these days man?

Marco Robalo just told me he met you in Los Angeles

I'm pretty good

yeah usc was cool

how are you