ITT: Beautiful equations

>>7922610
What does it mean? I guess Aut(G) implies G is some algebraic structure, probably a group. and M might be a moduli space.

Thats my best guess.

>>7922670
Automorphism group.
Self isomorphisms, they all have inverses. So Aut(g) is always a group no matter what object you are working with. For example G could be a set, a tolopogical space, a differential structure, a group, ring, feild or vector space.

The cool thing is you can look at a automorphism group and get some nice group theory out of anything you can define an isomorphism for.

>>7922670
Aut(G) is the autism group.

>>7922790
he obviously knows that, it's how he was able to deduce that G is some algebraic structure
and he's right, G usually is a group
he's right about the moduli spaces too, the subscript on a moduli space represents moduli stacks of stable curves of genus g with n marked points
i don't know what the bar means

this is definitely some fucked up research number theory
i'd start with faber's papers, and then try looking through some of mumford's stuff

>>7923359
the bar means compactification, in this case probably the deligne-mumford compactification

i don't think it's number theoretic at all, more in the realm of complex geometry, the things in square brackets [] are probably homology classes since 'virt' usually means to take the virtual class

>>7922610
Looks like the mackey formula applied but I'm a representation theory noob so I barely know what that is. Frigging algebraists with their bizarre and inconsistent notations.

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looks like a poma paper to me
here's a bit of her work

[eqn]\mathcal{L}_{\mathrm{QED}} = \overline{\psi} (i \gamma^\mu D_\mu - m) \psi - \frac{1}{4} F_{\mu \nu} F^{\mu \nu}[/eqn]
>inb4 feynman memes

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can somebody find the paper the OP equation is from
i've been looking for an hour and i can't find it

>>7922610
Beautiful things shouldn't have such convoluted notations.

>>7923653
have you even seen old mathematics notation
everybody had their own set of notation and they would spend a good three or four pages explaining what their shitty system of underscores and lines of vertical dots meant
i'm not sure when notation became standardized but i do know it was a relatively recent thing

tl;dr beauty transcends appearance