This Week’s Finds in Mathematical Physics (Week 263)
Posted by John Baez
In week263 of This Week’s Finds, see the deep atmosphere of Titan:
Then read about the work of John Thompson and Jacques Tits, who won the 2008 Abel Prize. Learn how to build a group as a layer cake with simple groups as layers. And see an example of a BruhatTits building!
Here are some questions I had when writing this Week’s Finds:
 People think the atmosphere of Titan looks red because of tholins. But what are tholins, exactly? I want to see the actual chemical structure of some tholins! How are they related to polycyclic aromatic hydrocarbons (discussed in week258)? Do they both fit into some grand chemical cycle that takes place out in space? Why are places like Titan, Triton and Ixion so full of tholins?
 What’s the importance of the result John Thompson proved for his PhD thesis — the nilpotence of Frobenius kernels? It seems cool, and related to groupoidification, but I don’t grok it.

What the heck is really going on with finite simple groups? Yes, that’s a very broad question… but I want to find some way to sink my teeth into this subject, and I’m not sure how to proceed. The classification theorem seems too technical for me to enjoy at this stage of my development. I really like thinking of finite groups as symmetry groups of ‘incidence geometries’, so maybe I should learn about Mathieu groups as symmetries of Steiner systems and codes, the Higman–Sims group as symmetries of the Higman–Sims graph, and so on. It’s a little intimidating to think about things like this, though:
What are the overarching ideas? Maybe I should start by taking another crack at Conway and Sloane’s Sphere Packings, Lattices, and Groups, or the 2volume Geometry of Sporadic Groups by Ivanov and Shpectorov.  What’s a definition of building that I can remember and explain? I’ve been through lots of examples, so I know the idea, but I haven’t thought about the definition lately, and I learned from writing this Week that it’s not crisp in my mind. I’d like to explain it clearly enough to provide an introduction for what Todd Trimble wrote about buildings! Hmm, maybe I should just reread what he wrote, and then explain it, so I remember it.
Given the depressingly puny response to my last list of questions I’m not sure it makes sense to continue asking them here — but maybe this is the sort of thing that you have to do for a while before people catch on.
(I would include these questions in the version on my website — that might work better — but I don’t really want more email. I’d like people to answer on this blog!)
Re: This Week’s Finds in Mathematical Physics (Week 263)
Would it be helpful to say “nonabelian group cohomology” here, instead of “nonabelian cohomology”?
I have become accustomed to thinking of “nonabelian cohomology” as the classification of $G$torsors ($G$bundles) on spaces, for $G$ some $n$group, or equivalently as the descent with coefficients in an $n$group.
That seems to be the way the term has been used by J. Giraud, John Roberts, Ross Street, Larry Breen and others, and it is the way it seems to be used in the approach to $\infty$stacks via simplicial presheaves by Jardine, Toën and others.
I am thinking of nonabelian group cohomology as the special case of equivariant nonabelian cohomology over a point.
It’s just a matter of terminology, of course.