We are Ivan and Rachel Andrus. We are living in Budapest while Ivan is studying for a Ph.D. in Mathematics. Rachel, Avery (the little munchkin) and Evelyn (the littler munchkin) have fun while he’s at school.
Ivan likes Mathematics, computers, violin, food (especially the good and foreign kinds), and playing with the kids.
Rachel likes Neuroscience, baking, cooking, food blogs, karate, and when Ivan plays with the kids.
This is our life. Or some of it anyway.
I greatly appreciated your Periodic table for the CFSGs. I am an amatuer who has been trying to get a grip on this topic for a while, with moderate success. I tend to want as concrete, geometric interpretation for the groups as I can get, which is easy for the classical ones via the regular poyhedra. I keep reading that all FSG’s have a correspondence with particular geometric objects, but other than the Leech lattice I can’t find specifics. Is this true for all FSGs or is it just wishful thinking?
I certainly have no expertise in that area. All the Lie-type groups, and the alternating groups, are associated with “buildings” (about which I know nothing). They were introduced by Tits in the 1950’s. As I understand it, there is currently work being done (e.g. here) trying to find a coherent set of geometries for the sporadic groups. You may (or may not) enjoy this article about the Matthieu groups and their geometries, and this paper which has some background about the general case. I’m sure there are better resources, but I couldn’t find them.
I would actually like to put a picture behind each of the groups in the table, but I didn’t get around to it since I don’t know that much about it. Once you get it figured out, let me know. :-)