In seminar today, Okun pointed out the following interesting observation; for any finitely generated group , you can define its growth series , where is the length of the shortest word for . The first observation is that is often a rational function, in which case makes sense. The second […]

Cartan proved that every finite-dimensional real Lie algebra comes from a connected, simply-connected Lie group . I hadn’t known the proof of this result (and apparently it is rather uglier than one might hope), but Gorbatsevich, V. V. Construction of a simply connected group with a given Lie algebra.(Russian) Uspekhi […]

What can be said about the history of static electricity? Did Greek science know about it? Any medieval experiments with static electricity? It’s sort of interesting that people knew about magnetism and electricity for hundreds of years before finding many good uses for that knowledge (granted, compasses and potentially batteries for electroplating, but these […]