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 […]

I tried making bread, but with significantly less flour than neccessary (and therefore, far more water than needed). The result was very much like cooked paste. It was pointed out to me that since the essence of bread is flour, trying to get by with less flour was undermining the very essence of […]

Jenn is a fabulous program for visualizing the Cayley graphs of finite Coxeter groups. The pictures are absolutely beautiful (oh, symmetry!).

Sometimes I’m scared that, at some point in my past, I opened a pair of parentheses without closing them. Even worse, I’m sure I’ve feared this very thing in the past. Then again, maybe this is the common fear of all schemers: that our whole lives might now be a parenthetical comment.

I gave a couple of seminar talks on Lück, W. Approximating -invariants by their finite-dimensional analogues. Geom. Funct. Anal. 4 (1994), no. 4, 455—481. Here’s the main result in the paper. Let be a CW-complex, and filter as with so that . Let be […]

Perhaps a half-dozen times in the past week, I’ve read sentences with contain the phrase “must needs.” I have never considered this construction before; frankly, it sounds totally bizarre to my inner ear (my spiritual inner ear, that is). Thus, it must needs be that I’ve been teleported to another world, a world in which […]

I gave a seminar talk on Herlihy, Maurice; Rajsbaum, Sergio Algebraic topology and distributed computing—-a primer. Computer science today, 203—217, Lecture Notes in Comput. Sci., 1000, Springer, Berlin, 1995. This paper doesn’t do it (but Rajsbaum’s MSRI talk did), but the result can be reformulated combinatorially, so that the algebraic topology […]

I’m still trying to find (two!) new roommates (since my current roommate bought a place, and is moving out on December 15th). If you know anybody who would like to move in with me, I’d love to know about it. There are some pictures of my home.