I gave a Farb student seminar talk on a lovely paper, Davis, Michael W. Groups generated by reflections and aspherical manifolds not covered by Euclidean space. Ann. of Math. (2) 117 (1983), no. 2, 293—324. I also used some of the material in Davis, Michael W. Exotic aspherical manifolds. […]

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 […]

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

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 […]

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 […]

Today in Geometry/Topology seminar, quasihomomorphisms were discussed, i.e., the set of maps such that is uniformly bounded, modulo the relation of being a bounded distance apart. These come up when defining rotation and translation numbers, for instance. Anyway, Uri Bader mentioned that these quasihomomorphisms form a field, isomorphic to , under pointwise […]

There are some questions about outer space that I would like to be able to answer. Some nice survey articles look to be: Bestvina, Mladen The topology of . Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 373—384, Higher Ed. Press, Beijing, 2002. and also: […]

By the Gauss-Bonnet theorem, the volume of a hyperbolic 4-manifold is proportional to its Euler characteristic. There are examples, constructed explicitly in Ratcliffe, John G.; Tschantz, Steven T. The volume spectrum of hyperbolic 4-manifolds. Experiment. Math. 9 (2000), no. 1, 101—125. of hyperbolic 4-manifolds with every positive integer as their […]

Gromov, M.; Piatetski-Shapiro, I. Nonarithmetic groups in Lobachevsky spaces. Inst. Hautes Études Sci. Publ. Math. No. 66 (1988), 93—103. Vinberg, … Margulis’ amazing arithmeticity theorem says that irreducible lattices in Lie groups of high () rank are arithmetic. But has rank 1, so a question is how to produce non-arithmetic lattices. […]

From Recent Advances in the Langlands Program, quoted in This Week’s Finds: First of all, it should be remarked that according to the Tannakian phylosophy, one can reconstruct a group from the category of its finite-dimensional representations, equipped with the structure of the tensor product. I suppose one should think of […]