Today, I was about to sit down and read a paper (in French—I may not speak in tongues, but apparently I can read in tongues, so to speak!), and I thought to myself about how nice it would be to have a cookie. I went to Uncle Joe’s, I went to the Classics Cafe, […]

Someone contacted me with some questions about Bayesian document clustering; with that inspiration and a free afternoon a few weeks ago, I took a Hebrew bible and built a matrix where equals the frequency of the -th (Hebrew!) word in the -th chapter of Genesis. I calculated its singular value decomposition (supposedly […]

There are usually courses at Mathcamp about surfaces; there should be courses about orbifolds! For instance, knowing that the smallest hyperbolic orbifold is the (2,3,7)-orbifold, having orbifold Euler characteristic , immediately gives that a closed hyperbolic surface of genus has no more than isometries (preserving orientation); this is “Hurwitz’ theorem.” Just to […]

At a recent Pizza Seminar, Matt Day gave a lovely talk explaining why it isn’t possible to classify 4-manifolds. An algorithm for deciding whether two closed 4-manifolds are homeomorphic gives an algorithm for deciding whether a closed 4-manifold is simply connected, and therefore (since every finitely presented group is the fundamental group of a 4-manifold), and […]

This is a question I wandered into accidentally years ago now, which I think other people might be amused to think about (or more likely, put on an abstract algebra exam). Let be a group, and a subgroup of . Is always isomorphic to , for some subgroups ? But beware!—I […]