Disks in the Heisenberg Group (4/6/05)
This is probably my favorite talk out of all those I've given as of
summer of 2006. It featured a proof by pictures of the fact that H,
the 3-dimensional integral Heisenberg group, is not automatic, and
there's even a teaser trailer! Originally,
this was going to serve as a warm-up to my oral exam, in which I was
hoping to present a proof that SL(3,Z) is not automatic, but alas, I
couldn't understand how to compute the norm of a particular
differential form (and my advisor advised against me bothering the
great professor Epstein with such a trivial concern).
Here are some notes of an earlier,
more technical version of the talk. The trailer shows big disks in the
Cayley graph of the H (with respect to a natural generating set), and
I made it with SketchUp, way
before Google gobbled them up.
Cayley graph of H:
Disk with boundary w1:
And disk with boundary w2:
From above:
From side:
From below:
