From: matthew thomas gealy <mtgealy@midway.uchicago.edu>
Subject: Re: What is differential geometry (esp. w.r.t computability theory)?
Date: Sun, 3 Dec 2000 22:54:28 -0600
Newsgroups: sci.math
Summary: [missing]

> > I saw an announcement recently that Robert I. Soare is giving a lecture
> > on Computability Theory and Differential Geometry. I know what
> > computability theory is. Are these two areas particularly related?

I believe that the lecture would be related to recent work of Profs.
Alex Nabutovsky (I think from Toronto) and Shmuel Weinberger (Chicago).
One looks at Riem/Diff (the set up Riemannian metrics on a manifold up to
diffeomorphism, certainly on object from differential geometry), and
discovers that it has a fractal structure, where the fractal nature is
determined by non-trivial knowledge of computability theory.  A paper
relevant to this is

#68 The fractal nature of Riem/Diff I
at 
http://www.math.uchicago.edu/~shmuel/Bibliography.html