ABSTRACT
		(Fifteen Minute Contributed Talk)

	AMS BOULDER MEETING ON COMPUTABILITY THEORY 
	            JUNE 12-18, 1999

SPEAKER: Robert I. Soare, University of Chicago
TITLE: Computability and Differential Geometry
ABSTRACT:

Fix a manifold of dimension greater or equal five.  We consider
results in a recent paper by Alex Nabutovsky (Montreal) and Shmuel
Weinberger (Univ. of Chicago) for the structure RIEM/DIFF, the space
of Riemannian metrics on M modulo diffeomorphisms.  The authors show
how geometric problems, such as determining the depth of a local
minimum or the distance from one to another corresponds to a
computably enumerable sets.  We also consider a certain sequence of
c.e. sets which the author asked us to construct in order to sharpen
his results.