Workshop on Geometric Group Theory and Computer Science
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			      Venue

	July 5-9, 1998. Mount Holyoke College, South Hadley, MA.
	
	This workshop is one of the 1998 AMS-IMS-SIAM Joint Summer 
	Research Conferences in the Mathematical Sciences. See the 
	October, November or December AMS Notices for more information.
	

			Organizing Committee

	Gilbert Baumslag, Martin Bridson, James Cannon, 
	Robert Gilman (chair), Michael Shapiro


		Partial List of Speakers and Participants

	John Cannon, David Epstein, Steven Gersten, Susan Hermiller, 
	Chuck Miller, Sarah Rees, Mark Sapir, Charles Sims, 
	Paul Schupp, John Stallings.

         
                    	Scientific Program

Over the last several years the study of groups given by generators and
relations has been invigorated by an influx of ideas from geometry,
topology and computer science; the resulting collection of techniques
and points of view has become known as geometric group theory.  The
workshop is devoted to computer theoretic aspects of this new field. 

	     Automatic Groups and Word Hyperbolic Groups

Automatic groups and word hyperbolic groups are perhaps the best known
products of geometric group theory.  At the beginning of the century Max
Dehn solved the word and conjugacy problems for fundamental groups of
orientable surfaces by making use of the underlying hyperbolic geometry.
Dehn's ideas led to the theory of small cancellation groups and more
recently to some striking connections between geometry and finite
automata.  The geometry of the known compact 3-manifolds is reflected by
restrictions on the structure of their fundamental groups, and in many
cases the spirit of these restrictions is captured by the fact that
multiplication in the fundamental group can be carried out by finite
automata.  This fact leads to the definition of automatic groups and to
previously unsuspected connections with computer science.

Word hyperbolic groups are algebraic analogs of groups acting
cocompactly on spaces of negative curvature.  They are defined by
imposing geometric conditions on the Cayley diagram of a group.  It is
remarkable that these groups are also characterized by concepts from
computer science.  They are precisely the groups whose word problem can
be solved by a length reducing rewriting system confluent at the
identity.

              Further Connections with Computer Science

Another line of research, initiated by computer scientists, concerns the
structure of a group and the properties of the formal language of all
words
defining the identity with respect to a fixed set of generators.  This
program has produced a number of interesting results, among them the
characterization of groups with a free subgroup of finite index as those
groups whose word problem is a context-free language, and a 
complexity-theoretic analog of the Higman Embedding Theorem.

Geometric group theory has also inspired new approaches to computation
with finitely presented groups.  It is well known that almost all
questions about these groups are recursively unsolvable. The computational
challenge is to devise programs which will work often enough to be
useful.