Speaker:  Sarah Rees, University of Newcastle, UK

Title: Harnessing geometry for computation in group theory

Abstract:
The family of automatic groups was defined by Thurston after
it was recognised that the underlying geometry of compact hyperbolic
manifolds could facilitate computation with their fundamental groups.
     G = < x_1, ..., x_n | r_1, ..., r_m >
is automatic if it possesses a set of representative words
which (a) is recognised by a finite state automaton (the most
basic form of theoretic computer) and (b) satisfies a particular
geometric `fellow traveller' condition. (For hyperbolic groups, the
set of all geodesic words satisfies the necessary conditions.)

This talk will briefly introduce automatic groups, 
explaining how their properties may be exploited computationally.
We shall look also at various non-automatic groups which, for
geometrical or computational reasons, seem to have a right to be
automatic, but are not, and examine ways in which this family of
groups might sensibly be extended.