January 28:
Speaker: Ted Turner (SUNY Albany)
Title: Test elements in torsion free hyperbolic groups
Abstract: A Test Element g in a group G is an element with the property that
any endomorphism 
fixing g is an automorphism. At first glance, one would imagine
test elements to be rather rare, but quite the opposite seems to be the case.
A test element in a non-alelian free group is characterized by the fact that it lies
in no proper retract and such elements abound.
I will discuss the techniques used to understand test elements and progress on the
following conjecture.
CONJECTURE. Every torsion free hyperbolic group has test elements.