AGR Seminar: Prof. George Willis -- Amenability, measure and randomness in groups

This colloquium will explain some of the background and significance of the concept of
amenability.  Arguments with finite groups frequently, without remark, count the number
of elements in a subset or average a function over the group.  It is usually important
in these arguments that the result of the calculation is invariant under translation.
Such calculations cannot be so readily made in infinite groups but the concepts of
amenability and translation invariant measure on a group in some ways take their place.
The talk will explain this and also say how random walks relate to these same ideas.