Ian Leary

Smith groups and Kropholler's hierarchy
joint with Goulnara Arzhantseva, Martin Bridson, Tadeusz                     
Januszkiewicz, Peter Kropholler, Ashot Minasyan and Jacek                     
\'Swi\c{a}tkowski)

We construct infinite groups that have strong fixed-point
properties for actions on finite-dimensional spaces.  These
methods also allow us to construct groups that demonstrate
that Kropholler's hierarchy of groups is far longer than was
previously known.