 He is a leading expert in splittings and accessibility of discrete groups, groups acting on graphs and trees, JSJ-decompositions, the topology of 3-manifolds and the structure of their fundamental groups.Since 1971 several mathematicians have been working on Wall's conjecture, posed by Wall in a 1971 paper, which said that all finitely generated groups are accessible.Roughly, this means that every finitely generated group can be constructed from finite and one-ended groups via a finite number of amalgamated free products and HNN extensions over finite subgroups.