Sigurdur Helgason will continue his research into the range and kernel of the Radon transform associated with a double fibration of a homogeneous space. A prototypical question here involves determining a function on a sphere from knowledge of its averages over all great subspheres of a given dimension. Helgason will be joined by David Vogan who will investigate unipotent unitary representations of real semisimple groups. It is relatively easy to see from dimensionality considerations that certain Radon transforms are not injective, this typically happens in the case of codimension at least two. Whereas in the linear or codimension one case the transform is injective. Helgason's work is directed towards a description of the kernel in the former case and towards inversion formulas in the latter situation. One of Vogan's goals is to find a precise definition of unipotent representation using geometric techniques. This will involve an attempt to relate two previously investigated approaches.
