# Representation Theory, Complex Analysis and Integral Geometry

Hausdorff Trimester Program

June - August 2007

A program joint with the Max-Planck-Institute for Mathematics.

**Organizers: **Simon Gindikin, Bernhard Krötz

**HIM coordinators: **Omer Offen, Eitan Sayag

Integral Geometry has its origins in the 19th century where one studies integral transforms of geometric nature. An important later example is the Radon transform, which starting with the inversion formula led to remarkable explicit formulas. In trying to generalize this explicit analysis one was looking for more general geometric structures where something like this can be done. As often in mathematics large symmetry is a great help and the most symmetric objects are Lie groups, here complex semi simple Lie groups, and related homogeneous spaces. This way representation theory entered in a very natural way and plays a central role in the modern development.

The aim of the program was to bring together experts from the different mathematical areas which are involved into the subject to stimulate discussions and new research. To educate the younger people (and not only the younger) several lecture series by outstanding mathematicians were organized.

The program was originally planned at the Max Planck Institute on a smaller scale, which in particular meant that senior mathematicians dominated. The foundation of the Hausdorff Institute allowed to enlarge the program significantly by mainly inviting additional young researchers of very high level.