Prof. Dr. Bachir Bekka, Université de Rennes I, Vortrag: Dynamics of groups of affine transformations of homogeneous spaces
Donnerstag, 02.06.2016 16:30 im Raum M5
Abstract : Interesting examples of group actions on measure spaces are given by actions on homogeneous spaces. The setting is as follows.
Let G be a locally compact group (often a Lie group or a linear algebraic group) and H a lattice in G.
Every group of affine transformations of G preserving H acts on the homogeneous space G/H in a measure preserving way.
We will discuss some questions concerning these actions, such as ergodicity, existence of a spectral gap or strong ergodicity
(in the sense of K. Schmidt). The results we will present concern two classes of groups, requiring different approaches:
the case where G is semisimple and the acting group a consists of translations and the case where G is nilpotent and the acting group
consists of automorphisms.