Geometry and Dynamics of Homeomorphisms in Dimensions 1 and 2

Time/Place:  This Seminar will take place as a Blockseminar in the week 17-21 Februar.

Topic: Although the classification of compact manifolds of dimension 1 and 2 is well known, the dynamics of automorphisms and group actions is very rich. In the one-dimensional case, in which case one considers actions on the circle, one can use the order structure to obtain obstructions. The most prominent example of this kind are obstructions to actions of higher rank lattices, giving results on the so-called Zimmer programme. For example any action of a finite index subgroup of $SL(3,\Z)$ that acts on the circle must have finite image.  The first 8 talks of the Seminar will focus on actions of this kind.

A key tool to understand the dynamics of actions on the circle is the so-called Poincare rotation number. This can be generalised to higher dimension and in the last part of the seminar we will consider this generalization particularly in the case of the 2-trous and will explore the relation to dynamics. We will also discuss the geometry of groups in terms of (stable) commutator lengths.

Programme: You can find a preliminary list of talks of talks here.

Further Information: In case of questions please do not hesitate to contact me jonathan.bowden@ur.de