Arithmetic Groups

The Nielsen-Thurston theory of surface homeomorphism can be thought of as a surface analogue to the Jordan Canonical Form.  I will discuss my progress in developing a similar decomposition for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour.  This forms a significant barrier to translating specific arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!