Free group automorphisms seem to share a lot with surface homeomorphisms. While tools for studying mapping class groups do not always have counterparts in the free group setting, it has nevertheless been extremely fruitful to mimic these tools as much as we can. This talk will describe our attempt to develop one important missing analogue. Nielsen--Thurston theory gives a canonical representation of a surface homeomorphism's isotopy class. Currently, no such canonical representation of free group outer automorphisms exists.
In the introductory talk, I will describe the Nielsen--Thurston theory in some detail and outline the proof of this canonical representation. For the research talk, I will discuss the main obstacles to carrying out the same argument with free group automorphisms. Fortunately, it appears these obstacles are surmountable and I will discuss some partial results in this direction.
Join Zoom meeting ID 978 1075 8446 or via the link below. Passcode: A group is called an ________ group if it admits an invariant mean. (8 letters, lowercase)