Free group automorphisms from a logician's point of view
Abstract
We will record some surprising and lesser-known properties of free groups, and use these to give a model theoretic analysis of free group automorphisms and orbits under Aut(F). This will result in a neat geometric description of (a logic-flavoured analogue of) algebraic closures in a free group. An almost immediate corollary will be that elementary subgroups of a free group are free factors.
I will assume no familiarity with first-order logic and model theory - the beginning of the talk will be devoted to familiarize everyone with the few required notions.
Higher Teichmüller spaces
Abstract
The Teichmüller space for a closed surface of genus g is the space of marked complex/hyperbolic structures on the surface. Teichmüller space also identifies with the space of Fuchsian representations of the fundamental group into PSL(2,R) (mod conjugation). Higher Teichmüller theory concerns special representations of surface (or hyperbolic) groups into higher rank Lie groups of non-compact type.