Polynomial invariants of graph maps and applications to Out(Fn) and Mod(Sgn)

Mapping classes on surfaces and outer automorphisms of the free group define dynamical systems that can often be described in terms of graph maps.   In this  talk we present algebraic and geometric invariants of graph maps and relate these to  the corresponding invariants in the geometric setting,  In particular, we present a unified way to view  Alexander polynomials and the lesser known Teichmueller polynomials.  This talk is based on joint work with Kasra Rafi and Yael Algom-Kfir.