abstract: Tropical geometry is a field in which polyhedral geometry and combinatorics are used to describe degenerations in algebraic geometry: the tropical moduli space is a polyhedral complex that can be thought of as the “space of paths to infinity” in moduli space.
Thurston showed that postcritically finite rational functions can be thought of as fixed points of a pullback map on Teichmuller space; Koch showed that the pullback map descends to an algebraic correspondence on moduli space. We give a preliminary description of the tropical moduli space correspondence, and its relationship with Thurston’s pullback map.