Moduli Spaces and Arithmetic Dynamics

Joseph H. Silverman, Brown University, Providence, RI, USA

The monograph is an expanded version of Silverman's lecture notes from a workshop held in May 2010, on the topic of moduli spaces of dynamical systems. It is a pleasure to read, as much as it was a pleasure to attend the lectures. Silverman writes well: he explains the mathematics clearly and includes many explicit examples. Best of all, he has peppered the text with leading questions and side remarks, opening doors to hundreds of potential research projects. It will be a useful reference for students and senior researchers alike. ...Every chapter of this monograph offers multiple entries, many conjectural, in the "Silverman dictionary." For anyone already familiar with both the arithmetic theory of elliptic curves and the traditionally analytic results about these dynamical systems, recent results in arithmetic dynamics make the analogies beautifully apparent; with this book, Silverman helps the rest of us to appreciate the similarities." - Laura De Marco, University of Illinois at Chicago

• PrefaceIntroductionModuli spaces associated to dynamical systemsThe geometry of dynamical moduli spacesDynamical moduli spaces–Further topicsDynatomic polynomials and dynamical modular curvesCanonical heightsPostcritically finite mapsField of moduli and field of definitionSchedule of talks at the Bellairs workshopGlossaryBibliographyIndex