New mathematical research in arithmetic dynamics In The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from arithmetic geometry and holomorphic dynamics, they prove an "unlikely intersection" statement for such pairs, thereby demonstrating strong rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many postcritically finite parameters, proving the dynamical Andre-Oort conjecture for curves in this context, originally stated by Baker and DeMarco. This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.

Book Information
ISBN 9780691235479
Author Charles Favre
Format Paperback
Page Count 252
Imprint Princeton University Press
Publisher Princeton University Press
Weight(grams) 156g