The Arithmetic of Polynomial Dynamical Pairs (AMS-214)

<p><b>New mathematical research in arithmetic dynamics</b><br><br>In <i>The Arithmetic of Polynomial Dynamical Pairs</i>, 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 André-Oort conjecture for curves in this context, originally stated by Baker and DeMarco.<br><br>This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.</p>