Arithmetic of Polynomial Dynamical Pairs

<p><b>New mathematical research in arithmetic dynamics</b> <p/>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. <p/>This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.</p>