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 Andr�-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.

About the Author

Charles Favre is a CNRS senior researcher based at the �cole Polytechnique in Paris. He is the coauthor of The Valuative Tree and the coeditor of Berkovich Spaces and Applications. Thomas Gauthier is professor of mathematics at the Universit� Paris-Saclay.

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