Description

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 André-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.

The Arithmetic of Polynomial Dynamical Pairs: (AMS-214)

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New mathematical research in arithmetic dynamicsIn The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical... Read more

    Publisher: Princeton University Press
    Publication Date: 14/06/2022
    ISBN13: 9780691235479, 978-0691235479
    ISBN10: 0691235473

    Number of Pages: 252

    Non Fiction , Mathematics & Science , Education

    Description

    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 André-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.

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