The Arithmetic of Polynomial Dynamical Pairs: (AMS-214)
- Published (US):
- Jun 14, 2022
- Published (UK):
- Jul 5, 2022
- 6.13 x 9.25 in.
- 18 b/w illus.
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.