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

Charles Favre and Thomas Gauthier present new mathematical research in arithmetic dynamics, studying one-dimensional algebraic families of pairs given by a polynomial with a marked point. They prove an "unlikely intersection" statement and describe families in the moduli space of polynomials, proving the dynamical André-Oort conjecture for curves. This research area combines sophisticated tools from various branches of mathematics.

Format: Paperback / softback
Length: 252 pages
Publication date: 14 June 2022
Publisher: Princeton University Press

In their groundbreaking work, Charles Favre and Thomas Gauthier delve into the realm of arithmetic dynamics, presenting a fresh perspective on the study of one-dimensional algebraic families of polynomial dynamical pairs. Through the fusion of techniques from arithmetic geometry and holomorphic dynamics, the authors unveil an intriguing "unlikely intersection" statement, showcasing the remarkable rigidity properties of these pairs. Their research extends further to encompass one-dimensional families in the moduli space of polynomials with infinitely many postcritically finite parameters, ultimately proving the dynamical André-Oort conjecture for curves within this context. This groundbreaking exploration invites scholars and enthusiasts alike to venture into a vibrant and rapidly evolving research domain, where the convergence of diverse mathematical disciplines yields profound insights and breakthroughs.

In their groundbreaking work, Charles Favre and Thomas Gauthier delve into the realm of arithmetic dynamics, presenting a fresh perspective on the study of one-dimensional algebraic families of polynomial dynamical pairs. Through the fusion of techniques from arithmetic geometry and holomorphic dynamics, the authors unveil an intriguing "unlikely intersection" statement, showcasing the remarkable rigidity properties of these pairs. Their research extends further to encompass one-dimensional families in the moduli space of polynomials with infinitely many postcritically finite parameters, ultimately proving the dynamical André-Oort conjecture for curves within this context. This groundbreaking exploration invites scholars and enthusiasts alike to venture into a vibrant and rapidly evolving research domain, where the convergence of diverse mathematical disciplines yields profound insights and breakthroughs.

Weight: 398g
Dimension: 155 x 234 x 17 (mm)
ISBN-13: 9780691235479