The Arithmetic of Polynomial Dynamical Pairs
Title | The Arithmetic of Polynomial Dynamical Pairs PDF eBook |
Author | Charles Favre |
Publisher | Princeton University Press |
Pages | 252 |
Release | 2022-06-14 |
Genre | Mathematics |
ISBN | 0691235473 |
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
Title | The Arithmetic of Polynomial Dynamical Pairs PDF eBook |
Author | Charles Favre |
Publisher | Princeton University Press |
Pages | 252 |
Release | 2022-06-14 |
Genre | Mathematics |
ISBN | 0691235481 |
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.
Ramification Theoretic Methods in Algebraic Geometry
Title | Ramification Theoretic Methods in Algebraic Geometry PDF eBook |
Author | Shreeram Abhyankar |
Publisher | |
Pages | 118 |
Release | 1959 |
Genre | Algebraic fields |
ISBN |
Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127
Title | Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 PDF eBook |
Author | Gerd Faltings |
Publisher | Princeton University Press |
Pages | 118 |
Release | 2016-03-02 |
Genre | Mathematics |
ISBN | 1400882478 |
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
Polynomials, Dynamics, and Choice
Title | Polynomials, Dynamics, and Choice PDF eBook |
Author | Scott Crass |
Publisher | CRC Press |
Pages | 190 |
Release | 2022-08-23 |
Genre | Mathematics |
ISBN | 1000637085 |
Working out solutions to polynomial equations is a mathematical problem that dates from antiquity. Galois developed a theory in which the obstacle to solving a polynomial equation is an associated collection of symmetries. Obtaining a root requires "breaking" that symmetry. When the degree of an equation is at least five, Galois Theory established that there is no formula for the solutions like those found in lower degree cases. However, this negative result doesn't mean that the practice of equation-solving ends. In a recent breakthrough, Doyle and McMullen devised a solution to the fifth-degree equation that uses geometry, algebra, and dynamics to exploit icosahedral symmetry. Polynomials, Dynamics, and Choice: The Price We Pay for Symmetry is organized in two parts, the first of which develops an account of polynomial symmetry that relies on considerations of algebra and geometry. The second explores beyond polynomials to spaces consisting of choices ranging from mundane decisions to evolutionary algorithms that search for optimal outcomes. The two algorithms in Part I provide frameworks that capture structural issues that can arise in deliberative settings. While decision-making has been approached in mathematical terms, the novelty here is in the use of equation-solving algorithms to illuminate such problems. Features Treats the topic—familiar to many—of solving polynomial equations in a way that’s dramatically different from what they saw in school Accessible to a general audience with limited mathematical background Abundant diagrams and graphics.
Flows on Homogeneous Spaces. (AM-53), Volume 53
Title | Flows on Homogeneous Spaces. (AM-53), Volume 53 PDF eBook |
Author | Louis Auslander |
Publisher | Princeton University Press |
Pages | 107 |
Release | 2016-03-02 |
Genre | Mathematics |
ISBN | 1400882028 |
The description for this book, Flows on Homogeneous Spaces. (AM-53), Volume 53, will be forthcoming.
Curvature and Betti Numbers. (AM-32), Volume 32
Title | Curvature and Betti Numbers. (AM-32), Volume 32 PDF eBook |
Author | Salomon Bochner Trust |
Publisher | Princeton University Press |
Pages | 190 |
Release | 2016-03-02 |
Genre | Mathematics |
ISBN | 1400882206 |
The description for this book, Curvature and Betti Numbers. (AM-32), Volume 32, will be forthcoming.