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Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces
This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is self-contained, including an overview of preliminaries for each respective topic. This approach captures the spirit of the original lectures, which prepared graduate students and those new to the field for the technical talks in the program. The four chapters turn the spotlight on the following pivotal themes: The basic notions of o-minimal geometry, which build to the proof of the Ax–Schanuel con...
Do Not Erase
A photographic exploration of mathematicians’ chalkboards “A mathematician, like a painter or poet, is a maker of patterns,” wrote the British mathematician G. H. Hardy. In Do Not Erase, photographer Jessica Wynne presents remarkable examples of this idea through images of mathematicians’ chalkboards. While other fields have replaced chalkboards with whiteboards and digital presentations, mathematicians remain loyal to chalk for puzzling out their ideas and communicating their research. Wynne offers more than one hundred stunning photographs of these chalkboards, gathered from a diverse group of mathematicians around the world. The photographs are accompanied by essays from each math...
O-Minimality and Diophantine Geometry
This book brings the researcher up to date with recent applications of mathematical logic to number theory.
Algorithmic Number Theory
This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, July 2006. The book presents 37 revised full papers together with 4 invited papers selected for inclusion. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.
Point-Counting and the Zilber–Pink Conjecture
Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.
Algorithmic Number Theory
An introduction to number theory for beginning graduate students with articles by the leading experts in the field.
Computational Aspects of Modular Forms and Galois Representations
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounde...
The Oxford Handbook of Intellectual Property Law
A comprehensive overview of intellectual property law, this handbook will be a vital read for all invested in the field of IP law. Topics include the foundations of IP law; its emergence and development in various jurisdictions; its rules and principles; and current issues arising from the existence and operation of IP law in a political economy.
Model Theory and the Philosophy of Mathematical Practice
Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.
Improving Breast Imaging Quality Standards
Mammography is an important tool for detecting breast cancer at an early stage. When coupled with appropriate treatment, early detection can reduce breast cancer mortality. At the request of Congress, the Food and Drug Administration (FDA) commissioned a study to examine the current practice of mammography and breast cancer detection, with a focus on the FDA's oversight via the Mammography Quality Standards Act (MQSA), to identify areas in need of improvement. Enacted in 1993, MQSA provides a general framework for ensuring national quality standards in facilities performing screening mammography, requires that each mammography facility be accredited and certified, and mandates that facilitie...
