Panoramas et Syntheses Volume: 52
2017; 284 pp; Softcover
MSC: Primary 03; 11; 14; 22;
Print ISBN: 978-2-85629-856-5
Following Faltings and Vojta's work proving the Mordell-Lang conjecture for abelian varieties and Raynaud's work proving the Manin-Mumford conjecture, many new diophantine questions appeared, often described as problems of unlikely intersections. The arithmetic of moduli spaces of abelian varieties and, more generally, Shimura varieties has been parallel-developed around the central Andre-Oort conjecture. These two themes can be placed in a common frame?the Zilber-Pink conjecture.
This volume is an introduction to these problems and to the various techniques used: geometry, height theory, reductive groups and Hodge theory, Shimura varieties, and model theory via the notion of o-minimal structure. The volume contains texts corresponding to courses presented at CIRM in May 2011 by Philipp Habegger, Gael Remond, Thomas Scanlon, Emmanuel Ullmo, and Andrei Yafaev, and an ample introduction by E. Ullmo centered on the notion of bi-algebraicity aimed at a presentation of the general setting.
Graduate students and researchers interested in the Zilber-Pink conjecture.
A publication of the Societe Mathematique de France
This book gives a detailed structure theory for semisimple Lie algebras over arbitrary fields of characteristic 0. Starting from the well-known classification over algebraically closed fields via root systems, the author mimics the language of reductive groups, so that part of his work can be seen as an introduction to a simpler version of Borel-Tits theory. But the author also expresses his results in the language of classical (matrix) algebra as well as Galois cohomology.
Memoires de la Societe Mathematique de France Volume: 151
2017; 147 pp; Softcover
MSC: Primary 17;
Print ISBN: 978-2-85629-859-6
In the second part of this book, the author focuses on p-adic fields and achieves a complete classification of semisimple Lie algebras over them. This classification consists essentially of a list of so-called Satake-Tits diagrams, which extend the Dynkin diagrams from the split case. Several instructive examples and historical notes supplement the text. This book can be used as the basis for a lecture on semisimple Lie algebras beyond the beginner's level and as a reference for researchers.
Graduate students, research mathematicians, and historians of mathematics.
Advanced Lectures in Mathematics Volume 37
Published: 18 July 2017
Publisher: International Press of Boston, Inc.
Paperback
1246 pages
The International Congress of Chinese Mathematicians (ICCM) is an important event among the large international community of mathematicians of Chinese descent. The sixth Congress was held at Taipei, Taiwan in July 2013.
Proceedings of the Sixth International Congress of Chinese Mathematicians presents the plenary talks and more than 60 invited talks from the Congress, reflecting the latest developments in mathematics. It is an important reference for researchers in all fields of mathematics, and makes a valuable addition to the collection of a university library.
This is a set comprising the following volumes, which may be purchased independently:
Proceedings of the Sixth International Congress of Chinese Mathematicians, Volume I (vol. 36 of the ALM series)
Proceedings of the Sixth International Congress of Chinese Mathematicians, Volume II (vol. 37 of the ALM series)
This volume is part of the Advanced Lectures in Mathematics book series.
Paperback
Hardback
August 2, 2017 by Chapman and Hall/CRC
Textbook
ISBN 9781138430372
Description
Offers a mathematical framework for problem solving - not just a catalog of theorems
Offers a classification of cubic curves by their singular points - a result typically not available at this level
Includes a section on Watt's curve and the various types of cycloid
Presents numerous examples-accessible, yet giving rise to intriguing complexities
Contains practical exercises that reinforce understanding of theory and pique interest in the subject
Includes MATLAB programs for drawing sized curves
Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving.
Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. The author begins with the basics, then takes students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limacons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness.
The uniqueness of this treatment lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations.
The result is a practical text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies.
Preliminaries
Lines, Circles and Conics
Conics: General Position
Some Higher Algebraic and Transcendental Curves
Parameters, Tangents, Normals. Contact, Inflexions
Undulations
Cusps, Non-Regular Points
Curvature
Curvature Applications
Circle of Curvature
Limacons
Evolutes
Parallels, Involutes
Roulettes
Envelopes
Singular Points of Algebraic Curves
Projective Curves
Series on Knots and Everything: Volume 61
284pp Dec 2017
ISBN: 978-981-3228-61-0 (hardcover)
This volume is the result of the author's many-years of research in this field. These results were presented in the author's two books, Introduction to the Algorithmic Measurement Theory (Moscow, Soviet Radio, 1977), and Codes of the Golden Proportion (Moscow, Radio and Communications, 1984), which had not been translated into English and are therefore not known to English-speaking audience. This volume sets forth new informational and arithmetical fundamentals of computer and measurement systems based on Fibonacci p-codes and codes of the golden p-proportions, and also on Bergman's system and "golden" ternary mirror-symmetrical arithmetic. The book presents some new historical hypotheses concerning the origin of the Egyptian calendar and the Babylonian numeral system with base 60 (dodecahedral hypothesis), as well as about the origin of the Mayan's calendar and their numeral system with base 20 (icosahedral hypothesis). The book is intended for the college and university level. The book will also be of interest to all researchers, who use the golden ratio and Fibonacci numbers in their subject areas, and to all readers who are interested to the history of mathematics.
Preface
Introduction
Acknowledgements
Preliminary Historical and Mathematical Information
A New View on Numeral Systems: Unusual Hypotheses, Surprising Properties and Applications
Bergman's System, "Golden" Number Theory and Mirror-Symmetrical Arithmetic
Fibonacci p-Codes, and Concept of Fibonacci Computers
Codes of the Golden p-Proportions and Their Applications in Computer Science and "Golden" Metrology
Readership: Researchers in mathematics and computer science.