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Selected Papers on Classical Analysis
This volume contains papers that originally appeared in Japanese in the journal Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers here are in the general area of mathematical analysis as it pertains to free probability theory.
Japan on the Silk Road
Japan on the Silk Road provides for the first time the historical background indispensable for understanding Japan's current perspectives and policies in the vast area of Eurasia across the Middle East and Central Asia. Japanese diplomats, military officers, archaeologists, and linguists traversed the Silk Road, involving Japan in the Great Game and exploring ancient civilizations.The book exposes the entanglements of pre-war Japanese Pan-Asianism with Pan-Islamism, Turkic nationalism and Mongolian independence as a global history of imperialism. Japanese connections to Ottoman Turkey, India, Egypt, Iran, Afghanistan, and China at the same time reveal a discrete global narrative of cosmopoli...
The Cremona Group and Its Subgroups
The goal of this book is to present a portrait of the n n-dimensional Cremona group with an emphasis on the 2-dimensional case. After recalling some crucial tools, the book describes a naturally defined infinite dimensional hyperbolic space on which the Cremona group acts. This space plays a fundamental role in the study of Cremona groups, as it allows one to apply tools from geometric group theory to explore properties of the subgroups of the Cremona group as well as the degree growth and dynamical behavior of birational transformations. The book describes natural topologies on the Cremona group, codifies the notion of algebraic subgroups of the Cremona groups and finishes with a chapter on the dynamics of their actions. This book is aimed at graduate students and researchers in algebraic geometry who are interested in birational geometry and its interactions with geometric group theory and dynamical systems.
Discrete Painlevé Equations
Discrete Painlevé equations are nonlinear difference equations, which arise from translations on crystallographic lattices. The deceptive simplicity of this statement hides immensely rich mathematical properties, connecting dynamical systems, algebraic geometry, Coxeter groups, topology, special functions theory, and mathematical physics. This book necessarily starts with introductory material to give the reader an accessible entry point to this vast subject matter. It is based on lectures that the author presented as principal lecturer at a Conference Board of Mathematical Sciences and National Science Foundation conference in Texas in 2016. Instead of technical theorems or complete proofs, the book relies on providing essential points of many arguments through explicit examples, with the hope that they will be useful for applied mathematicians and physicists.
The Richness of the History of Mathematics
This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.
History of civilizations of Central Asia
Part One: The Historical, Social and Economic SettingDuring the eight centuries covered in this volume, the new faith of Islam arose in Arabia and gradually spread eastwards and northwards, eventually affecting much of Central Asia, the southern fringes of Siberia and the eastern regions of China. These were also the centuries in which nomadic and military empires arose in the heart of Asia, impinging on the history of adjacent, well-established civilizations and cultures (China, India, Islamic Western Asia and Christian eastern and central Europe) to an unparalleled extent. Lamaist Buddhism established itself inthe Mongolian region and in Tibet and Islam among the Turkish people of Transoxania, southern Siberia and Xinjiang. It was in Eastern Europe, above all in Russia, that the Turco-Mongol Golden Horde was to have a major, enduring influence on the course of the region's history.
Differential Galois Theory through Riemann-Hilbert Correspondence
Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. ...
