Iwasawa Theory 2012

Author: Athanasios Bouganis
Publisher: Springer
ISBN: 3642552455
Format: PDF, ePub, Docs
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This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida’s theory of p-adic modular forms and big Galois representations play a crucial part. Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan).

Primes and Knots

Author: Toshitake Kohno
Publisher: American Mathematical Soc.
ISBN: 0821834568
Format: PDF, Mobi
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This volume deals systematically with connections between algebraic number theory and low-dimensional topology. Of particular note are various inspiring interactions between number theory and low-dimensional topology discussed in most papers in this volume. For example, quite interesting are the use of arithmetic methods in knot theory and the use of topological methods in Galois theory. Also, expository papers in both number theory and topology included in the volume can help a wide group of readers to understand both fields as well as the interesting analogies and relations that bring them together.

Aspects of Galois Theory

Author: Helmut Völklein
Publisher: Cambridge University Press
ISBN: 9780521637473
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Collection of articles by leading experts in Galois theory, focusing on the Inverse Galois Problem.

New Trends in Algebraic Geometry

Author: K. Hulek
Publisher: Cambridge University Press
ISBN: 9780521646598
Format: PDF, Docs
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Seventeen articles from the most outstanding contemporary topics in algebraic geometry.

Arithmetic and Geometry

Author: Luis Dieulefait
Publisher: Cambridge University Press
ISBN: 1107462541
Format: PDF, Mobi
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The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.

Complexity Science

Author: Robin Ball
Publisher: Cambridge University Press
ISBN: 1107513553
Format: PDF, ePub, Mobi
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Complexity science is the study of systems with many interdependent components. Such systems - and the self-organization and emergent phenomena they manifest - lie at the heart of many challenges of global importance. This book is a coherent introduction to the mathematical methods used to understand complexity, with plenty of examples and real-world applications. It starts with the crucial concepts of self-organization and emergence, then tackles complexity in dynamical systems using differential equations and chaos theory. Several classes of models of interacting particle systems are studied with techniques from stochastic analysis, followed by a treatment of the statistical mechanics of complex systems. Further topics include numerical analysis of PDEs, and applications of stochastic methods in economics and finance. The book concludes with introductions to space-time phases and selfish routing. The exposition is suitable for researchers, practitioners and students in complexity science and related fields at advanced undergraduate level and above.