Download or read book Algebraic Modeling of Topological and Computational Structures and Applications written by Sofia Lambropoulou and published by Springer. This book was released on 2017-12-14 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a workshop in connection with the research project Thales on Algebraic Modeling of Topological and Computational Structures and Applications, held at the National Technical University of Athens, Greece in July 2015. The reader will benefit from the innovative approaches to tackling difficult questions in topology, applications and interrelated research areas, which largely employ algebraic tools.

Download or read book American journal of mathematics written by and published by . This book was released on 2004 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics in Galois Theory written by Jean-Pierre Serre and published by CRC Press. This book was released on 2016-04-19 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt constructi

Download or read book Moduli of Curves written by Joe Harris and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results and open problems about important topics which are not covered in detail.

Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Download or read book Galois Groups over written by Y. Ihara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the offspring of a week-long workshop on "Galois groups over Q and related topics," which was held at the Mathematical Sciences Research Institute during the week March 23-27, 1987. The organizing committee consisted of Kenneth Ribet (chairman), Yasutaka Ihara, and Jean-Pierre Serre. The conference focused on three principal themes: 1. Extensions of Q with finite simple Galois groups. 2. Galois actions on fundamental groups, nilpotent extensions of Q arising from Fermat curves, and the interplay between Gauss sums and cyclotomic units. 3. Representations of Gal(Q/Q) with values in GL(2)j deformations and connections with modular forms. Here is a summary of the conference program: • G. Anderson: "Gauss sums, circular units and the simplex" • G. Anderson and Y. Ihara: "Galois actions on 11"1 ( ••• ) and higher circular units" • D. Blasius: "Maass forms and Galois representations" • P. Deligne: "Galois action on 1I"1(P-{0, 1, oo}) and Hodge analogue" • W. Feit: "Some Galois groups over number fields" • Y. Ihara: "Arithmetic aspect of Galois actions on 1I"1(P - {O, 1, oo})" - survey talk • U. Jannsen: "Galois cohomology of i-adic representations" • B. Matzat: - "Rationality criteria for Galois extensions" - "How to construct polynomials with Galois group Mll over Q" • B. Mazur: "Deforming GL(2) Galois representations" • K. Ribet: "Lowering the level of modular representations of Gal( Q/ Q)" • J-P. Serre: - Introductory Lecture - "Degree 2 modular representations of Gal(Q/Q)" • J.

Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

Download or read book Reviews in Number Theory 1984 96 written by and published by . This book was released on 1997 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Crystals Associated to Barsotti Tate Groups written by William Messing and published by Springer. This book was released on 2006-11-08 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Rational Points on Modular Elliptic Curves written by Henri Darmon and published by American Mathematical Soc.. This book was released on 2004 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.

Download or read book Arithmetic Duality Theorems written by J. S. Milne and published by . This book was released on 1986 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.

Download or read book Cyclotomic Fields and Zeta Values written by John Coates and published by Springer Science & Business Media. This book was released on 2006-10-03 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two leading workers in the field, this brief but elegant book presents in full detail the simplest proof of the "main conjecture" for cyclotomic fields. Its motivation stems not only from the inherent beauty of the subject, but also from the wider arithmetic interest of these questions. From the reviews: "The text is written in a clear and attractive style, with enough explanation helping the reader orientate in the midst of technical details." --ZENTRALBLATT MATH

Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Download or read book Galois Representations in Arithmetic Algebraic Geometry written by A. J. Scholl and published by Cambridge University Press. This book was released on 1998-11-26 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.

Download or read book Rational Points on Varieties written by Bjorn Poonen and published by American Mathematical Soc.. This book was released on 2017-12-13 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.

Download or read book p adic Differential Equations written by Kiran S. Kedlaya and published by Cambridge University Press. This book was released on 2010-06-10 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.