Open Problems And Surveys Of Contemporary Mathematics
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Open Problems And Surveys Of Contemporary Mathematics
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Author : Lizhen Ji
language : en
Publisher:
Release Date : 2013
Open Problems And Surveys Of Contemporary Mathematics written by Lizhen Ji and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Geometry, Differential categories.
Surveys In Contemporary Mathematics
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Author : Nicholas Young
language : en
Publisher: Cambridge University Press
Release Date : 2008
Surveys In Contemporary Mathematics written by Nicholas Young and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Education categories.
A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.
Surveys In Modern Mathematics
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Author : Viktor Vasilʹevich Prasolov
language : en
Publisher: Cambridge University Press
Release Date : 2005-04-14
Surveys In Modern Mathematics written by Viktor Vasilʹevich Prasolov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-14 with Mathematics categories.
Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups.
Rationality Problems In Algebraic Geometry
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Author : Arnaud Beauville
language : en
Publisher: Springer
Release Date : 2016-12-06
Rationality Problems In Algebraic Geometry written by Arnaud Beauville and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-06 with Mathematics categories.
Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.
Open Problems In Mathematics
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Author : John Forbes Nash, Jr.
language : en
Publisher: Springer
Release Date : 2016-07-05
Open Problems In Mathematics written by John Forbes Nash, Jr. and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-05 with Mathematics categories.
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.
Surveys On Discrete And Computational Geometry
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Author : Jacob E. Goodman
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Surveys On Discrete And Computational Geometry written by Jacob E. Goodman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This volume contains nineteen survey papers describing the state of current research in discrete and computational geometry as well as a set of open problems presented at the 2006 AMS-IMS-SIAM Summer Research Conference Discrete and Computational Geometry--Twenty Years Later, held in Snowbird, Utah, in June 2006. Topics surveyed include metric graph theory, lattice polytopes, the combinatorial complexity of unions of geometric objects, line and pseudoline arrangements, algorithmic semialgebraic geometry, persistent homology, unfolding polyhedra, pseudo-triangulations, nonlinear computational geometry, $k$-sets, and the computational complexity of convex bodies.
Trends In Contemporary Mathematics
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Author : Vincenzo Ancona
language : en
Publisher: Springer
Release Date : 2014-08-27
Trends In Contemporary Mathematics written by Vincenzo Ancona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-27 with Mathematics categories.
The topics faced in this book cover a large spectrum of current trends in mathematics, such as Shimura varieties and the Lang lands program, zonotopal combinatorics, non linear potential theory, variational methods in imaging, Riemann holonomy and algebraic geometry, mathematical problems arising in kinetic theory, Boltzmann systems, Pell's equations in polynomials, deformation theory in non commutative algebras. This work contains a selection of contributions written by international leading mathematicians who were speakers at the "INdAM Day", an initiative born in 2004 to present the most recent developments in contemporary mathematics.
Derived Algebraic Geometry
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Author : Renaud Gauthier
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-01-29
Derived Algebraic Geometry written by Renaud Gauthier and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-29 with Mathematics categories.
Convexity From The Geometric Point Of View
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2024-07-14
Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.
Elliptic Curves Second Edition
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Author : James S Milne
language : en
Publisher: World Scientific
Release Date : 2020-08-20
Elliptic Curves Second Edition written by James S Milne and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-20 with Mathematics categories.
This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses.An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer.Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work.The first three chapters develop the basic theory of elliptic curves.For this edition, the text has been completely revised and updated.