Recent Advances in Algebraic Geometry

Author: Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa

Publisher: Cambridge University Press

ISBN: 110764755X

Category: Mathematics

Page: 447

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A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

Foliation Theory in Algebraic Geometry

Author: Paolo Cascini,James McKernan,Jorge Vitório Pereira

Publisher: Springer

ISBN: 3319244604

Category: Mathematics

Page: 216

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Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classification of psuedoeffective codimension one distributions. Foliations play a fundamental role in algebraic geometry, for example in the proof of abundance for threefolds and to a solution of the Green-Griffiths conjecture for surfaces of general type with positive Segre class. The purpose of this volume is to foster communication and enable interactions between experts who work on holomorphic foliations and birational geometry, and to bring together leading researchers to demonstrate the powerful connection of ideas, methods, and goals shared by these two areas of study./div

Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics

Author: Pramod M. Achar,Dijana Jakelić,Kailash C. Misra,Milen Yakimov

Publisher: American Mathematical Society

ISBN: 0821898523

Category: Mathematics

Page: 280

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This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.

Recent Advances in Hodge Theory

Period Domains, Algebraic Cycles, and Arithmetic

Author: Matt Kerr,Gregory Pearlstein

Publisher: Cambridge University Press

ISBN: 110754629X

Category: Mathematics

Page: 528

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Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

Advances in Elliptic Curve Cryptography

Author: Ian F. Blake,Gadiel Seroussi,Nigel P. Smart

Publisher: Cambridge University Press

ISBN: 9781139441223

Category: Mathematics

Page: N.A

View: 6982

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Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways to cryptographic protocols that hold great promise. Notions such as provable security, side channel analysis and the Weil descent technique have also grown in importance. This second volume addresses these advances and brings the reader up to date. Prominent contributors to the research literature in these areas have provided articles that reflect the current state of these important topics. They are divided into the areas of protocols, implementation techniques, mathematical foundations and pairing based cryptography. Each of the topics is presented in an accessible, coherent and consistent manner for a wide audience that will include mathematicians, computer scientists and engineers.

Surveys in Combinatorics, 1997

Author: British Combinatorial Conference

Publisher: Cambridge University Press

ISBN: 9780521598408

Category: Mathematics

Page: 338

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The invited lectures given at the 16th. British Combinatorial Conference, July 1997 at Queen Mary and Westfield College.

New Developments in Topology

Author: John Frank Adams,Graeme Segal

Publisher: Cambridge University Press

ISBN: 0521203546

Category: Mathematics

Page: 128

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Eleven of the fourteen invited speakers at a symposium held by the Oxford Mathematical Institute in June 1972 have revised their contributions and submitted them for publication in this volume. The present papers do not necessarily closely correspond with the original talks, as it was the intention of the volume editor to make this book of mathematical rather than historical interest. The contributions will be of value to workers in topology in universities and polytechnics.

Revue de mathématique élémentaires

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

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Elemente der Mathematik (EL) publishes survey articles about important developments in the field of mathematics; stimulating shorter communications that tackle more specialized questions; and papers that report on the latest advances in mathematics and applications in other disciplines. The journal does not focus on basic research. Rather, its articles seek to convey to a wide circle of readers - teachers, students, engineers, professionals in industry and administration - the relevance, intellectual challenge and vitality of mathematics today. The Problems Section, covering a diverse range of exercises of varying degrees of difficulty, encourages an active grappling with mathematical problems.

Geometry of Low-Dimensional Manifolds: Volume 2

Symplectic Manifolds and Jones-Witten Theory

Author: Donaldson/Thomas,London Mathematical Society

Publisher: Cambridge University Press

ISBN: 9780521400015

Category: Mathematics

Page: 260

View: 8835

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These volumes are based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects (topology, differential and algebraic geometry and mathematical physics) interact.

Advances in Homotopy Theory

Papers in Honour of I M James, Cortona 1988

Author: S. Salamon,B. Steer

Publisher: Cambridge University Press

ISBN: 9780521379076

Category: Mathematics

Page: 177

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This is a collection of the recorded lectures given at a conference to celebrate the 60th birthday of Professor Ioan James, who has made significant contributions to homotopy theory, highlighting problems and initiating new methods. The present volume contains papers from internationally distinguished research workers that reflect recent exciting breakthroughs in this field. It will be important for all homotopy theorists as both a statement of current research and as a signpost for new directions. This should prove interesting to research workers in algebraic topology.

Groups, Combinatorics and Geometry

Author: Martin W. Liebeck,Jan Saxl

Publisher: Cambridge University Press

ISBN: 0521406854

Category: Mathematics

Page: 489

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This volume contains a collection of papers on the subject of the classification of finite simple groups.

Elliptic Curves in Cryptography

Author: I. Blake,G. Seroussi,N. Smart

Publisher: Cambridge University Press

ISBN: 9780521653749

Category: Computers

Page: 204

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This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.

Introduction to the Representation Theory of Compact and Locally Compact Groups

Author: Alain Robert

Publisher: Cambridge University Press

ISBN: 0521289750

Category: Mathematics

Page: 205

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Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.

Arithmetic of Blowup Algebras

Author: Wolmer V. Vasconcelos

Publisher: Cambridge University Press

ISBN: 9780521454841

Category: Mathematics

Page: 329

View: 6921

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This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.