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Calabi-Yau Manifolds and Related Geometries

Calabi-Yau Manifolds and Related Geometries
Author: Mark Gross
Publisher: Springer Science & Business Media
Total Pages: 245
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642190049

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This is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory. Proofs or sketches are given for many important results. From the reviews: "An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry....This is an excellent and useful book." --MATHEMATICAL REVIEWS


Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds
Author: Radu Laza
Publisher: Springer Science & Business Media
Total Pages: 613
Release: 2013-06-12
Genre: Mathematics
ISBN: 146146403X

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In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.


New Trends in Algebraic Geometry

New Trends in Algebraic Geometry
Author: Klaus Hulek
Publisher: Cambridge University Press
Total Pages: 500
Release: 1999-05-13
Genre: Mathematics
ISBN: 9780521646598

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This book is the outcome of the 1996 Warwick Algebraic Geometry EuroConference, containing 17 survey and research articles selected from the most outstanding contemporary research topics in algebraic geometry. Several of the articles are expository: among these a beautiful short exposition by Paranjape of the new and very simple approach to the resolution of singularities; a detailed essay by Ito and Nakamura on the ubiquitous A,D,E classification, centred around simple surface singularities; a discussion by Morrison of the new special Lagrangian approach to giving geometric foundations to mirror symmetry; and two deep, informative surveys by Siebert and Behrend on Gromow-Witten invariants treating them from the point of view of algebraic and symplectic geometry. The remaining articles cover a wide cross-section of the most significant research topics in algebraic geometry. This includes Gromow-Witten invariants, Hodge theory, Calabi-Yau 3-folds, mirror symmetry and classification of varieties.


Applications of Algebraic Geometry to Coding Theory, Physics and Computation

Applications of Algebraic Geometry to Coding Theory, Physics and Computation
Author: Ciro Ciliberto
Publisher: Springer Science & Business Media
Total Pages: 343
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401010110

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An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision. Contributions on more fundamental aspects of algebraic geometry include expositions related to counting points on varieties over finite fields, Mori theory, linear systems, Abelian varieties, vector bundles on singular curves, degenerations of surfaces, and mirror symmetry of Calabi-Yau manifolds.


Perspectives On String Phenomenology

Perspectives On String Phenomenology
Author: Gordon Kane
Publisher: World Scientific
Total Pages: 446
Release: 2014-12-23
Genre: Science
ISBN: 9814602698

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The remarkable recent discovery of the Higgs boson at the CERN Large Hadron Collider completed the Standard Model of particle physics and has paved the way for understanding the physics which may lie beyond it. String/M theory has emerged as a broad framework for describing a plethora of diverse physical systems, which includes condensed matter systems, gravitational systems as well as elementary particle physics interactions. If string/M theory is to be considered as a candidate theory of Nature, it must contain an effectively four-dimensional universe among its solutions that is indistinguishable from our own. In these solutions, the extra dimensions of string/M theory are “compactified” on tiny scales which are often comparable to the Planck length. String phenomenology is the branch of string/M theory that studies such solutions, relates their properties to data, and aims to answer many of the outstanding questions of particle physics beyond the Standard Model.This book contains perspectives on string phenomenology from some of the leading experts in the field. Contributions will range from pedagogical general overviews and perspectives to more technical reviews. We hope that the reader will get a sense of the significant progress that has been made in the field in recent years (e.g. in the topic of moduli stabilization) as well as the topics currently being researched, outstanding problems and some perspectives for the future.


Discovering Mathematics with Magma

Discovering Mathematics with Magma
Author: Wieb Bosma
Publisher: Springer Science & Business Media
Total Pages: 387
Release: 2007-07-10
Genre: Computers
ISBN: 3540376348

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Based on the ontology and semantics of algebra, the computer algebra system Magma enables users to rapidly formulate and perform calculations in abstract parts of mathematics. Edited by the principal designers of the program, this book explores Magma. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory. Includes case studies describing computations underpinning new theoretical results.


Symbolic and Numerical Scientific Computation

Symbolic and Numerical Scientific Computation
Author: Franz Winkler
Publisher: Springer Science & Business Media
Total Pages: 399
Release: 2003-06-30
Genre: Computers
ISBN: 3540405542

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This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Symbolic and Numerical Scientific Computation, SNSC 2001, held in Hagenberg, Austria, in September 2001. The 19 revised full papers presented were carefully selected during two rounds of reviewing and improvement. The papers are organized in topical sections on symbolics and numerics of differential equations, symbolics and numerics in algebra and geometry, and applications in physics and engineering.