An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

Author: Martin Schlichenmaier

Publisher: Springer Science & Business Media

ISBN: 3540711759

Category: Science

Page: 217

View: 8275

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This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.
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Quantum Field Theory III: Gauge Theory

A Bridge between Mathematicians and Physicists

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 3642224210

Category: Mathematics

Page: 1126

View: 689

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In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).
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Algebraic Curves

Towards Moduli Spaces

Author: Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov

Publisher: Springer

ISBN: 3030029433

Category: Mathematics

Page: 231

View: 1452

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This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework
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Geometry, Topology, and Mathematical Physics

S.P. Novikov's Seminar, 2006-2007

Author: V. M. Buchstaber,I. M. Krichever

Publisher: American Mathematical Soc.

ISBN: 9780821890769

Category: Mathematics

Page: 284

View: 905

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This volume contains a selection of papers based on presentations given in 2006-2007 at the S. P. Novikov Seminar at the Steklov Mathematical Institute in Moscow. Novikov's diverse interests are reflected in the topics presented in the book. The articles address topics in geometry, topology, and mathematical physics. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
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Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs

Author: S. M. Natanzon

Publisher: American Mathematical Soc.

ISBN: 9780821889657

Category: Mathematics

Page: N.A

View: 945

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The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field theory. The present book is devoted to the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic curves, the space of mappings, and also superanalogs of all these spaces. The book can be used by researchers and graduate students working in algebraic geometry, topology, and mathematical physics.
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Riemann Surfaces and Algebraic Curves

Author: Renzo Cavalieri,Eric Miles

Publisher: Cambridge University Press

ISBN: 110714924X

Category: Mathematics

Page: 200

View: 836

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Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.
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Computational Approach to Riemann Surfaces

Author: Alexander I. Bobenko,Christian Klein

Publisher: Springer Science & Business Media

ISBN: 3642174124

Category: Mathematics

Page: 257

View: 4888

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This volume is a well structured overview of existing computational approaches to Riemann surfaces as well as those under development. It covers the software tools currently available and provides solutions to partial differential equations and surface theory.
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Analysis and Mathematical Physics

Author: Björn Gustafsson,Alexander Vasil'ev

Publisher: Springer Science & Business Media

ISBN: 9783764399061

Category: Mathematics

Page: 514

View: 1271

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Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.
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