Sylvie Paycha's Books

Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory

Villa de Leyva, Colombia, 9-27 July 2001

By: Hernan Ocampo,Sylvie Paycha,Alexander Cardona

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Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory

Villa de Leyva, Colombia, 9-27 July 2001

By: Hernan Ocampo,Sylvie Paycha,Alexander Cardona

This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.

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Page Count

495

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World Scientific

Published Date

ISBN 10

9812381317

ISBN 13

9789812381316

Geometric Methods for Quantum Field Theory

Proceedings of the Summer School : Villa de Leyva, Colombia, 12-30 July 1999

By: Hernan Ocampo,Sylvie Paycha,Andres Reyes

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Geometric Methods for Quantum Field Theory

Proceedings of the Summer School : Villa de Leyva, Colombia, 12-30 July 1999

By: Hernan Ocampo,Sylvie Paycha,Andres Reyes

Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, SeibergOCoWitten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist''s and the mathematician''s perspective complement each other, leading to new mathematical and physical concepts and results. This volume introduces the reader to some basic mathematical and physical tools and methods required to follow the recent developments in some active areas of mathematical physics, including duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups. It comprises seven self-contained lectures, which should progressively give the reader a precise idea of some of the techniques used in these areas, as well as a few short communications presented by young participants at the school. Contents: Lectures: Introduction to Differentiable Manifolds and Symplectic Geometry (T Wurzbacher); Spectral Properties of the Dirac Operator and Geometrical Structures (O Hijazi); Quantum Theory of Fermion Systems: Topics Between Physics and Mathematics (E Langmann); Heat Equation and Spectral Geometry. Introduction for Beginners (K Wojciechowski); Renormalized Traces as a Geometric Tool (S Paycha); Concepts in Gauge Theory Leading to Electric-Magnetic Duality (T S Tsun); An Introduction to Seiberg-Witten Theory (H Ocampo); Short Communications: Remarks on Duality, Analytical Torsion and Gaussian Integration in Antisymmetric Field Theories (A Cardona); Multiplicative Anomaly for the e-Regularized Determinant (C Ducourtioux); On Cohomogeneity One Riemannian Manifolds (S M B Kashani); A Differentiable Calculus on the Space of Loops and Connections (M Reiris); Quantum Hall Conductivity and Topological Invariants (A Reyes); Determinant of the Dirac Operator Over the Interval [0, ] (F Torres-Ardila). Readership: Mathematicians and physicists.

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530

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World Scientific

Published Date

ISBN 10

9812810579

ISBN 13

9789812810571

Regularised Integrals, Sums and Traces

An Analytic Point of View

By: Sylvie Paycha

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Regularised Integrals, Sums and Traces

An Analytic Point of View

By: Sylvie Paycha

``Regularization techniques'' is the common name for a variety of methods used to make sense of divergent series, divergent integrals, or traces of linear operators in infinite-dimensional spaces. Such methods are often indispensable in problems of number theory, geometry, quantum field theory, and other areas of mathematics and theoretical physics. However arbitrary and noncanonical they might seem at first glance, regularized sums, integrals, and traces often contain canonical concepts, and the main purpose of this book is to illustrate and explain this. This book provides a unified and self-contained mathematical treatment of various regularization techniques. The author shows how to derive regularized sums, integrals, and traces from certain canonical building blocks of the original divergent object. In the process of putting together these ``building blocks'', one encounters many problems and ambiguities caused by various so-called anomalies, which are investigated and explained in detail. Nevertheless, it turns out that the corresponding canonical sums, integrals, sums, and traces are well behaved, thus making the regularization procedure possible and manageable. This new unified outlook on regularization techniques in various fields of mathematics and in quantum field theory can serve as an introduction for anyone from a beginning mathematician interested in the subject to an experienced physicist who wants to gain a unified outlook on techniques he/she uses on a daily basis.

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203

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853678

ISBN 13

9780821853672

European Women in Mathematics

Proceedings of the Tenth General Meeting, Malta, 24-30 August 2001

By: Emilia Mezzetti,Sylvie Paycha

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European Women in Mathematics

Proceedings of the Tenth General Meeting, Malta, 24-30 August 2001

By: Emilia Mezzetti,Sylvie Paycha

This volume can be divided into two parts: a purely mathematical part with contributions on finance mathematics, interactions between geometry and physics and different areas of mathematics; another part on the popularization of mathematics and the situation of women in mathematics.

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420

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World Scientific

Published Date

ISBN 10

9812381902

ISBN 13

9789812381903

European Women in Mathematics

Proceedings of the 13th General Meeting, University of Cambridge, UK, 3-6 September 2007

By: Catherine Hobbs,Sylvie Paycha

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European Women in Mathematics

Proceedings of the 13th General Meeting, University of Cambridge, UK, 3-6 September 2007

By: Catherine Hobbs,Sylvie Paycha

This volume offers a unique collection of outstanding contributions from renowned women mathematicians who met in Cambridge for a conference under the auspices of European Women in Mathematics (EWM). These contributions serve as excellent surveys of their subject areas, including symplectic topology, combinatorics and number theory. The volume moreover sheds light on prominent women mathematicians who worked in Cambridge in the late 19th and early 20th centuries by providing an insightful historical introduction at the beginning of the volume. The volume concludes with short contributions from women mathematicians from across Europe working in various areas of mathematics ranging from group theory to magnetic fields.

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210

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World Scientific

Published Date

ISBN 10

9814277673

ISBN 13

9789814277679

Geometric, Algebraic and Topological Methods for Quantum Field Theory

Proceedings of the 2011 Villa de Leyva Summer School, Villa de Leyva, Colombia, 4-22 July 2011

By: Sylvie Payche

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Geometric, Algebraic and Topological Methods for Quantum Field Theory

Proceedings of the 2011 Villa de Leyva Summer School, Villa de Leyva, Colombia, 4-22 July 2011

By: Sylvie Payche

Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory. This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.

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378

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World Scientific

Published Date

ISBN 10

9814460052

ISBN 13

9789814460057

Chaos on the Interval

By: Sylvie Ruette

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Chaos on the Interval

By: Sylvie Ruette

The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the “most interesting” part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gives complete proofs and addresses both graduate students and researchers.

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231

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147042956X

ISBN 13

9781470429560

Geometric and Topological Methods for Quantum Field Theory

Summer School on Geometric and Topological Methods for Quantum Field Theory, July 11-29, 2005, Villa de Leyva, Colombia

By: Sylvie Paycha,Bernardo Uribe

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Geometric and Topological Methods for Quantum Field Theory

Summer School on Geometric and Topological Methods for Quantum Field Theory, July 11-29, 2005, Villa de Leyva, Colombia

By: Sylvie Paycha,Bernardo Uribe

This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.

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272

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821840622

ISBN 13

9780821840627

European Women in Mathematics

Proceedings of the Tenth General Meeting, Malta, 24-30 August 2001

By: Emilia Mezzetti,Sylvie Paycha

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European Women in Mathematics

Proceedings of the Tenth General Meeting, Malta, 24-30 August 2001

By: Emilia Mezzetti,Sylvie Paycha

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Solve jigsaw puzzle

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Page Count

420

Publisher

World Scientific

Published Date

ISBN 10

9812381902

ISBN 13

9789812381903

Regularised Integrals, Sums and Traces

An Analytic Point of View

By: Sylvie Paycha

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Regularised Integrals, Sums and Traces

An Analytic Point of View

By: Sylvie Paycha

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Solve jigsaw puzzle

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Page Count

203

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853678

ISBN 13

9780821853672

European Women in Mathematics

Proceedings of the 13th General Meeting, University of Cambridge, UK, 3-6 September 2007

By: Catherine Hobbs,Sylvie Paycha

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European Women in Mathematics

Proceedings of the 13th General Meeting, University of Cambridge, UK, 3-6 September 2007

By: Catherine Hobbs,Sylvie Paycha

Deformation quantisation and connections / S. Gutt -- What is symplectic geometry? / D. McDuff -- Regular permutation groups and Cayley graphs / C.E. Praeger -- Arithmetic of elliptic curves through the ages / R. Sujatha -- Tricritical points and liquid-solid critical lines / A. Aitta -- Elastic waves in rods of rectangular cross section / A.A. Bondarenko -- Natural extensions for the golden mean / K. Dajani & C. Kalle -- An equivariant tietze extension theorem for proper actions of locally compact groups / A. Feragen -- On uniform tangential approximation by lacunary power series / G. Harutyunyan -- Cyclic division algebras in apace-time coding : a brief overview / C. Hollanti -- And what became of the women? / C. Series -- Three great Girton mathematicians / R.M. Williams -- What about the women now? / R.M. Williams -- Mathematics in society (taking into account gender-aspects) - a one-semester course (BSc) / C. Scharlach

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210

Publisher

World Scientific

Published Date

ISBN 10

9814277681

ISBN 13

9789814277686

Book's by Sylvie Paycha

Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory

Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory

Geometric Methods for Quantum Field Theory

Geometric Methods for Quantum Field Theory

Regularised Integrals, Sums and Traces

Regularised Integrals, Sums and Traces

European Women in Mathematics

European Women in Mathematics

European Women in Mathematics

European Women in Mathematics

Geometric, Algebraic and Topological Methods for Quantum Field Theory

Geometric, Algebraic and Topological Methods for Quantum Field Theory

Chaos on the Interval

Chaos on the Interval

Geometric and Topological Methods for Quantum Field Theory

Geometric and Topological Methods for Quantum Field Theory

European Women in Mathematics

European Women in Mathematics

Regularised Integrals, Sums and Traces

Regularised Integrals, Sums and Traces

European Women in Mathematics

European Women in Mathematics

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