Conformal Invariance

Conformal Invariance

Conformally invariance has proven spectacularly useful for the understanding of two-dimensional phase transitions of classical systems at equilibrium. This volume presents an introduction to non-local observables such as loops and interfaces. It is explained how they arise from specific physical contexts and how to use conformal invariance to determine their properties. Stochastic Loewner Evolution represents an important conceptual advance, whose consequences provoked considerable interest by physicists and mathematicians alike. In this book, after an introductory chapter on the elements of conformal invariance, both the conceptual foundations of Stochastic Loewner Evolution as well as extensive numerical tests will be described. This is followed by applications to geometric phase transitions such as percolation or polymer systems, with particular attention to surface effects. The informal style of the book makes its contents accessible to graduate students and non-specialist readers from other fields.

Conformal Invariance

Stochastic Geometry, Spatial Statistics and Random Fields

Stochastic Geometry, Spatial Statistics and Random Fields

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

Stochastic Geometry, Spatial Statistics and Random Fields

Vector and Geometric Calculus

Vector and Geometric Calculus

This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. It is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one.

Vector and Geometric Calculus

Linear and Geometric Algebra

Linear and Geometric Algebra

This textbook for the first undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. Geometric algebra is an extension of linear algebra. It enhances the treatment of many linear algebra topics. And geometric algebra does much more. Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas. They provide a unified mathematical language for many areas of physics, computer science, and other fields. The book can be used for self study by those comfortable with the theorem/proof style of a mathematics text. This is a second printing, corrected and slightly revised. Visit the book’s web site for more information: http: //faculty.luther.edu/ macdonal/laga I commend Alan Macdonald for his excellent book! His exposition is clean and spare. He has done a fine job of engineering a gradual transition from standard views of linear algebra to the perspective of geometric algebra. The book is sufficiently conventional to be adopted as a textbook by an adventurous teacher without getting flack from colleagues. Yet it leads to gems of geometric algebra that are likely to delight thoughtful students and surprise even the most experienced instructors. — David Hestenes, Distinguished Research Professor, Arizona State University

Linear and Geometric Algebra

Advanced Theory of Mechanisms and Machines

Advanced Theory of Mechanisms and Machines

A new approach to the theory of mechanisms and machines, based on a lecture course for mechanical engineering students at the St. Petersburg State Technical University. The material differs from traditional textbooks due to its more profound elaboration of the methods of structural, geometric, kinematic and dynamic analysis. These established and novel methods take into account the needs of modern machine design as well as the potential of computers.

Advanced Theory of Mechanisms and Machines

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms provides a complete analytical approach to the invention of new robot mechanisms and the analysis of existing designs based on a unified mathematical description of the kinematic and geometric constraints of mechanisms.

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms

The W3 Algebra

The W3 Algebra

‘W’ algebras are nonlinear generalizations of Lie algebras that arise in the context of two-dimensional conformal field theories when one explores higher-spin extensions of the Virasoro algebra. They provide the underlying symmetry algebra of certain string generalizations which allow the extended world sheet gravity. This book presents such gravity theories, concentrating on the algebra of physical operators determined from an analysis of the corresponding BRST cohomology. It develops the representation theory of ‘W’ algebras needed to extend the standard techniques which were so successful in treating linear algebras. For certain strings corresponding to ‘W’N gravity we show that the operator cohomology has a natural geometric model. This result suggests new directions for the study of ‘W’ geometry.

The W3 Algebra

Lectures on Algebra, Volume 1

Lectures on Algebra, Volume 1

This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author’s fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author’s lectures at Purdue University over the last few years.

Lectures on Algebra, Volume 1

Geometric Algebra And Applications to Physics

Geometric Algebra And Applications to Physics

Bringing geometric algebra to the mainstream of physics pedagogy, Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics, but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations.

Geometric Algebra And Applications to Physics

Algebraic Cycles, Sheaves, Shtukas and Moduli

Algebraic Cycles, Sheaves, Shtukas and Moduli

The articles in this volume are devoted to: – moduli of coherent sheaves; – principal bundles and sheaves and their moduli; – new insights into Geometric Invariant Theory; – stacks of shtukas and their compactifications; – algebraic cycles vs. commutative algebra; – Thom polynomials of singularities; – zero schemes of sections of vector bundles. The main purpose is to give ‘friendly’ introductions to the above topics through a series of comprehensive texts starting from a very elementary level and ending with a discussion of current research. In these texts, the reader will find classical results and methods as well as new ones. The book is addressed to researchers and graduate students in algebraic geometry, algebraic topology and singularity theory. Most of the material presented in the volume has not appeared in books before. Contributors: Jean-Marc Drzet, Toms L. Gmez, Adrian Langer, Piotr Pragacz, Alexander H. W. Schmitt, Vasudevan Srinivas, Ngo Dac Tuan, Andrzej Weber

Algebraic Cycles, Sheaves, Shtukas and Moduli