Orbifolds in Mathematics and Physics

Proceedings of a Conference on Mathematical Aspects of Orbifold String Theory, May 4-8, 2001, University of Wisconsin, Madison, Wisconsin

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Author: Alejandro Adem,Jack Morava,Yongbin Ruan

Publisher: American Mathematical Soc.

ISBN: 0821829904

Category: Mathematics

Page: 358

View: 4915

This book publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. The recent explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory. The present volume contains information not fully covered in the published literature, and presents an interdisciplinary look at orbifold problems. Topics such as stacks, vertex operator algebras, branes, groupoids, K-theory and quantum cohomology are discussed. The book reflects the thinking of distinguished investigators working in the areas of mathematical physics, algebraic geometry, algebraic topology, symplectic geometry and representation theory. Advanced graduate students and researchers working in these areas, as well as those interested in connections between mathematical subject areas, will find this book of interest.

Orbifolds in Mathematics and Physics

Proceedings of a Conference on Mathematical Aspects of Orbifold String Theory, May 4-8, 2001, University of Wisconsin, Madison, Wisconsin

DOWNLOAD NOW »

Author: Alejandro Adem,Jack Morava,Yongbin Ruan

Publisher: American Mathematical Soc.

ISBN: 0821829904

Category: Mathematics

Page: 358

View: 4310

This book publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. The recent explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory. The present volume contains information not fully covered in the published literature, and presents an interdisciplinary look at orbifold problems. Topics such as stacks, vertex operator algebras, branes, groupoids, K-theory and quantum cohomology are discussed. The book reflects the thinking of distinguished investigators working in the areas of mathematical physics, algebraic geometry, algebraic topology, symplectic geometry and representation theory. Advanced graduate students and researchers working in these areas, as well as those interested in connections between mathematical subject areas, will find this book of interest.

Recent Progress in Intersection Theory

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Author: Geir Ellingsrud,Angelo Vistoli

Publisher: Springer Science & Business Media

ISBN: 9780817641221

Category: Mathematics

Page: 327

View: 6265

The articles in this volume are an outgrowth of an International Confer­ ence in Intersection Theory that took place in Bologna, Italy (December 1997). In a somewhat unorthodox format aimed at both the mathematical community as well as summer school students, talks were research-oriented as well as partly expository. There were four series of expository talks by the following people: M. Brion, University of Grenoble, on Equivariant Chow groups and applications; H. Flenner, University of Bochum, on Joins and intersections; E. M. Friedlander, Northwestern University, on Intersection products for spaces of algebraic cycles; R. Laterveer, University of Strasbourg, on Bigraded Chow (co)homology. Four introductory papers cover the following topics and bring the reader to the forefront of research: 1) the excess intersection algorithm of Stuckrad and Vogel, combined with the deformation to the normal cone, together with many of its geo­ metric applications; 2) new and very important homotopy theory techniques that are now used in intersection theory; 3) the Bloch-Beilinson filtration and the theory of motives; 4) algebraic stacks, the modern language of moduli theory. Other research articles concern such active fields as stable maps and Gromov-Witten invariants, deformation theory of complex varieties, and others. Organizers of the conference were Rudiger Achilles, Mirella Manaresi, and Angelo Vistoli, all from the University of Bologna; the scientific com­ mittee consisted of Geir Ellingsrud, University of Oslo, William Fulton, University of Michigan at Ann Arbor, and Angelo Vistoli. The conference was financed by the European Union (contract no.

Fundamental Algebraic Geometry

Grothendieck's FGA Explained

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Author: Barbara Fantechi

Publisher: American Mathematical Soc.

ISBN: 0821842455

Category: Mathematics

Page: 339

View: 3958

Alexander Grothendieck introduced many concepts into algebraic geometry; they turned out to be astoundingly powerful and productive and truly revolutionized the subject. Grothendieck sketched his new theories in a series of talks at the Seminaire Bourbaki between 1957 and 1962 and collected his write-ups in a volume entitled ``Fondements de la Geometrie Algebrique,'' known as FGA. Much of FGA is now common knowledge; however, some of FGA is less well known, and its full scope is familiar to few. The present book resulted from the 2003 ``Advanced School in Basic Algebraic Geometry'' at the ICTP in Trieste, Italy. The book aims to fill in Grothendieck's brief sketches. There are four themes: descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. Most results are proved in full detail; furthermore, newer ideas are introduced to promote understanding, and many connections are drawn to newer developments. The main prerequisite is a thorough acquaintance with basic scheme theory. Thus this book is a valuable resource for anyone doing algebraic geometry.

Mathematics and Culture in Europe

Mathematics in Art, Technology, Cinema, and Theatre

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Author: M. Manaresi

Publisher: Springer

ISBN: N.A

Category: Mathematics

Page: 405

View: 3861

Predicated on the notion that mathematics has been a growing source of aesthetic inspiration in culture, this volume celebrates where the two intermesh. It is a meditation on the performances and cultural events, all mathematics-related, performed in Bologna in 2004, is dedicated to all those who are curious about mathematics, but also more generally about theatre, cinema, literature, arts and science. Thanks to the DVD, one can readers can relive various events through the voices and the images of the participants.

A Plethora of Polyhedra in Origami

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Author: John Montroll

Publisher: Courier Corporation

ISBN: 9780486422718

Category: Crafts & Hobbies

Page: 120

View: 4909

Step-by-step instructions and 970 clear diagrams show beginning and experienced paperfolders how to create 27 amazing polyhedra from one sheet of paper. Graded according to difficulty, the projects range from a simple cube, tetrahedron and octahedron to a challenging rhombic dodecahedron, sunken icosahedron, and an antidiamond with pentagonal base.

The Ideal Element in Law

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Author: Roscoe Pound

Publisher: N.A

ISBN: 9780865973251

Category: Law

Page: 432

View: 3920

Roscoe Pound, former dean of Harvard Law School, delivered a series of lectures at the University of Calcutta in 1948. In these lectures, he criticized virtually every modern mode of interpreting the law because he believed the administration of justice had lost its grounding and recourse to enduring ideals. Now published in the U.S. for the first time, Pound's lectures are collected in Liberty Fund's The Ideal Element in Law, Pound's most important contribution to the relationship between law and liberty. The Ideal Element in Law was a radical book for its time and is just as meaningful today as when Pound's lectures were first delivered. Pound's view of the welfare state as a means of expanding government power over the individual speaks to the front-page issues of the new millennium as clearly as it did to America in the mid-twentieth century. Pound argues that the theme of justice grounded in enduring ideals is critical for America. He views American courts as relying on sociological theories, political ends, or other objectives, and in so doing, divorcing the practice of law from the rule of law and the rule of law from the enduring ideal of law itself. Roscoe Pound is universally recognized as one of the most important legal minds of the early twentieth century. Considered by many to be the dean of American jurisprudence, Pound was a former Justice of the Supreme Court of Nebraska and served as dean of Harvard Law School from 1916 to 1936. Please note: This title is available as an ebook for purchase on Amazon, Barnes and Noble, and iTunes.

The Theory of Gauge Fields in Four Dimensions

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Author: H. Blaine Lawson

Publisher: American Mathematical Soc.

ISBN: 0821807080

Category: Mathematics

Page: 101

View: 9703

Lawson's expository lectures, presented at a CBMS Regional Conference held in Santa Barbara in August 1983, provide an indepth examination of the recent work of Simon Donaldson, and is of special interest to both geometric topologists and differential geometers. This work has excited particular interest, in light of Mike Freedman's recent profound results: the complete classification, in the simply connected case, of compact topological 4-manifolds.Arguing from deep results in gauge field theory, Donaldson has proved the nonexistence of differentiable structures on certain compact 4-manifolds. Together with Freedman's results, Donaldson's work implies the existence of exotic differentiable structures in $\mathbb R^4$-a wonderful example of the results of one mathematical discipline yielding startling consequences in another. The lectures are aimed at mature mathematicians with some training in both geometry and topology, but they do not assume any expert knowledge. In addition to a close examination of Donaldson's arguments, Lawson also presents, as background material, the foundation work in gauge theory (Uhlenbeck, Taubes, Atiyah, Hitchin, Singer, et al.) which underlies Donaldson's work.

Lectures on Hilbert Schemes of Points on Surfaces

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Author: Hiraku Nakajima

Publisher: American Mathematical Soc.

ISBN: 0821819569

Category: Mathematics

Page: 132

View: 2583

This beautifully written book deals with one shining example: the Hilbert schemes of points on algebraic surfaces ... The topics are carefully and tastefully chosen ... The young person will profit from reading this book. --Mathematical Reviews The Hilbert scheme of a surface $X$ describes collections of $n$ (not necessarily distinct) points on $X$. More precisely, it is the moduli space for 0-dimensional subschemes of $X$ of length $n$. Recently it was realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory--even theoretical physics. The discussion in the book reflects this feature of Hilbert schemes. One example of the modern, broader interest in the subject is a construction of the representation of the infinite-dimensional Heisenberg algebra, i.e., Fock space. This representation has been studied extensively in the literature in connection with affine Lie algebras, conformal field theory, etc. However, the construction presented in this volume is completely unique and provides an unexplored link between geometry and representation theory. The book offers an attractive survey of current developments in this rapidly growing subject. It is suitable as a text at the advanced graduate level.

Lectures on Division Algebras

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Author: David J. Saltman

Publisher: American Mathematical Soc.

ISBN: 0821809792

Category: Mathematics

Page: 120

View: 5538

This volume is based on lectures on division algebras given at a conference held at Colorado State University. Although division algebras are a very classical object, this book presents this ""classical"" material in a new way, highlighting current approaches and new theorems, and illuminating the connections with a variety of areas in mathematics.

Triangle Des Pensées

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Author: Alain Connes,André Lichnerowicz,Marcel P. Schützenberger

Publisher: The Rosen Publishing Group

ISBN: 9780821826140

Category: Mathematics

Page: 179

View: 566

Our view of the world today is fundamentally influenced by twentieth century results in physics and mathematics. Here, three members of the French Academy of Sciences: Alain Connes, Andre Lichnerowicz, and Marcel Paul Schutzenberger, discuss the relations among mathematics, physics and philosophy, and other sciences. Written in the form of conversations among three brilliant scientists and deep thinkers, the book touches on, among others, the following questions: Is there a ``primordial truth'' that exists beyond the realm of what is provable? More generally, is there a distinction between what is true in mathematics and what is provable? How is mathematics different from other sciences? How is it the same? Does mathematics have an ``object'' or an ``object of study'', the way physics, chemistry and biology do? Mathematics is a lens, through which we view the world. Connes, Lichnerowicz, and Schutzenberger examine that lens, to understand how it affects what we do see, but also to understand how it limits what we can see. How does a well-informed mathematician view fundamental topics of physics, such as: quantum mechanics, general relativity, quantum gravity, grand unification, and string theory? What are the relations between computational complexity and the laws of physics? Can pure thought alone lead physicists to the right theories, or must experimental data be the driving force? How should we compare Heisenberg's arrival at matrix mechanics from spectral data to Einstein's arrival at general relativity through his thought experiments? The conversations are sprinkled with stories and quotes from outstanding scientists, which enliven the discourse. The book will make you think again about things that you once thought were quite familiar. Alain Connes is one of the founders of non-commutative geometry. He holds the Chair of Analysis and Geometry at the College de France. He was awarded the Fields Medal in 1982. In 2001, he was awarded the Crafoord Prize by The Royal Swedish Academy of Sciences. Andre Lichnerowicz, mathematician, noted geometer, theoretical physicist, and specialist in general relativity, was a professor at the College de France. Marcel Paul Schutzenberger made brilliant contributions to combinatorics and graph theory. He was simultaneously a medical doctor, a biologist, a psychiatrist, a linguist, and an algebraist.

Handbook of Moduli

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Author: Gavril Farkas,Ian Morrison

Publisher: N.A

ISBN: 9781571462589

Category: Moduli theory

Page: 594

View: 3823

Ergodic Theory via Joinings

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Author: Eli Glasner

Publisher: American Mathematical Soc.

ISBN: 1470419513

Category:

Page: 384

View: 1014

This book introduces modern ergodic theory. It emphasizes a new approach that relies on the technique of joining two (or more) dynamical systems. This approach has proved to be fruitful in many recent works, and this is the first time that the entire theory is presented from a joining perspective. Another new feature of the book is the presentation of basic definitions of ergodic theory in terms of the Koopman unitary representation associated with a dynamical system and the invariant mean on matrix coefficients, which exists for any acting groups, amenable or not. Accordingly, the first part of the book treats the ergodic theory for an action of an arbitrary countable group. The second part, which deals with entropy theory, is confined (for the sake of simplicity) to the classical case of a single measure-preserving transformation on a Lebesgue probability space.

Lectures on the Geometry of Quantization

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Author: Sean Bates,Alan Weinstein

Publisher: American Mathematical Soc.

ISBN: 9780821807989

Category: Geometric quantization

Page: 137

View: 9272

These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.

Recurrence Sequences

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Author: Graham Everest, Alf van der Poorten,Igor Shparlinski,Thomas Ward

Publisher: American Mathematical Soc.

ISBN: 1470423154

Category:

Page: 318

View: 9050

Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.

Concise Numerical Mathematics

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Author: Robert Plato

Publisher: American Mathematical Soc.

ISBN: 9780821834145

Category: Mathematics

Page: 453

View: 3730

This textbook is a concise introduction to the fundamental concepts and methods of numerical mathematics. The author manages to cover the many important topics while avoiding redundancies and using well-chosen examples and exercises. The exposition is supplemented by numerous figures. Work estimates and pseudo codes are provided for many algorithms, which can be easily converted to computer programs. Topics covered include interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic. The book is suitable as a text for a first course in numerical methods for mathematics students or students in neighboring fields, such as engineering, physics, and computer science. In general, the author assumes only a knowledge of calculus and linear algebra.

Consequences of the Axiom of Choice

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Author: Paul Howard,Jean E. Rubin

Publisher: American Mathematical Soc.

ISBN: 0821809776

Category: Mathematics

Page: 432

View: 9928

This book, Consequences of the Axiom of Choice, is a comprehensive listing of statements that have been proved in the last 100 years using the axiom of choice. Each consequence, also referred to as a form of the axiom of choice, is assigned a number. Part I is a listing of the forms by number. In this part each form is given together with a listing of all statements known to be equivalent to it (equivalent in set theory without the axiom of choice). In Part II the forms are arranged by topic. In Part III we describe the models of set theory which are used to show non-implications between forms. Part IV, the notes section, contains definitions, summaries of important sub-areas and proofs that are not readily available elsewhere. Part V gives references for the relationships between forms and Part VI is the bibliography. Part VII is contained on the floppy disk which is enclosed in the book. It contains a table with form numbers as row and column headings. The entry in the table in row $n$, column $k$ gives the status of the implication ``form $n$ implies form $k$''. Software for easily extracting information from the table is also provided. Features: complete summary of all the work done in the last 100 years on statements that are weaker than the axiom of choice software provided gives complete, convenient access to information about relationships between the various consequences of the axiom of choice and about the models of set theory descriptions of more than 100 models used in the study of the axiom of choice an extensive bibliography About the software: Tables 1 and 2 are accessible on the PC-compatible software included with the book. In addition, the program maketex.c in the software package will create TeX files containing copies of Table 1 and Table 2 which may then be printed. (Tables 1 and 2 are also available at the authors' Web sites: http://www.math.purdue.edu/$\sim$jer/ or http://www.emunix.emich.edu/$\sim$phoward/.) Detailed instructions for setting up and using the software are included in the book's Introduction, and technical support is available directly from the authors.