# Search Results for "free-loop-spaces-in-geometry-and-topology-including-the-monograph-symplectic-cohomology-and-viterbo-s-theorem-by-mohammed-abouzaid-irma-lectures-in-mathematics-theoretical-physics"

## Free Loop Spaces in Geometry and Topology

*Including the Monograph Symplectic Cohomology and Viterbo's Theorem by Mohammed Abouzaid*

**Author**: Mohammed Abouzaid**Publisher:**European Mathematical Society**ISBN:**9783037191538**Category:**Loop spaces**Page:**494**View:**8687

In the late 1990s, two initially unrelated developments brought free loop spaces into renewed focus. In 1999, Chas and Sullivan introduced a wealth of new algebraic operations on the homology of these spaces under the name of string topology, the full scope of which is still not completely understood. A few years earlier, Viterbo had discovered a first deep link between the symplectic topology of cotangent bundles and the topology of their free loop space. In the past 15 years, many exciting connections between these two viewpoints have been found. Still, researchers working on one side of the story often know quite little about the other. One of the main purposes of this book is to facilitate communication between topologists and symplectic geometers thinking about free loop spaces. It was written by active researchers who approach the topic from both perspectives and provides a concise overview of many of the classical results. The book also begins to explore the new directions of research that have emerged recently. One highlight is the research monograph by M. Abouzaid, which proves a strengthened version of Viterbo's isomorphism between the homology of the free loop space of a manifold and the symplectic cohomology of its cotangent bundle, following a new strategy. The book grew out of a learning seminar on free loop spaces held at Strasbourg University in 2008-2009 and should be accessible to graduate students with a general interest in the topic. It focuses on introducing and explaining the most important aspects, rather than offering encyclopedic coverage, while providing the interested reader with a broad basis for further studies and research.

## Lyapunov Exponents of Linear Cocycles

*Continuity via Large Deviations*

**Author**: Pedro Duarte,Silvius Klein**Publisher:**Springer**ISBN:**9462391246**Category:**Mathematics**Page:**263**View:**1552

The aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.

## Moonwatch Only

*60 Years of OMEGA Speedmaster*

**Author**: Grégoire Rossier,Anthony Marquie**Publisher:**Watchprint.com Sarl**ISBN:**9782940506170**Category:****Page:**566**View:**9857

-A new edition of this definitive book, marking the 60th anniversary of the Speedmaster -Includes new features and additional historical information "The OMEGA Speedmaster Professional - the Moonwatch - has done things that no other timepiece has done and it has been worn in places that only a few human beings have been." - Captain Eugene Cernan, last man on the moon "It is an indescribable reference work and a true must-have for every Speedmaster collector." - Forbes There are very few timepieces in the world that deserve a definitive and comprehensive book. The OMEGA Speedmaster Professional Moonwatch is one of them. Initially designed for automobile racing teams and engineers, the Omega Speedmaster embarked on a very different trajectory when NASA chose it to accompany astronauts heading for the Moon in 1965. Its involvement in the space adventure has propelled the Moonwatch to the top of the list of celebrated timepieces. After years of research and observation, the authors present a complete panorama of the Moonwatch in a systematic work that is both technical and attractive, making it the unparalleled reference book for this legendary watch. This new edition, marking the 60th anniversary of the Speedmaster, has been enriched with numerous new features and additional historical information. Contents: Foreword by Raynald Aeschlimann, President and CEO of OMEGA; Foreword by Captain Eugene Cernan, Commander of Apollo 17; Why a Speedmaster Moonwatch guide?; Part 1 - Speedmaster History; 1, Major Dates; 2, Speedmaster and NASA 25; Part 2 - Main Components and Accessories; 1, An Original Approach; 2, The Caliber; 3, The Caseband; 4, The Dial; 5, The Bezel; 6, The Hands; 7, The Caseback; 8, The Crown; 9, The Pushers; 10, The Glass; 11, The Bracelet; 12, The Presentation Box; 13, The Documents; Part 3 - The Models; 1, Introduction; 2, Standard Production; 3, Special and Limited Series; 4, Personalized Models and Special Projects; 5, The Alaska Project; Part 4 - 60 Years of Innovation; Part 5 - How to Start Collecting Speedmasters; 1, Budget; 2, Choosing a Model; 3, Sales Channels; Part 6 - Appendices; 1, Model Codes; 2, Tables & Bibliography; 3, Contributions; 4, Identification Aid

## Combinatorial and Additive Number Theory

*CANT 2011 and 2012*

**Author**: Melvyn B. Nathanson**Publisher:**Springer**ISBN:**1493916017**Category:**Mathematics**Page:**312**View:**3530

This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems and future challenges in number theory.

## Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

**Author**: John Guckenheimer,P.J. Holmes**Publisher:**Springer Science & Business Media**ISBN:**1461211409**Category:**Mathematics**Page:**462**View:**9867

An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

## Contact and Symplectic Topology

**Author**: Frédéric Bourgeois,Vincent Colin,András Stipsicz**Publisher:**Springer Science & Business Media**ISBN:**3319020366**Category:**Science**Page:**530**View:**8330

Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.

## The Mathematical Education of Teachers II

**Author**: Conference Board of the Mathematical Sciences**Publisher:**American Mathematical Soc.**ISBN:**0821869264**Category:**Mathematics**Page:**86**View:**9816

This report is a resource for those who teach mathematics and statistics to pre-K-12 mathematics teachers, both future teachers and those who already teach in our nation's schools. The report makes recommendations for the mathematics that teachers should know and how they should come to know that mathematics.

## Geometric Group Theory

**Author**: Mladen Bestvina,Michah Sageev,Karen Vogtmann**Publisher:**American Mathematical Soc.**ISBN:**1470412276**Category:**Mathematics**Page:**339**View:**2230

Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

## 3-manifold Groups

**Author**: Matthias Aschenbrenner,Stefan Friedl,Henry Wilton**Publisher:**Erich Schmidt Verlag GmbH & Co. KG**ISBN:**9783037191545**Category:**Fundamental groups (Mathematics)**Page:**215**View:**7157

The field of 3-manifold topology has made great strides forward since 1982 when Thurston articulated his influential list of questions. Primary among these is Perelman's proof of the Geometrization Conjecture, but other highlights include the Tameness Theorem of Agol and Calegari-Gabai, the Surface Subgroup Theorem of Kahn-Markovic, the work of Wise and others on special cube complexes, and, finally, Agol's proof of the Virtual Haken Conjecture. This book summarizes all these developments and provides an exhaustive account of the current state of the art of 3-manifold topology, especially focusing on the consequences for fundamental groups of 3-manifolds. As the first book on 3-manifold topology that incorporates the exciting progress of the last two decades, it will be an invaluable resource for researchers in the field who need a reference for these developments. It also gives a fast-paced introduction to this material. Although some familiarity with the fundamental group is recommended, little other previous knowledge is assumed, and the book is accessible to graduate students. The book closes with an extensive list of open questions which will also be of interest to graduate students and established researchers.

## A Spinorial Approach to Riemannian and Conformal Geometry

**Author**: Jean-Pierre Bourguignon,Oussama Hijazi,Jean-Louis Milhorat,Sergiu Moroianu**Publisher:**Erich Schmidt Verlag GmbH & Co. KG**ISBN:**9783037191361**Category:**Clifford algebras**Page:**452**View:**4042

The book gives an elementary and comprehensive introduction to Spin Geometry, with particular emphasis on the Dirac operator, which plays a fundamental role in differential geometry and mathematical physics. After a self-contained presentation of the basic algebraic, geometrical, analytical and topological ingredients, a systematic study of the spectral properties of the Dirac operator on compact spin manifolds is carried out. The classical estimates on eigenvalues and their limiting cases are discussed next, highlighting the subtle interplay of spinors and special geometric structures. Several applications of these ideas are presented, including spinorial proofs of the Positive Mass Theorem or the classification of positive Kahler-Einstein contact manifolds. Representation theory is used to explicitly compute the Dirac spectrum of compact symmetric spaces. The special features of the book include a unified treatment of $\mathrm{Spin^c}$ and conformal spin geometry (with special emphasis on the conformal covariance of the Dirac operator), an overview with proofs of the theory of elliptic differential operators on compact manifolds based on pseudodifferential calculus, a spinorial characterization of special geometries, and a self-contained presentation of the representation-theoretical tools needed in order to apprehend spinors. This book will help advanced graduate students and researchers to get more familiar with this beautiful, though not sufficiently known, domain of mathematics with great relevance to both theoretical physics and geometry.

## Toroidal Embeddings 1

**Author**: G. Kempf,F. Knudsen,D. Mumford,B. Saint-Donat**Publisher:**Springer**ISBN:**3540377557**Category:**Mathematics**Page:**210**View:**5904

## Analysis and Numerics of Partial Differential Equations

**Author**: Franco Brezzi,Piero Colli Franzone,Ugo Pietro Gianazza,Gianni Gilardi**Publisher:**Springer Science & Business Media**ISBN:**8847025923**Category:**Mathematics**Page:**366**View:**9297

This volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.

## Tempered Homogeneous Function Spaces

**Author**: Hans Triebel**Publisher:**European Mathematical Society**ISBN:**9783037191552**Category:**Function spaces**Page:**130**View:**874

This book deals with homogeneous function spaces of Besov-Sobolev type within the framework of tempered distributions in Euclidean $n$-space based on Gauss-Weierstrass semi-groups. Related Fourier-analytical descriptions and characterizations in terms of derivatives and differences are incorporated after as so-called domestic norms. This approach avoids the usual ambiguities modulo polynomials when homogeneous function spaces are considered in the context of homogeneous tempered distributions. These notes are addressed to graduate students and mathematicians having a working knowledge of basic elements of the theory of function spaces, especially of Besov-Sobolev type. In particular, the book might be of interest for researchers dealing with (nonlinear) heat and Navier-Stokes equations in homogeneous function spaces.

## Handbook of Teichmüller Theory

**Author**: Athanase Papadopoulos**Publisher:**European Mathematical Society**ISBN:**9783037190555**Category:**Teichmüller spaces**Page:**874**View:**3679

## Algebraic Complexity Theory

**Author**: Peter Bürgisser,Michael Clausen,Amin Shokrollahi**Publisher:**Springer Science & Business Media**ISBN:**3662033380**Category:**Mathematics**Page:**618**View:**2164

The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.

## Momentum Maps and Hamiltonian Reduction

**Author**: Juan-Pablo Ortega,Tudor Ratiu**Publisher:**Springer Science & Business Media**ISBN:**9780817643072**Category:**Mathematics**Page:**501**View:**1472

* Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. * Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.

## Arithmetic of L-functions

**Author**: Cristian Popescu,Karl Rubin,Alice Silverberg**Publisher:**American Mathematical Soc.**ISBN:**0821886983**Category:**Mathematics**Page:**499**View:**2774

The overall theme of the 2009 IAS/PCMI Graduate Summer School was connections between special values of $L$-functions and arithmetic, especially the Birch and Swinnerton-Dyer Conjecture and Stark's Conjecture. These conjectures are introduced and discussed in depth, and progress made over the last 30 years is described. This volume contains the written versions of the graduate courses delivered at the summer school. It would be a suitable text for advanced graduate topics courses on the Birch and Swinnerton-Dyer Conjecture and/or Stark's Conjecture. The book will also serve as a reference volume for experts in the field.

## Lectures on Mathematics

**Author**: Felix Klein**Publisher:**N.A**ISBN:**N.A**Category:**Mathematics**Page:**109**View:**5045

## An Imaginary Tale

*The Story of √-1*

**Author**: Paul J. Nahin**Publisher:**Princeton University Press**ISBN:**9781400833894**Category:**Mathematics**Page:**296**View:**1215

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.

## Making Sense of Mathematics for Teaching Grades 6-8

*(Unifying Topics for an Understanding of Functions, Statistics, and Probability)*

**Author**: Edward C. Nolan,Juli K. Dixon**Publisher:**Solution Tree Press**ISBN:**194249646X**Category:**Education**Page:**176**View:**2483

Develop a deep understanding of mathematics. This user-friendly resource presents grades 6–8 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Make connections between elementary fraction-based content to fraction operations taught in the middle grades. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, and modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to grow as both learners and teachers of mathematics. Gain clarity about the most productive progression of mathematical teaching and learning for grades 6–8. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Fraction Operations and Integer Concepts and Operations 2 Ratios and Proportional Relationships 3 Equations, Expressions, and Inequalities 4 Functions 5 Measurement and Geometry 6 Statistics and Probability Epilogue: Next Steps References and Resources Index