Topology Ergodic Theory Real Algebraic Geometry

Author : Vladimir G. Turaev,Anatoliĭ Moiseevich Vershik
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 49,5 Mb
Release : 2001
Category : Biography & Autobiography
ISBN : 0821827405

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Topology, Ergodic Theory, Real Algebraic Geometry by Vladimir G. Turaev,Anatoliĭ Moiseevich Vershik Pdf

This volume is dedicated to the memory of the Russian mathematician, V.A. Rokhlin (1919-1984). It is a collection of research papers written by his former students and followers, who are now experts in their fields. The topics in this volume include topology (the Morse-Novikov theory, spin bordisms in dimension 6, and skein modules of links), real algebraic geometry (real algebraic curves, plane algebraic surfaces, algebraic links, and complex orientations), dynamics (ergodicity, amenability, and random bundle transformations), geometry of Riemannian manifolds, theory of Teichmuller spaces, measure theory, etc. The book also includes a biography of Rokhlin by Vershik and two articles which should prove of historical interest.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,8 Mb
Release : 2001
Category : Electronic
ISBN : 147043413X

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Topology, Ergodic Theory, Real Algebraic Geometry by Anonim Pdf

Author : Selman Akbulut
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 48,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821802922

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Real Algebraic Geometry and Topology by Selman Akbulut Pdf

This book contains the proceedings of the Real Algebraic Geometry-Topology Conference, held at Michigan State University in December 1993. Presented here are recent results and discussions of new ideas pertaining to such topics as resolution theorems, algebraic structures, topology of nonsingular real algebraic sets, and the distribution of real algebraic sets in projective space.

Author : Robert J. Zimmer
Publisher : University of Chicago Press
Page : 724 pages
File Size : 51,5 Mb
Release : 2019-12-23
Category : Mathematics
ISBN : 9780226568270

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Group Actions in Ergodic Theory, Geometry, and Topology by Robert J. Zimmer Pdf

Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 48,7 Mb
Release : 1968-12-31
Category : Electronic
ISBN : 0821896423

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Thirteen Papers on Group Theory, Algebraic Geometry and Algebraic Topology by Anonim Pdf

Author : Vladimir Igorevich Arnolʹd,Maxim Kontsevich,Anton Zorich
Publisher : Unknown
Page : 128 pages
File Size : 48,6 Mb
Release : 1999
Category : Electronic
ISBN : 1470434083

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Pseudoperiodic Topology by Vladimir Igorevich Arnolʹd,Maxim Kontsevich,Anton Zorich Pdf

This volume offers an account of the present state of the art in pseudoperiodic topology-a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors ... have done much to s.

Author : Vladimir Igorevich Arnolʹd,Maxim Kontsevich,Anton Zorich
Publisher : American Mathematical Soc.
Page : 196 pages
File Size : 54,6 Mb
Release : 1999
Category : Mathematics
ISBN : 082182094X

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Pseudoperiodic Topology by Vladimir Igorevich Arnolʹd,Maxim Kontsevich,Anton Zorich Pdf

This volume offers an account of the present state of the art in pseudoperiodic topology--a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors ... have done much to show how modern mathematics begets, from this sea of pathological counterexamples, remarkable general and universal laws, whose discovery would be unthinkable and whose formulation would be impossible in the naive set-theoretical setting."

Author : Anatoly M. Vershik,Victor M. Buchstaber,Andrey V. Malyutin
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 44,9 Mb
Release : 2021-08-30
Category : Education
ISBN : 9781470456641

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Topology, Geometry, and Dynamics: V. A. Rokhlin-Memorial by Anatoly M. Vershik,Victor M. Buchstaber,Andrey V. Malyutin Pdf

Vladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.

Author : Solomon Lefschetz
Publisher : American Mathematical Soc.
Page : 428 pages
File Size : 47,9 Mb
Release : 1930-12-31
Category : Mathematics
ISBN : 9780821846032

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Topology by Solomon Lefschetz Pdf

Lefschetz's Topology was written in the period in between the beginning of topology, by Poincare, and the establishment of algebraic topology as a well-formed subject, separate from point-set or geometric topology. At this time, Lefschetz had already proved his first fixed-point theorems. In some sense, the present book is a description of the broad subject of topology into which Lefschetz's theory of fixed points fits. Lefschetz takes the opportunity to describe some of the important applications of his theory, particularly in algebraic geometry, to problems such as counting intersections of algebraic varieties. He also gives applications to vector distributions, complex spaces, and Kronecker's characteristic theory.

Author : L.A. Bunimovich,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 53,7 Mb
Release : 2000-04-05
Category : Mathematics
ISBN : 3540663169

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Dynamical Systems, Ergodic Theory and Applications by L.A. Bunimovich,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik Pdf

This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

Author : Sergeĭ Vladimirovich Matveev
Publisher : European Mathematical Society
Page : 112 pages
File Size : 41,6 Mb
Release : 2006
Category : Mathematics
ISBN : 303719023X

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Lectures on Algebraic Topology by Sergeĭ Vladimirovich Matveev Pdf

Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.

Author : Frédéric Mangolte
Publisher : Springer Nature
Page : 453 pages
File Size : 40,7 Mb
Release : 2020-09-21
Category : Mathematics
ISBN : 9783030431044

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Real Algebraic Varieties by Frédéric Mangolte Pdf

This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous.They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable. This book is intended for two kinds of audiences: it accompanies the reader, familiar with algebra and geometry at the masters level, in learning the basics of this rich theory, as much as it brings to the most advanced reader many fundamental results often missing from the available literature, the “folklore”. In particular, the introduction of topological methods of the theory to non-specialists is one of the original features of the book. The first three chapters introduce the basis and classical methods of real and complex algebraic geometry. The last three chapters each focus on one more specific aspect of real algebraic varieties. A panorama of classical knowledge is presented, as well as major developments of the last twenty years in the topology and geometry of varieties of dimension two and three, without forgetting curves, the central subject of Hilbert's famous sixteenth problem. Various levels of exercises are given, and the solutions of many of them are provided at the end of each chapter.

Author : Robert J. Zimmer,Dave Witte Morris
Publisher : American Mathematical Soc.
Page : 103 pages
File Size : 40,6 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780821883365

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Ergodic Theory, Groups, and Geometry by Robert J. Zimmer,Dave Witte Morris Pdf

"The study of group actions on manifolds is the meeting ground of a variety of mathematical areas. In particular, interesting geometric insights can be obtained by applying measure-theoretic techniques. This book provides an introduction to some of the important methods, major developments, and open problems in the subject. It is slightly expanded from lectures given by Zimmer at the CBMS conference at the University of Minnesota. The main text presents a perspective on the field as it was at that time. Comments at the end of each chapter provide selected suggestions for further reading, including references to recent developments."--BOOK JACKET.

Author : Thorsten Theobald
Publisher : American Mathematical Society
Page : 312 pages
File Size : 45,6 Mb
Release : 2024-04-17
Category : Mathematics
ISBN : 9781470474317

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Real Algebraic Geometry and Optimization by Thorsten Theobald Pdf

This book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications. Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required.

Author : David Kerr,Hanfeng Li
Publisher : Springer
Page : 431 pages
File Size : 40,8 Mb
Release : 2017-02-09
Category : Mathematics
ISBN : 9783319498478

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Ergodic Theory by David Kerr,Hanfeng Li Pdf

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.