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Geometry and Dynamics of Groups and Spaces

Author: Mikhail Kapranov

Publisher: Springer Science & Business Media

Published: 2008-03-05

Total Pages: 759

ISBN-13: 3764386088

Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.

Geometry and Dynamics in Gromov Hyperbolic Metric Spaces

Author: Tushar Das

Publisher: American Mathematical Soc.

Published: 2017-04-14

Total Pages: 321

ISBN-13: 1470434652

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This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.

Geometry, Rigidity, and Group Actions

Author: Robert J. Zimmer

Publisher: University of Chicago Press

Published: 2011-04-15

Total Pages: 659

ISBN-13: 0226237893

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The study of group actions is more than 100 years old but remains a widely studied topic in a variety of mathematic fields. A central development in the last 50 years is the phenomenon of rigidity, whereby one can classify actions of certain groups. This book looks at rigidity.

Dynamics, Geometry, Number Theory

Author: David Fisher

Publisher: University of Chicago Press

Published: 2022-02-07

Total Pages: 573

ISBN-13: 022680402X

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"Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--

Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces

Author: M. Bachir Bekka

Publisher: Cambridge University Press

Published: 2000-05-11

Total Pages: 214

ISBN-13: 9780521660303

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This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.

Foliations and the Geometry of 3-Manifolds

Author: Danny Calegari

Publisher: Oxford University Press on Demand

Published: 2007-05-17

Total Pages: 378

ISBN-13: 0198570082

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This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.

Moduli Spaces and Arithmetic Dynamics

Author: Joseph H. Silverman

Publisher: American Mathematical Soc.

Published:

Total Pages: 151

ISBN-13: 0821885030

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Geometry Of Time-spaces: Non-commutative Algebraic Geometry, Applied To Quantum Theory

Author: Olav Arnfinn Laudal

Publisher: World Scientific

Published: 2011-03-21

Total Pages: 154

ISBN-13: 9814460702

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This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory of phase spaces, and its canonical Dirac derivation. The book starts with a new definition of time, relative to which the set of mathematical velocities form a compact set, implying special and general relativity. With this model in mind, a general Quantum Theory is developed and shown to fit with the classical theory. In particular the “toy”-model used as example, contains, as part of the structure, the classical gauge groups u(1), su(2) and su(3), and therefore also the theory of spin and quarks, etc.