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Author: V. Ovsienko
Publisher: Cambridge University Press
ISBN: 9781139455916
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject.
Author: V. Ovsienko
Publisher: Cambridge University Press
ISBN: 9781139455916
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject.
Author: Jürgen Richter-Gebert
Publisher: Springer Science & Business Media
ISBN: 3642172865
Category : Mathematics
Languages : en
Pages : 573
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Book Description
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
Author: Valentin Ovsienko
Publisher:
ISBN: 9780511265068
Category : Projective differential geometry
Languages : en
Pages : 249
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Book Description
Author: Jaume Amorós
Publisher: American Mathematical Soc.
ISBN: 0821804987
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This book is an exposition of what is currently known about the fundamental groups of compact Kähler manifolds. This class of groups contains all finite groups and is strictly smaller than the class of all finitely presentable groups. For the first time ever, this book collects together all the results obtained in the last few years which aim to characterize those infinite groups which can arise as fundamental groups of compact Kähler manifolds. Most of these results are negative ones, saying which groups don not arise. The methods and techniques used form an attractive mix of topology, differential and algebraic geometry, and complex analysis. The book would be useful to researchers and graduate students interested in any of these areas, and it could be used as a textbook for an advanced graduate course. One of its outstanding features is a large number of concrete examples. The book contains a number of new results and examples which have not appeared elsewhere, as well as discussions of some important open questions in the field.
Author: Dirk J. Struik
Publisher: Courier Corporation
ISBN: 0486485951
Category : Mathematics
Languages : en
Pages : 306
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Book Description
This undergraduate text develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. 1953 edition.
Author: Ernest Julius Wilczynski
Publisher:
ISBN:
Category : Projective differential geometry
Languages : en
Pages : 322
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Book Description
Author: Victor Prasolov
Publisher: Cambridge University Press
ISBN: 9781139441124
Category : Mathematics
Languages : en
Pages : 364
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Book Description
This collection of articles from the Independent University of Moscow is derived from the Globus seminars held there. They are given by world authorities, from Russia and elsewhere, in various areas of mathematics and are designed to introduce graduate students to some of the most dynamic areas of mathematical research. The seminars aim to be informal, wide-ranging and forward-looking, getting across the ideas and concepts rather than formal proofs, and this carries over to the articles here. Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups. The volume as a whole is a fascinating and exciting overview of contemporary mathematics.
Author: M. Amélia Bastos
Publisher: Springer
ISBN: 303480816X
Category : Mathematics
Languages : en
Pages : 379
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Book Description
This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geometry of difference Lax operators).
Author: Andrés Navas
Publisher: University of Chicago Press
ISBN: 0226569500
Category : Mathematics
Languages : en
Pages : 310
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Book Description
In recent years scholars from a variety of branches of mathematics have made several significant developments in the theory of group actions. Groups of Circle Diffeomorphisms systematically explores group actions on the simplest closed manifold, the circle. As the group of circle diffeomorphisms is an important subject in modern mathematics, this book will be of interest to those doing research in group theory, dynamical systems, low dimensional geometry and topology, and foliation theory. The book is mostly self-contained and also includes numerous complementary exercises, making it an excellent textbook for undergraduate and graduate students.
Author: Devin Griffiths
Publisher: JHU Press
ISBN: 1421420775
Category : Literary Criticism
Languages : en
Pages : 353
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Book Description
How did literature shape nineteenth-century science? Erasmus Darwin and his grandson, Charles, were the two most important evolutionary theorists of eighteenth- and nineteenth-century Britain. Although their ideas and methods differed, both Darwins were prolific and inventive writers: Erasmus composed several epic poems and scientific treatises, while Charles is renowned both for his collected journals (now titled The Voyage of the Beagle) and for his masterpiece, The Origin of Species. In The Age of Analogy, Devin Griffiths argues that the Darwins’ writing style was profoundly influenced by the poets, novelists, and historians of their era. The Darwins, like other scientists of the time, labored to refashion contemporary literary models into a new mode of narrative analysis that could address the contingent world disclosed by contemporary natural science. By employing vivid language and experimenting with a variety of different genres, these writers gave rise to a new relational study of antiquity, or “comparative historicism,” that emerged outside of traditional histories. It flourished instead in literary forms like the realist novel and the elegy, as well as in natural histories that explored the continuity between past and present forms of life. Nurtured by imaginative cross-disciplinary descriptions of the past—from the historical fiction of Sir Walter Scott and George Eliot to the poetry of Alfred Tennyson—this novel understanding of history fashioned new theories of natural transformation, encouraged a fresh investment in social history, and explained our intuition that environment shapes daily life. Drawing on a wide range of archival evidence and contemporary models of scientific and literary networks, The Age of Analogy explores the critical role analogies play within historical and scientific thinking. Griffiths also presents readers with a new theory of analogy that emphasizes language's power to foster insight into nature and human society. The first comparative treatment of the Darwins’ theories of history and their profound contribution to the study of both natural and human systems, this book will fascinate students and scholars of nineteenth-century British literature and the history of science.
