riemann surfaces oxford graduate texts in mathematics

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Riemann Surfaces

Author : Simon Donaldson
ISBN : 9780198526391
Genre : Mathematics
File Size : 26. 41 MB
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An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.

Integrable Systems

Author : N.J. Hitchin
ISBN : 9780199676774
Genre : Mathematics
File Size : 28. 98 MB
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Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.

A Course In Complex Analysis And Riemann Surfaces

Author : Wilhelm Schlag
ISBN : 9780821898475
Genre : Mathematics
File Size : 27. 74 MB
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Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.

Moduli Spaces Of Riemann Surfaces

Author : Benson Farb
ISBN : 9780821898871
Genre : Mathematics
File Size : 79. 15 MB
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Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures 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 book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. 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.

Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces

Author : William Mark Goldman
ISBN : 9780821841365
Genre : Mathematics
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This expository article details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. The authors construct an equivalence between the deformation theories of flat connections and Higgs pairs. This provides an identification of moduli spaces arising in different contexts. The moduli spaces are real Lie groups. From each context arises a complex structure, and the different complex structures define a hyperkahler structure. The twistor space, real forms, and various group actions are computed explicitly in terms of the Jacobian of $X$. The authors describe the moduli spaces and their geometry in terms of the Riemann period matrix of $X$. This is the simplest case of the theory developed by Hitchin, Simpson and others. The authors emphasize its formal aspects that generalize to higher rank Higgs bundles over higher dimensional Kahler manifolds.

In The Tradition Of Ahlfors Bers Vii

Author : Ara S. Basmajian
ISBN : 9781470426514
Genre : Functions
File Size : 47. 88 MB
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The Ahlfors–Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmüller theory, hyperbolic geometry, and partial differential equations. Today we see the influence of Ahlfors and Bers on algebraic geometry, mathematical physics, dynamics, probability, geometric group theory, number theory and topology. Recent years have seen a flowering of this legacy with an increased interest in their work. This current volume contains articles on a wide variety of subjects that are central to this legacy. These include papers in Kleinian groups, classical Riemann surface theory, Teichmüller theory, mapping class groups, geometric group theory, and statistical mechanics.

Quasiconformal Maps And Teichm Ller Theory

Author : Alastair Fletcher
ISBN : 0198569262
Genre : Mathematics
File Size : 37. 44 MB
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Based on a series of graduate lectures given by Vladimir Markovic at the University of Warwick in spring 2003, this book is accessible to those with a grounding in complex analysis looking for an introduction to the theory of quasiconformal maps and Teichm�ller theory. Assuming some familiarity with Riemann surfaces and hyperbolic geometry, topics covered include the Gr�tzch argument, analytical properties of quasiconformal maps, the Beltrami differential equation, holomorphic motions and Teichm�ller spaces. Where proofs are omitted, references to where they may be found are always given, and the text is clearly illustrated throughout with diagrams, examples, and exercises for the reader.

Stochastic Analysis And Diffusion Processes

Author : Gopinath Kallianpur
ISBN : 9780199657070
Genre : Mathematics
File Size : 37. 47 MB
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Beginning with the concept of random processes and Brownian motion and building on the theory and research directions in a self-contained manner, this book provides an introduction to stochastic analysis for graduate students, researchers and applied scientists interested in stochastic processes and their applications.

Nonlinearity

Author :
ISBN : OSU:32435067849869
Genre : Mathematical analysis
File Size : 77. 63 MB
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Documenta Mathematica

Author :
ISBN : UOM:39015060986083
Genre : Mathematics
File Size : 27. 37 MB
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