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Introduction to Compact Riemann Surfaces and Dessins D'Enfants

Introduction to Compact Riemann Surfaces and Dessins D'Enfants

  • Author: Ernesto Girondo,Gabino González-Diez
  • Publisher: Cambridge University Press
  • ISBN: 0521519632
  • Category: Mathematics
  • Page: 298
  • View: 6065
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An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi-Grothendieck theory of dessins d'enfants.

Dessins d'Enfants on Riemann Surfaces

Dessins d'Enfants on Riemann Surfaces

  • Author: Gareth A. Jones,Jürgen Wolfart
  • Publisher: Springer
  • ISBN: 3319247115
  • Category: Mathematics
  • Page: 259
  • View: 6175
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This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces. The first part of the book presents basic material, guiding the reader through the current field of research. A key point of the second part is the interplay between the automorphism groups of dessins and their Riemann surfaces, and the action of the absolute Galois group on dessins and their algebraic curves. It concludes by showing the links between the theory of dessins and other areas of arithmetic and geometry, such as the abc conjecture, complex multiplication and Beauville surfaces. Dessins d'Enfants on Riemann Surfaces will appeal to graduate students and all mathematicians interested in maps, hypermaps, Riemann surfaces, geometric group actions, and arithmetic.

Rigidity and Symmetry

Rigidity and Symmetry

  • Author: Robert Connelly,Asia Ivić Weiss,Walter Whiteley
  • Publisher: Springer
  • ISBN: 1493907816
  • Category: Mathematics
  • Page: 374
  • View: 5893
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This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.

Symmetries in Graphs, Maps, and Polytopes

Symmetries in Graphs, Maps, and Polytopes

5th SIGMAP Workshop, West Malvern, UK, July 2014

  • Author: Jozef Širáň,Robert Jajcay
  • Publisher: Springer
  • ISBN: 3319304518
  • Category: Mathematics
  • Page: 332
  • View: 2459
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This volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d’enfant.Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In Graphs, Maps, and Polytopes Workshop 2014 was the fifth in a series of workshops. The initial workshop, organized by Steve Wilson in Flagstaff, Arizona, in 1998, was followed in 2002 and 2006 by two meetings held in Aveiro, Portugal, organized by Antonio Breda d’Azevedo, and a fourth workshop held in Oaxaca, Mexico, organized by Isabel Hubard in 2010.This book should appeal to both specialists and those seeking a broad overview of what is happening in the area of symmetries of discrete objects and structures.iv>

Complex Functions

Complex Functions

An Algebraic and Geometric Viewpoint

  • Author: Gareth A. Jones,David Singerman
  • Publisher: Cambridge University Press
  • ISBN: 9780521313667
  • Category: Mathematics
  • Page: 342
  • View: 5156
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Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics. At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations. In this book the authors give elementary accounts of many aspects of classical complex function theory including Möbius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. A distinctive feature of their presentation is the way in which they have incorporated into the text many interesting topics from other branches of mathematics. This book is based on lectures given to advanced undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread application throughout mathematics.

An Invitation to Algebraic Geometry

An Invitation to Algebraic Geometry

  • Author: Karen E. Smith,Lauri Kahanpää,Pekka Kekäläinen,William Traves
  • Publisher: Springer Science & Business Media
  • ISBN: 1475744978
  • Category: Mathematics
  • Page: 164
  • View: 2673
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This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Geometry of Riemann Surfaces

Geometry of Riemann Surfaces

  • Author: Frederick P. Gardiner,Gabino González-Diez,Christos Kourouniotis
  • Publisher: Cambridge University Press
  • ISBN: 0521733073
  • Category: Mathematics
  • Page: 395
  • View: 4776
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Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, conformal dynamics, discrete groups, algebraic curves and more. This collection of articles presents original research and expert surveys of important related topics, making the field accessible to research workers, graduate students and teachers.

A Radical Approach to Lebesgue's Theory of Integration

A Radical Approach to Lebesgue's Theory of Integration

  • Author: David M. Bressoud
  • Publisher: Cambridge University Press
  • ISBN: 0521884748
  • Category: Mathematics
  • Page: 329
  • View: 7826
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Meant for advanced undergraduate and graduate students in mathematics, this introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author tells the story of the mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of Jordan, Borel, and Lebesgue.

An Introduction to Our Dynamic Planet

An Introduction to Our Dynamic Planet

  • Author: Nick Rogers,Stephen Blake
  • Publisher: Cambridge University Press
  • ISBN: 9780521494243
  • Category: Science
  • Page: 390
  • View: 1073
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At last, an undergraduate textbook integrating the geophysics, geochemistry, and petrology of the Earth to explain plate tectonics and geodynamics.

Quantum Triangulations

Quantum Triangulations

Moduli Spaces, Strings, and Quantum Computing

  • Author: Mauro Carfora,Annalisa Marzuoli
  • Publisher: Springer Science & Business Media
  • ISBN: 3642244394
  • Category: Science
  • Page: 284
  • View: 4742
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Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.

Introduction to Modeling Biological Cellular Control Systems

Introduction to Modeling Biological Cellular Control Systems

  • Author: Weijiu Liu
  • Publisher: Springer Science & Business Media
  • ISBN: 8847024900
  • Category: Mathematics
  • Page: 272
  • View: 3448
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This textbook contains the essential knowledge in modeling, simulation, analysis, and applications in dealing with biological cellular control systems. In particular, the book shows how to use the law of mass balance and the law of mass action to derive an enzyme kinetic model - the Michaelis-Menten function or the Hill function, how to use a current-voltage relation, Nernst potential equilibrium equation, and Hodgkin and Huxley's models to model an ionic channel or pump, and how to use the law of mass balance to integrate these enzyme or channel models into a complete feedback control system. The book also illustrates how to use data to estimate parameters in a model, how to use MATLAB to solve a model numerically, how to do computer simulations, and how to provide model predictions. Furthermore, the book demonstrates how to conduct a stability and sensitivity analysis on a model.

Algebraic curves

Algebraic curves

an introduction to algebraic geometry

  • Author: William Fulton
  • Publisher: Addison-Wesley
  • ISBN: N.A
  • Category: Mathematics
  • Page: 226
  • View: 6915
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Lectures on the Mordell-Weil Theorem

Lectures on the Mordell-Weil Theorem

  • Author: Jean-Pierre Serre
  • Publisher: Springer Science & Business Media
  • ISBN: 3663106322
  • Category: Technology & Engineering
  • Page: 218
  • View: 5615
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The book is based on a course given by J.-P. Serre at the Collège de France in 1980 and 1981. Basic techniques in Diophantine geometry are covered, such as heights, the Mordell-Weil theorem, Siegel's and Baker's theorems, Hilbert's irreducibility theorem, and the large sieve. Included are applications to, for example, Mordell's conjecture, the construction of Galois extensions, and the classical class number 1 problem. Comprehensive bibliographical references.

Problems on Mapping Class Groups and Related Topics

Problems on Mapping Class Groups and Related Topics

  • Author: Benson Farb
  • Publisher: American Mathematical Soc.
  • ISBN: 0821838385
  • Category: Mathematics
  • Page: 371
  • View: 648
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The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.

Plane Algebraic Curves

Plane Algebraic Curves

  • Author: BRIESKORN,KNÖRRER
  • Publisher: Birkhäuser
  • ISBN: 3034850972
  • Category: Mathematics
  • Page: 721
  • View: 1599
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An Introduction to the Theory of Numbers

An Introduction to the Theory of Numbers

  • Author: Godfrey Harold Hardy,E. M. Wright,Roger Heath-Brown,Joseph Silverman
  • Publisher: Oxford University Press
  • ISBN: 9780199219865
  • Category: Mathematics
  • Page: 621
  • View: 5902
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An Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. This Sixth Edition has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter on one of the mostimportant developments in number theory -- modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader and the clarityof exposition is retained throughout making this textbook highly accessible to undergraduates in mathematics from the first year upwards.

Graphs on Surfaces and Their Applications

Graphs on Surfaces and Their Applications

  • Author: Sergei K. Lando,Alexander K. Zvonkin
  • Publisher: Springer Science & Business Media
  • ISBN: 3540383611
  • Category: Mathematics
  • Page: 455
  • View: 3923
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Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

2016 MATRIX Annals

2016 MATRIX Annals

  • Author: Jan de Gier,Cheryl E. Praeger,Terence Tao
  • Publisher: Springer
  • ISBN: 3319722999
  • Category: Mathematics
  • Page: 656
  • View: 1488
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MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: Higher Structures in Geometry and Physics (Chapters 1-5 and 18-21); Winter of Disconnectedness (Chapter 6 and 22-26); Approximation and Optimisation (Chapters 7-8); Refining C*-Algebraic Invariants for Dynamics using KK-theory (Chapters 9-13); Interactions between Topological Recursion, Modularity, Quantum Invariants and Low-dimensional Topology (Chapters 14-17 and 27). The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.

Complex Algebraic Curves

Complex Algebraic Curves

  • Author: Frances Clare Kirwan
  • Publisher: Cambridge University Press
  • ISBN: 9780521423533
  • Category: Mathematics
  • Page: 264
  • View: 4668
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This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.

Topics on Riemann Surfaces and Fuchsian Groups

Topics on Riemann Surfaces and Fuchsian Groups

  • Author: E. Bujalance,Emilio Bujalance García,Paul Allan Mirecki,A. F. Costa,Jason BeDuhn,E. Martínez,Ernesto Martínez
  • Publisher: Cambridge University Press
  • ISBN: 9780521003506
  • Category: Mathematics
  • Page: 177
  • View: 5724
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Introduction to Riemann surfaces for graduates and researchers, giving refreshingly new insights into the subject.