Ramified Surfaces

Author : Michael Friedman
Publisher : Springer Nature
Page : 258 pages
File Size : 45,7 Mb
Release : 2022-09-26
Category : Mathematics
ISBN : 9783031057205

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Ramified Surfaces by Michael Friedman Pdf

The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezon’s program of braid monodromy factorization. By focusing on how the research on one specific curve changed during the 20th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20th century, considering this curve as an intersection of several research approaches and methods. Researchers in the history of science and of mathematics as well as mathematicians will certainly find this book interesting and appealing, contributing to the growing research on the history of algebraic geometry and its changing images.

Author : Michael Friedman (Of Humboldt-Universität zu Berlin)
Publisher : Unknown
Page : 0 pages
File Size : 48,8 Mb
Release : 2022
Category : Electronic books
ISBN : 8303105728

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Ramified Surfaces by Michael Friedman (Of Humboldt-Universität zu Berlin) Pdf

The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezons program of braid monodromy factorization. By focusing on how the research on one specific curve changed during the 20th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20th century, considering this curve as an intersection of several research approaches and methods. Researchers in the history of science and of mathematics as well as mathematicians will certainly find this book interesting and appealing, contributing to the growing research on the history of algebraic geometry and its changing images.

Author : Rolf Nevanlinna
Publisher : Springer
Page : 383 pages
File Size : 40,7 Mb
Release : 2013-12-20
Category : Mathematics
ISBN : 9783642855900

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Analytic Functions by Rolf Nevanlinna Pdf

The present monograph on analytic functions coincides to a lar[extent with the presentation of the modern theory of single-value analytic functions given in my earlier works "Le theoreme de Picarc Borel et la theorie des fonctions meromorphes" (Paris: Gauthier-Villar 1929) and "Eindeutige analytische Funktionen" (Die Grundlehren dt mathematischen Wissenschaften in Einzeldarstellungen, VoL 46, 1: edition Berlin: Springer 1936, 2nd edition Berlin-Gottingen-Heidelberg Springer 1953). In these presentations I have strived to make the individual result and their proofs readily understandable and to treat them in the ligh of certain guiding principles in a unified way. A decisive step in thi direction within the theory of entire and meromorphic functions consiste- in replacing the classical representation of these functions through ca nonical products with more general tools from the potential theor (Green's formula and especially the Poisson-Jensen formula). On thi foundation it was possible to introduce the quantities (the characteristic the proximity and the counting functions) which are definitive for th

Author : Askold Khovanskii
Publisher : Springer Science & Business Media
Page : 86 pages
File Size : 54,5 Mb
Release : 2013-09-11
Category : Mathematics
ISBN : 9783642388415

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Galois Theory, Coverings, and Riemann Surfaces by Askold Khovanskii Pdf

The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to the topological Galois theory developed by the author. All results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers.

Author : Albert Fathi,François Laudenbach,Valentin Poénaru
Publisher : Princeton University Press
Page : 272 pages
File Size : 47,7 Mb
Release : 2021-07-13
Category : Mathematics
ISBN : 9781400839032

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Thurston's Work on Surfaces (MN-48) by Albert Fathi,François Laudenbach,Valentin Poénaru Pdf

This book provides a detailed exposition of William Thurston's work on surface homeomorphisms, available here for the first time in English. Based on material of Thurston presented at a seminar in Orsay from 1976 to 1977, it covers topics such as the space of measured foliations on a surface, the Thurston compactification of Teichmüller space, the Nielsen-Thurston classification of surface homeomorphisms, and dynamical properties of pseudo-Anosov diffeomorphisms. Thurston never published the complete proofs, so this text is the only resource for many aspects of the theory. Thurston was awarded the prestigious Fields Medal in 1982 as well as many other prizes and honors, and is widely regarded to be one of the major mathematical figures of our time. Today, his important and influential work on surface homeomorphisms is enjoying continued interest in areas ranging from the Poincaré conjecture to topological dynamics and low-dimensional topology. Conveying the extraordinary richness of Thurston's mathematical insight, this elegant and faithful translation from the original French will be an invaluable resource for the next generation of researchers and students.

Author : Sergei K. Lando,Alexander K. Zvonkin
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 43,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783540383611

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Graphs on Surfaces and Their Applications by Sergei K. Lando,Alexander K. Zvonkin Pdf

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.

Author : Wilhelm Schlag
Publisher : American Mathematical Society
Page : 402 pages
File Size : 40,8 Mb
Release : 2014-08-06
Category : Mathematics
ISBN : 9780821898475

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A Course in Complex Analysis and Riemann Surfaces by Wilhelm Schlag Pdf

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.

Author : Hershel M. Farkas,Irwin Kra
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220343

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Riemann Surfaces by Hershel M. Farkas,Irwin Kra Pdf

This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case, while basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the associated Abelian varities. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented, as are alternate proofs for the most important results, showing the diversity of approaches to the subject. Of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics.

Author : Régine Douady,Adrien Douady
Publisher : Springer Nature
Page : 462 pages
File Size : 47,8 Mb
Release : 2020-07-13
Category : Mathematics
ISBN : 9783030327965

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Algebra and Galois Theories by Régine Douady,Adrien Douady Pdf

Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.

Author : C. van den Berg,G. Forst,B. Fuglede
Publisher : Springer
Page : 331 pages
File Size : 53,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540391838

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Potential Theory: Copenhagen 1979 by C. van den Berg,G. Forst,B. Fuglede Pdf

Author : Leon Greenberg
Publisher : Princeton University Press
Page : 452 pages
File Size : 43,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881642

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Discontinuous Groups and Riemann Surfaces (AM-79), Volume 79 by Leon Greenberg Pdf

Study 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, May 21-25, 1973. The papers, by leading authorities, deal mainly with Fuchsian and Kleinian groups, Teichmüller spaces, Jacobian varieties, and quasiconformal mappings. These topics are intertwined, representing a common meeting of algebra, geometry, and analysis.

Author : Arkady Plotnitsky
Publisher : Springer Nature
Page : 307 pages
File Size : 53,5 Mb
Release : 2023-01-16
Category : Mathematics
ISBN : 9783031136788

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Logos and Alogon by Arkady Plotnitsky Pdf

This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book’s title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields.

Author : Vadim B. Kuznetsov
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 51,5 Mb
Release : 2024-06-29
Category : Mathematics
ISBN : 082187330X

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The Kowalevski Property by Vadim B. Kuznetsov Pdf

This book is a collection of survey articles on several topics related to the general notion of integrability. It stems from a workshop on ''Mathematical Methods of Regular Dynamics'' dedicated to Sophie Kowalevski. Leading experts introduce corresponding areas in depth. The book provides a broad overview of research, from the pioneering work of the nineteenth century to the developments of the 1970s through the present. The book begins with two historical papers by R. L. Cooke onKowalevski's life and work. Following are 15 research surveys on integrability issues in differential and algebraic geometry, classical complex analysis, discrete mathematics, spinning tops, Painleve equations, global analysis on manifolds, special functions, etc. It concludes with Kowalevski's famouspaper published in Acta Mathematica in 1889, ''Sur le probleme de la rotation d'un corps solide autour d'un point fixe''. The book is suitable for graduate students in pure and applied mathematics, the general mathematical audience studying integrability, and research mathematicians interested in differential and algebraic geometry, analysis, and special functions.

Author : Nagel, Sven
Publisher : KIT Scientific Publishing
Page : 296 pages
File Size : 45,7 Mb
Release : 2022-05-27
Category : Technology & Engineering
ISBN : 9783731511267

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Design of Cast Steel Components under Cyclic Loading by Nagel, Sven Pdf

This work presents a design approach that links fatigue resistance of cast steel component to permissible defect sizes. It is based on fractures mechanics, is in line with experiences of the last 60 years and validated by extensive experimental as well as numerical investigations on different scales and under consideration of real casting defects. By following established assessment methods, the design concept is adapted to practical building applications.

Author : Oleg Efimov
Publisher : CRC Press
Page : 524 pages
File Size : 53,9 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351093385

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Russian-English Dictionary of Mathematics by Oleg Efimov Pdf

An essential book for anyone using Russian mathematical and scientific literature Russian-English Dictionary of Mathematics embraces all major branches of mathematics from elementary topics to advanced studies in topology and discrete mathematics. Terms from the newest branches of mathematics, such as the theories of games, trees, knots, and braids, are included as well.Containing more than 27,000 entries, Russian-English Dictionary of Mathematics is larger and provides a broader scope than any other bilingual mathematics dictionary now in use. Many adjectives and verbs are included, and a copious amount of synonyms are provided for various terms. Secondary terms are grouped under principal terms for easier reference.Russian-English Dictionary of Mathematics provides the most comprehensive vocabulary aid available for translators, readers, and writers of Russian mathematical and scientific literature.