Download or read book Ramified Surfaces written by Michael Friedman and published by Springer Nature. This book was released on 2022-09-26 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analytic Functions written by Rolf Nevanlinna and published by Springer. This book was released on 2013-12-20 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Galois Theory Coverings and Riemann Surfaces written by Askold Khovanskii and published by Springer Science & Business Media. This book was released on 2013-09-11 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ramified Surfaces written by Michael Friedman (Of Humboldt-Universität zu Berlin) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Thurston s Work on Surfaces MN 48 written by Albert Fathi and published by Princeton University Press. This book was released on 2021-07-13 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Graphs on Surfaces and Their Applications written by Sergei K. Lando and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Riemann Surfaces and Algebraic Curves written by Renzo Cavalieri and published by Cambridge University Press. This book was released on 2016-09-26 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
Download or read book A Course in Complex Analysis and Riemann Surfaces written by Wilhelm Schlag and published by American Mathematical Society. This book was released on 2014-08-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Riemann Surfaces written by Hershel M. Farkas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebra and Galois Theories written by Régine Douady and published by Springer Nature. This book was released on 2020-07-13 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Logos and Alogon written by Arkady Plotnitsky and published by Springer Nature. This book was released on 2023-01-16 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Topology written by Tammo tom Dieck and published by European Mathematical Society. This book was released on 2008 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends starting an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (master's) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included.
Download or read book The Kowalevski Property written by Vadim B. Kuznetsov and published by American Mathematical Soc.. This book was released on with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Number Theory written by H. Koch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995
Download or read book Atlas of Seeds and Fruits of Central and East European Flora written by Vít Bojnanský and published by Springer Science & Business Media. This book was released on 2007-11-07 with total page 1079 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Atlas of Seeds and Fruits of Central and East-European Flora presents nearly 4,800 seed illustrations, supplemented with detailed seed descriptions, brief plant descriptions, and information on the locality and the native source of plants. The Carpathian flora covered here occurs not only in the Carpathian Mountains, but also in large lowlands extending towards the south, north and east and involves introduced and invading flora of more than 7,500 species. This publication is unique on two counts. Its scope extends to an unprecedented number of different plant seeds from a wide-ranging region. Moreover, it presents descriptions in unusual detail.
Download or read book Dynamics in One Complex Variable AM 160 written by John Milnor and published by Princeton University Press. This book was released on 2011-02-11 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.
