Author: Bertrand Eynard
Publisher: Springer Science & Business Media
ISBN: 3764387971
Category : Mathematics
Languages : en
Pages : 427
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Book Description
The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ... etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained. Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. Mor e generally, an important problem in algebraic geometry is to characterize the moduli spaces, by computing not only their volumes, but also other characteristic numbers called intersection numbers. Witten's conjecture (which was first proved by Kontsevich), was the assertion that Riemann surfaces can be obtained as limits of polygonal surfaces (maps), made of a very large number of very small polygons. In other words, the number of maps in a certain limit, should give the intersection numbers of moduli spaces. In this book, we show how that limit takes place. The goal of this book is to explain the "matrix model" method, to show the main results obtained with it, and to compare it with methods used in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions). The book intends to be self-contained and accessible to graduate students, and provides comprehensive proofs, several examples, and give s the general formula for the enumeration of maps on surfaces of any topology. In the end, the link with more general topics such as algebraic geometry, string theory, is discussed, and in particular a proof of the Witten-Kontsevich conjecture is provided.
Author: Jayadev S. Athreya
Publisher: American Mathematical Society
ISBN: 147047655X
Category : Mathematics
Languages : en
Pages : 195
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Book Description
This textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of translation flows, counting problems for saddle connections, and associated renormalization techniques. Proofs that go beyond the introductory nature of the book are deftly omitted, allowing readers to develop essential tools and motivation before delving into the literature. Beginning with the fundamental example of the flat torus, the book goes on to establish the three equivalent definitions of translation surface. An introduction to the moduli space of translation surfaces follows, leading into a study of the dynamics and ergodic theory associated to a translation surface. Counting problems and group actions come to the fore in the latter chapters, giving a broad overview of progress in the 40 years since the ergodicity of the Teichmüller geodesic flow was proven. Exercises are included throughout, inviting readers to actively explore and extend the theory along the way. Translation Surfaces invites readers into this exciting area, providing an accessible entry point from the perspectives of dynamics, ergodicity, and measure theory. Suitable for a one- or two-semester graduate course, it assumes a background in complex analysis, measure theory, and manifolds, while some familiarity with Riemann surfaces and ergodic theory would be beneficial.
Author: Avrum Stroll
Publisher: U of Minnesota Press
ISBN: 9781452902692
Category :
Languages : en
Pages : 252
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Book Description
Author: Thomas, Arthur H., Company, Philadelphia
Publisher:
ISBN:
Category :
Languages : en
Pages : 676
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Author:
Publisher:
ISBN:
Category : Administrative law
Languages : en
Pages : 1274
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Author:
Publisher: Government Printing Office
ISBN: 9780160884122
Category : Law
Languages : en
Pages : 488
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Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 1024
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Author: Elaine M. Keohane
Publisher: Elsevier Health Sciences
ISBN: 0323239064
Category : Medical
Languages : en
Pages : 917
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Book Description
Featuring hundreds of full-color photomicrographs, Rodak's Hematology: Clinical Principles and Applications, 5th Edition prepares you for a job in the clinical lab by exploring the essential aspects of hematology. It shows how to accurately identify cells, simplifies hemostasis and thrombosis concepts, and covers normal hematopoiesis through diseases of erythroid, myeloid, lymphoid, and megakaryocytic origins. This text also makes it easy to understand complementary testing areas such as flow cytometry, cytogenetics, and molecular diagnostics. Clinical lab experts Elaine Keohane, Larry Smith, and Jeanine Walenga also cover key topics such as working in a hematology lab, the parts and functions of the cell, and laboratory testing of blood cells and body fluid cells. Instructions for lab procedures include sources of possible errors along with comments. Case studies in each chapter provide opportunities to apply hematology concepts to real-life scenarios. Hematology instruments are described, compared, and contrasted. UPDATED, full-color illustrations make it easier to visualize hematology concepts and show what you'll encounter in the lab, with images appearing near their mentions in the text so you don't have to flip pages back and forth. Hematology/hemostasis reference ranges are listed on the inside front and back covers for quick reference. A bulleted summary makes it easy to review the important points in every chapter. Learning objectives begin each chapter and indicate what you should achieve, with review questions appearing at the end. A glossary of key terms makes it easy to find and learn definitions. NEW coverage of hematogones in the chapter on pediatric and geriatric hematology helps you identify these cells, a skill that is useful in diagnosing some pediatric leukemias. UPDATED chapter on molecular diagnostics covers new technology and techniques used in the lab.
Author: Hermann Sahli
Publisher:
ISBN:
Category : Diagnosis
Languages : en
Pages : 1332
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Book Description
Author: Kenneth C. Fugelsang
Publisher: Рипол Классик
ISBN: 5881474686
Category : History
Languages : en
Pages : 415
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Book Description
