Surveys in Geometry I

Surveys in Geometry I

Author: Athanase Papadopoulos

Publisher: Springer Nature

Published: 2022-02-18

Total Pages: 469

ISBN-13: 3030866955

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The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner. The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop—Gromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichmüller spaces and mapping class groups actions, translation surfaces and their dynamics, and complex higher-dimensional geometry. Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to current research trends in geometry.


Surveys in Geometry and Number Theory

Surveys in Geometry and Number Theory

Author: Nicholas Young

Publisher: Cambridge University Press

Published: 2007-01-18

Total Pages: 327

ISBN-13: 0521691826

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A collection of survey articles by leading young researchers, showcasing the vitality of Russian mathematics.


Noncommutative Geometry and Number Theory

Noncommutative Geometry and Number Theory

Author: Caterina Consani

Publisher: Springer Science & Business Media

Published: 2007-12-18

Total Pages: 374

ISBN-13: 3834803529

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In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.


Geometric Methods in Algebra and Number Theory

Geometric Methods in Algebra and Number Theory

Author: Fedor Bogomolov

Publisher: Springer Science & Business Media

Published: 2006-06-22

Total Pages: 365

ISBN-13: 0817644172

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* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry


Intersection Theory

Intersection Theory

Author: W. Fulton

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 483

ISBN-13: 3662024217

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From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cen turies, intersection theory has played a central role. Since its role in founda tional crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive his tory of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to devel op the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appen dices. Some of the examples, and a few of the later sections, require more spe cialized knowledge. The text is designed so that one who understands the con structions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should fa cilitate use as a reference.


Dynamics, Geometry, Number Theory

Dynamics, Geometry, Number Theory

Author: David Fisher

Publisher: University of Chicago Press

Published: 2022-02-07

Total Pages: 573

ISBN-13: 022680402X

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"Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--


3264 and All That

3264 and All That

Author: David Eisenbud

Publisher: Cambridge University Press

Published: 2016-04-14

Total Pages: 633

ISBN-13: 1107017084

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3264, the mathematical solution to a question concerning geometric figures.


Old and New Unsolved Problems in Plane Geometry and Number Theory

Old and New Unsolved Problems in Plane Geometry and Number Theory

Author: Victor Klee

Publisher: American Mathematical Soc.

Published: 2020-07-31

Total Pages: 333

ISBN-13: 1470454610

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Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. The second part contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references. Both parts contain exercises, with solutions. The book is aimed at both teachers and students of mathematics who want to know more about famous unsolved problems.


Surveys on Recent Developments in Algebraic Geometry

Surveys on Recent Developments in Algebraic Geometry

Author: Izzet Coskun

Publisher: American Mathematical Soc.

Published: 2017-07-12

Total Pages: 386

ISBN-13: 1470435578

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The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.


Surveys in Modern Mathematics

Surveys in Modern Mathematics

Author: Viktor Vasilʹevich Prasolov

Publisher: Cambridge University Press

Published: 2005-04-14

Total Pages: 360

ISBN-13: 0521547938

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Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups.