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| forum of math pi: Why Pi? Johnny Ball, 2009-08-31 Discover how maths applies to everything with Johnny Ball Join Johnny Ball as he shows your child that maths isn't just numbers and sums, it's a fundamental, incredible, magical way to find out how everything works. From Pi, the amazing number that's vital for so much of everyday life, to perfect proportions - did you know Leonardo da Vinci worked out a person's ear is one-third the length of their face? - discover how numbers, from ancient times to the modern day, have enabled us to explore, build and discover just about everything. With puzzles to solve, conundrums to crack and incredible tricks to show to friends, Johnny Ball will teach your child to become a mathmagician! |
| forum of math pi: Let's Play Math Denise Gaskins, 2012-09-04 |
| forum of math pi: Analysis Terence Tao, 2006 Providing an introduction to real analysis, this text is suitable for honours undergraduates. It starts at the very beginning - the construction of the number systems and set theory, then to the basics of analysis, through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. |
| forum of math pi: The Road to Reality Roger Penrose, 2021-06-09 **WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS** The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book. Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit. 'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin |
| forum of math pi: Morphing Joseph Choma, 2015-01-19 Cylinders, spheres and cubes are a small handful of shapes that can be defined by a single word. However, most shapes cannot be found in a dictionary. They belong to an alternative plastic world defined by trigonometry: a mathematical world where all shapes can be described under one systematic language and where any shape can transform into another. This visually striking guidebook clearly and systematically lays out the basic foundation for using these mathematical transformations as design tools. It is intended for architects, designers, and anyone with the curiosity to understand the link between shapes and the equations behind them. |
| forum of math pi: Computational Topology for Data Analysis Tamal Krishna Dey, Yusu Wang, 2022-03-10 Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks. |
| forum of math pi: Phi, Pi, e and i David Perkins, 2017 Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (φ, π, e and i), each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus. This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. These truths are described here via the work of such luminaries as Nilakantha, Liu Hui, Hemachandra, Khayyám, Newton, Wallis, and Euler. The book is written with the goal that an undergraduate student can read the book solo. With this goal in mind, the author provides endnotes throughout, in case the reader is unable to work out some of the missing steps. Those endnotes appear in the last chapter, Extra Help. Each chapter concludes with a series of exercises, all of which introduce new historical figures or content. |
| forum of math pi: Subgroup Growth Alexander Lubotzky, Dan Segal, 2012-12-06 Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and Strong Approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'. |
| forum of math pi: Landscape of 21st Century Mathematics Bogdan Grechuk, 2021-09-21 Landscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline. The theorems presented in this book have been selected among recent achievements whose statements can be fully appreciated without extensive background. Grouped by subject, the selected theorems represent all major areas of mathematics: number theory, combinatorics, analysis, algebra, geometry and topology, probability and statistics, algorithms and complexity, and logic and set theory. The presentation is self-contained with context, background and necessary definitions provided for each theorem, all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of a proof are given. Rigorous yet accessible, this book presents an array of breathtaking recent advances in mathematics. It is written for everyone with a background in mathematics, from inquisitive university students to mathematicians curious about recent achievements in areas beyond their own. |
| forum of math pi: Math Doesn't Suck Danica McKellar, 2007-08-02 This title has been removed from sale by Penguin Group, USA. |
| forum of math pi: Math Marilyn Burns, 1998 Humorously Uncovers the Reasons Behind Math's Dreadful Reputation and Shows us How we Can Help Prevent Our Own Children From Adopting Similar Phobic Attitudes |
| forum of math pi: Applied Analysis John K. Hunter, Bruno Nachtergaele, 2001 This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigor. The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields and graduate students in the sciences and engineering who want to learn analysis. A basic background in calculus, linear algebra and ordinary differential equations, as well as some familiarity with functions and sets, should be sufficient. |
| forum of math pi: Proposals for Research Gerry Stahl, 2011-01-11 My career has usually been funded by grants. Here are some of the proposals I wrote at the University of Colorado and at Drexel University. Successful grant proposals are tricky to write. The ones reproduced here might provide helpful examples. They may also provide explicit statements of some of the goals of my research over the years. |
| forum of math pi: Tensor Products of C*-algebras and Operator Spaces Gilles Pisier, 2020-02-27 Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students. |
| forum of math pi: Geometric Set Theory Paul B. Larson, Jindrich Zapletal, 2020-07-16 This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo–Fraenkel set theory without Axiom of Choice. The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation. |
| forum of math pi: Algebraic Geometry: Salt Lake City 2015 Richard Thomas, 2018-06-01 This is Part 2 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come. |
| forum of math pi: In the Tradition of Thurston II Ken’ichi Ohshika, Athanase Papadopoulos, 2022-08-02 The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups. |
| forum of math pi: The Calabi Problem for Fano Threefolds Carolina Araujo, Ana-Maria Castravet, Ivan Cheltsov, Kento Fujita, Anne-Sophie Kaloghiros, Jesus Martinez-Garcia, Constantin Shramov, Hendrik Süß, Nivedita Viswanathan, 2023-06-30 Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This book determines whether the general element of each family admits a Kähler–Einstein metric (and for many families, for all elements), addressing a question going back to Calabi 70 years ago. The book's solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, the book presents many different techniques to prove the existence of a Kähler–Einstein metric, containing many additional relevant results such as the classification of all Kähler–Einstein smooth Fano threefolds with infinite automorphism groups and computations of delta-invariants of all smooth del Pezzo surfaces. This book will be essential reading for researchers and graduate students working on algebraic geometry and complex geometry. |
| forum of math pi: Asymptotic Geometric Analysis, Part II Shiri Artstein-Avidan, Apostolos Giannopoulos, Vitali D. Milman, 2021-12-13 This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series. Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many very novel phenomena which influence other fields in mathematics, especially where a large data set is of main concern, or a number of parameters which becomes uncontrollably large. One of the important features of this new theory is in developing tools which allow studying high parametric families. Among the topics covered in the book are measure concentration, isoperimetric constants of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of geometric notions and inequalities. |
| forum of math pi: A Gebra Named Al Wendy Isdell, 2017 Trouble with her algebra homework leads Julie through a mysterious portal into the Land of Mathematics, where a zebra-like Imaginary Number and creatures representing Periodic Elements help her learn about math and chemistry in order to get home. |
| forum of math pi: In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius Maria Eulália Vares, Roberto Fernández, Luiz Renato Fontes, Charles M. Newman, 2021-03-25 This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series (In and Out of Equilibrium) and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory. |
| forum of math pi: Analytic Number Theory for Beginners Prapanpong Pongsriiam, 2023-06-02 This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. The text starts with a review of elementary number theory and continues on to present less commonly covered topics such as multiplicative functions, the floor function, the use of big $O$, little $o$, and Vinogradov notation, as well as summation formulas. Standard advanced topics follow, such as the Dirichlet $L$-function, Dirichlet's Theorem for primes in arithmetic progressions, the Riemann Zeta function, the Prime Number Theorem, and, new in this second edition, sieve methods and additive number theory. The book is self-contained and easy to follow. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes which include a chapter summary, open questions, historical background, and resources for further study. Since many topics in this book are not typically covered at such an accessible level, Analytic Number Theory for Beginners is likely to fill an important niche in today's selection of titles in this field. |
| forum of math pi: Equivalents of the Riemann Hypothesis Kevin Broughan, 2023-09-30 This third volume presents further equivalents to the Riemann hypothesis and explores its decidability. |
| forum of math pi: Equivalents of the Riemann Hypothesis: Volume 3, Further Steps towards Resolving the Riemann Hypothesis Kevin Broughan, 2023-09-30 This three-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 3 covers new arithmetic and analytic equivalences from numerous studies in the field, such as Rogers and Tao, and presents derivations which show whether the Riemann hypothesis is decidable. |
| forum of math pi: Around Langlands Correspondences Farrell Brumley, Maria Paula Gomez Aparicio, Alberto Minguez, 2017 Presents, through a mix of research and expository articles, some of the fascinating new directions in number theory and representation theory arising from recent developments in the Langlands program. Special emphasis is placed on nonclassical versions of the conjectural Langlands correspondences, where the underlying field is no longer the complex numbers. |
| forum of math pi: Ramanujan 125 Ae Ja Yee,, 2014-10-14 This volume contains the proceedings of an international conference to commemorate the 125th anniversary of Ramanujan's birth, held from November 5-7, 2012, at the University of Florida, Gainesville, Florida. Srinivasa Ramanujan was India's most famous mathematician. This volume contains research and survey papers describing recent and current developments in the areas of mathematics influenced by Ramanujan. The topics covered include modular forms, mock theta functions and harmonic Maass forms, continued fractions, partition inequalities, -series, representations of affine Lie algebras and partition identities, highly composite numbers, analytic number theory and quadratic forms. |
| forum of math pi: Arithmetic and Geometry over Local Fields Bruno Anglès, Tuan Ngo Dac, 2021-03-03 This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program Arithmetic and geometry of local and global fields which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics. |
| forum of math pi: Deformation of Artinian Algebras and Jordan Type Anthony Iarrobino, Pedro Macias Marques, Maria Evelina Rossi, Jean VallŠs, 2024-09-06 This volume contains the proceedings of the AMS-EMS-SMF Special Session on Deformations of Artinian Algebras and Jordan Type, held July 18?22, 2022, at the Universit‚ Grenoble Alpes, Grenoble, France. Articles included are a survey and open problems on deformations and relation to the Hilbert scheme; a survey of commuting nilpotent matrices and their Jordan type; and a survey of Specht ideals and their perfection in the two-rowed case. Other articles treat topics such as the Jordan type of local Artinian algebras, Waring decompositions of ternary forms, questions about Hessians, a geometric approach to Lefschetz properties, deformations of codimension two local Artin rings using Hilbert-Burch matrices, and parametrization of local Artinian algebras in codimension three. Each of the articles brings new results on the boundary of commutative algebra and algebraic geometry. |
| forum of math pi: Facets of Algebraic Geometry Paolo Aluffi, David Anderson, Milena Hering, Mircea Mustaţă, Sam Payne, 2022-04-07 Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry. |
| forum of math pi: A Remainder of One Elinor J Pinczes, 2002-08-26 When the queen of her bugs demands that her army march in even lines, Private Joe divides the marchers into more and more lines so that he will not be left out of the parade. |
| forum of math pi: Learning Flex 4 Alaric Cole, Elijah Robison, 2010-11-02 Learn Adobe Flex 4 in a fun and engaging way with this book's unique, hands-on approach. Using clear examples and step-by-step coaching from two experts, you'll create four applications that demonstrate fundamental Flex programming concepts. Throughout the course of this book, you’ll learn how to enhance user interaction with ActionScript, and create and skin a user interface with Flex’s UI components (MXML) and Adobe's new FXG graphics format. You'll also be trained to manage dynamic data, connect to a database using server-side script, and deploy applications to both the Web and the desktop. Learning Flex 4 offers tips and tricks the authors have collected from years of real-world experience, and straightforward explanations of object-oriented programming concepts to help you understand how Flex 4 works. Work with Flash Builder 4 and the Eclipse IDE Learn the basics of ActionScript, MXML, and FXG Design a Flex application layout Build an engaging user interface Add interactivity with ActionScript Handle user input with rich forms Link Flex to a server with PHP and MySQL Gather and display data Style applications and add effects, filters, and transitions Deploy applications to the Web, or to the desktop using Adobe AIR |
| forum of math pi: Vector-Valued Partial Differential Equations and Applications Bernard Dacorogna, Nicola Fusco, Stefan Müller, Vladimir Sverak, 2017-05-29 Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field. |
| forum of math pi: Singular Random Dynamics Massimiliano Gubinelli, Panagiotis E. Souganidis, Nikolay Tzvetkov, 2019-11-12 Written by leading experts in an emerging field, this book offers a unique view of the theory of stochastic partial differential equations, with lectures on the stationary KPZ equation, fully nonlinear SPDEs, and random data wave equations. This subject has recently attracted a great deal of attention, partly as a consequence of Martin Hairer's contributions and in particular his creation of a theory of regularity structures for SPDEs, for which he was awarded the Fields Medal in 2014. The text comprises three lectures covering: the theory of stochastic Hamilton–Jacobi equations, one of the most intriguing and rich new chapters of this subject; singular SPDEs, which are at the cutting edge of innovation in the field following the breakthroughs of regularity structures and related theories, with the KPZ equation as a central example; and the study of dispersive equations with random initial conditions, which gives new insights into classical problems and at the same time provides a surprising parallel to the theory of singular SPDEs, viewed from many different perspectives. These notes are aimed at graduate students and researchers who want to familiarize themselves with this new field, which lies at the interface between analysis and probability. |
| forum of math pi: Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) Boyan Sirakov, Paulo Ney De Souza, Marcelo Viana, 2019-02-27 The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios. |
| forum of math pi: The Arithmetic of Polynomial Dynamical Pairs Charles Favre, Thomas Gauthier, 2022-06-14 New mathematical research in arithmetic dynamics In The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from arithmetic geometry and holomorphic dynamics, they prove an “unlikely intersection” statement for such pairs, thereby demonstrating strong rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many postcritically finite parameters, proving the dynamical André-Oort conjecture for curves in this context, originally stated by Baker and DeMarco. This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics. |
| forum of math pi: Analytic And Combinatorial Number Theory: The Legacy Of Ramanujan - Contributions In Honor Of Bruce C. Berndt George E Andrews, Michael Filaseta, Ae Ja Yee, 2024-08-19 This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6-9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday.Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference. |
| forum of math pi: Extended Abstracts 2021/2022 Duván Cardona, |
| forum of math pi: Research Directions in Number Theory Jennifer S. Balakrishnan, Amanda Folsom, Matilde Lalín, Michelle Manes, 2019-08-01 These proceedings collect several number theory articles, most of which were written in connection to the workshop WIN4: Women in Numbers, held in August 2017, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. It collects papers disseminating research outcomes from collaborations initiated during the workshop as well as other original research contributions involving participants of the WIN workshops. The workshop and this volume are part of the WIN network, aimed at highlighting the research of women and gender minorities in number theory as well as increasing their participation and boosting their potential collaborations in number theory and related fields. |
| forum of math pi: Stable Klingen Vectors and Paramodular Newforms Jennifer Johnson-Leung, Brooks Roberts, Ralf Schmidt, 2023-12-27 This book describes a novel approach to the study of Siegel modular forms of degree two with paramodular level. It introduces the family of stable Klingen congruence subgroups of GSp(4) and uses this family to obtain new relations between the Hecke eigenvalues and Fourier coefficients of paramodular newforms, revealing a fundamental dichotomy for paramodular representations. Among other important results, it includes a complete description of the vectors fixed by these congruence subgroups in all irreducible representations of GSp(4) over a nonarchimedean local field. Siegel paramodular forms have connections with the theory of automorphic representations and the Langlands program, Galois representations, the arithmetic of abelian surfaces, and algorithmic number theory. Providing a useful standard source on the subject, the book will be of interest to graduate students and researchers working in the above fields. |
| forum of math pi: Arakelov Geometry and Diophantine Applications Emmanuel Peyre, Gaël Rémond, 2021-03-10 Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry. |
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