Theta Invariants Of Euclidean Lattices And Infinite Dimensional Hermitian Vector Bundles Over Arithmetic Curves PDF Download
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Author | : Jean-Benoît Bost |
Publisher | : Springer Nature |
Total Pages | : 365 |
Release | : 2020-08-21 |
Genre | : Mathematics |
ISBN | : 3030443299 |
Download Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves Book in PDF, ePub and Kindle
This book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves. It contains a complete description of the theta invariants which give rise to a closer parallel with the geometric case. The author then unfolds his theory of infinite Hermitian vector bundles over arithmetic curves and their theta invariants, which provides a conceptual framework to deal with the sequences of lattices occurring in many diophantine constructions. The book contains many interesting original insights and ties to other theories. It is written with extreme care, with a clear and pleasant style, and never sacrifices accessibility to sophistication.
Author | : Emmanuel Peyre |
Publisher | : Springer Nature |
Total Pages | : 469 |
Release | : 2021-03-10 |
Genre | : Mathematics |
ISBN | : 3030575594 |
Download Arakelov Geometry and Diophantine Applications Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : |
Total Pages | : 1380 |
Release | : 1981 |
Genre | : Associations, institutions, etc |
ISBN | : |
Download Associations' Publications in Print Book in PDF, ePub and Kindle
1981- in 2 v.: v.1, Subject index; v.2, Title index, Publisher/title index, Association name index, Acronym index, Key to publishers' and distributors' abbreviations.
Author | : Alexander A. Kirillov |
Publisher | : Cambridge University Press |
Total Pages | : 237 |
Release | : 2008-07-31 |
Genre | : Mathematics |
ISBN | : 0521889693 |
Download An Introduction to Lie Groups and Lie Algebras Book in PDF, ePub and Kindle
Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples
Author | : Benson Farb |
Publisher | : American Mathematical Soc. |
Total Pages | : 384 |
Release | : 2006-09-12 |
Genre | : Mathematics |
ISBN | : 0821838385 |
Download Problems on Mapping Class Groups and Related Topics Book in PDF, ePub and Kindle
The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Author | : Clay Mathematics Institute. Summer School |
Publisher | : American Mathematical Soc. |
Total Pages | : 396 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9780821837153 |
Download Strings and Geometry Book in PDF, ePub and Kindle
Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.
Author | : Carel Faber |
Publisher | : Springer Science & Business Media |
Total Pages | : 205 |
Release | : 2012-12-06 |
Genre | : Technology & Engineering |
ISBN | : 3322901726 |
Download Moduli of Curves and Abelian Varieties Book in PDF, ePub and Kindle
The Dutch Intercity Seminar on Moduli, which dates back to the early eighties, was an initiative of G. van der Geer, F. Oort and C. Peters. Through the years it became a focal point of Dutch mathematics and it gained some fame, also outside Holland, as an active biweekly research seminar. The tradition continues up to today. The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Hain, E. Looijenga, and F. Oort, originates from the seminar held in 1995--96. Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles.
Author | : Friedrich Hirzebruch |
Publisher | : Lecture Notes in Mathematics |
Total Pages | : 498 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : |
Download Arbeitstagung Bonn ... Book in PDF, ePub and Kindle
Author | : Steven D. Galbraith |
Publisher | : Cambridge University Press |
Total Pages | : 631 |
Release | : 2012-03-15 |
Genre | : Computers |
ISBN | : 1107013925 |
Download Mathematics of Public Key Cryptography Book in PDF, ePub and Kindle
This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Author | : William A. Stein |
Publisher | : American Mathematical Soc. |
Total Pages | : 290 |
Release | : 2007-02-13 |
Genre | : Mathematics |
ISBN | : 0821839608 |
Download Modular Forms, a Computational Approach Book in PDF, ePub and Kindle
This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.