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Author : J. B. Conrey,D. W. Farmer,F. Mezzadri,N. C. Snaith
Publisher : Unknown
Page : 368 pages
File Size : 54,9 Mb
Release : 2007
Category : Curves, Elliptic
ISBN : 1107372410
This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.
Author : J. B. Conrey
Publisher : Cambridge University Press
Page : 5 pages
File Size : 44,9 Mb
Release : 2007-02-08
Category : Mathematics
ISBN : 9780521699648
This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.
Author : David Loeffler,Sarah Livia Zerbes
Publisher : Springer
Page : 492 pages
File Size : 40,6 Mb
Release : 2017-01-15
Category : Mathematics
ISBN : 9783319450322
Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields.
Author : Chantal David,Matilde Lalín, Michelle Manes
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 55,7 Mb
Release : 2013-12-10
Category : Mathematics
ISBN : 9781470410223
The second Women in Numbers workshop (WIN2) was held November 6-11, 2011, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. During the workshop, group leaders presented open problems in various areas of number theory, and working groups tackled those problems in collaborations begun at the workshop and continuing long after. This volume collects articles written by participants of WIN2. Survey papers written by project leaders are designed to introduce areas of active research in number theory to advanced graduate students and recent PhDs. Original research articles by the project groups detail their work on the open problems tackled during and after WIN2. Other articles in this volume contain new research on related topics by women number theorists. The articles collected here encompass a wide range of topics in number theory including Galois representations, the Tamagawa number conjecture, arithmetic intersection formulas, Mahler measures, Newton polygons, the Dwork family, elliptic curves, cryptography, and supercongruences. WIN2 and this Proceedings volume are part of the Women in Numbers network, aimed at increasing the visibility of women researchers' contributions to number theory and at increasing the participation of women mathematicians in number theory and related fields. This book is co-published with the Centre de Recherches Mathématiques.
Author : Steven R. Finch
Publisher : Cambridge University Press
Page : 783 pages
File Size : 50,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9781108470599
Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson-Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl-Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton-Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Author : Gordon Blower
Publisher : Cambridge University Press
Page : 448 pages
File Size : 44,6 Mb
Release : 2009-10-08
Category : Mathematics
ISBN : 9781139481953
This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.
Author : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Page : 5396 pages
File Size : 50,9 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897
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.
Author : Leonid Andreevich Pastur,Mariya Shcherbina
Publisher : American Mathematical Soc.
Page : 650 pages
File Size : 51,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852859
Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.
Author : Cristian Popescu,Karl Rubin,Alice Silverberg
Publisher : American Mathematical Soc.
Page : 517 pages
File Size : 46,9 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 9780821886984
Author : M. T. Barlow
Publisher : Cambridge University Press
Page : 239 pages
File Size : 41,7 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9781107674424
Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.
Author : Domenico Marinucci,Giovanni Peccati
Publisher : Cambridge University Press
Page : 354 pages
File Size : 53,7 Mb
Release : 2011-08-25
Category : Mathematics
ISBN : 9781139499828
The authors present a comprehensive analysis of isotropic spherical random fields, with a view towards applications in cosmology. Any mathematician or statistician interested in these applications, especially the booming area of cosmic microwave background (CMB) radiation data analysis, will find the mathematical foundation they need in this book.
Author : Jan Krajíček
Publisher : Cambridge University Press
Page : 265 pages
File Size : 55,7 Mb
Release : 2010-12-23
Category : Mathematics
ISBN : 9781139493925
This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.
Author : Raf Cluckers,Johannes Nicaise,Julien Sebag
Publisher : Cambridge University Press
Page : 263 pages
File Size : 46,6 Mb
Release : 2011-09-22
Category : Mathematics
ISBN : 9781139501736
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.
Author : Patrick Hild
Publisher : Presses Univ. Franche-Comté
Page : 203 pages
File Size : 54,9 Mb
Release : 2010-03
Category : Electronic
ISBN : 9782848672823
Author : Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff
Publisher : Cambridge University Press
Page : 341 pages
File Size : 40,7 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781107552371
Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.
