Download or read book P adic Analysis and Mathematical Physics written by Vasili? Sergeevich Vladimirov and published by World Scientific. This book was released on 1994 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.
Download or read book p Adic Valued Distributions in Mathematical Physics written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I· We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo· These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.
Download or read book P adic Deterministic and Random Dynamics written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2004-10-18 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.
Download or read book P Adic Mathematical Physics written by Zoran Rakic and published by American Institute of Physics. This book was released on 2006-04-06 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this conference was recent developments in p-adic mathematical physics and related areas. The field of p-Adic mathematical physics was conceived in 1987 as a result of attempts to find non-Archimedean approaches to space-time at the Planck scale as well as to strings. Since then, many applications of p-adic numbers and adeles in physics and related sciences have emerged. Some of them are p-adic and adelic string theory, p-adic and adelic quantum mechanics and quantum field theory, ultrametricity of spin glasses, biological and hierarchical systems, p-adic dynamical systems, p-adic probability theory, p-adic models of cognitive processes and cryptography, as well as p-adic and adelic cosmology.
Download or read book Harmonic Wavelet and P Adic Analysis written by N. M. Chuong and published by World Scientific. This book was released on 2007 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mutual influence between mathematics and science and technology is becoming more and more widespread with profound connections among them being discovered. In particular, important connections between harmonic analysis, wavelet analysis and p-adic analysis have been found recently. This volume reports these findings and guides the reader towards the latest areas for further research. It is divided into two parts: harmonic, wavelet and p-adic analysis and p-adic and stochastic analysis.
Download or read book Berkeley Lectures on P adic Geometry written by Peter Scholze and published by Princeton University Press. This book was released on 2020-05-26 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
Download or read book From Number Theory to Physics written by Michel Waldschmidt and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti cal Physics. The first part is mathematically oriented; it deals mostly with ellip tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri bution can be read independently of the others. This volume originates in a meeting entitled Number Theory and Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num ber Theory which are the most actively used in their branch.
Download or read book A Primer on Mapping Class Groups written by Benson Farb and published by Princeton University Press. This book was released on 2012 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.
Download or read book Supersingular P adic L functions Maass Shimura Operators and Waldspurger Formulas written by Daniel Kriz and published by Princeton University Press. This book was released on 2021-11-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking contribution to number theory that unifies classical and modern results This book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the Katz canonical differential on the ordinary Igusa tower. Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters. He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology. This period can be viewed as a counterpart to Scholze's Hodge-Tate period, and the two periods satisfy a Legendre-type relation. Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators. Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified. These p-adic L-functions yield new p-adic Waldspurger formulas at special values.
Download or read book Ultrametric Calculus written by W. H. Schikhof and published by Cambridge University Press. This book was released on 2007-01-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ. This approach guarantees the reader quickly becomes acquainted with this equally 'real' analysis and appreciates its relevance. The reader's understanding is enhanced and deepened by the large number of exercises included throughout; these both test the reader's grasp and extend the text in interesting directions. As a consequence, this book will become a standard reference for professionals (especially in p-adic analysis, number theory and algebraic geometry) and will be welcomed as a textbook for advanced students of mathematics familiar with algebra and analysis.
Download or read book Representations of Real and P adic Groups written by Eng-chye Tan and published by World Scientific. This book was released on 2004 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on ?Representation Theory of Lie Groups? from July 2002 to January 2003. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.This invaluable volume collects the expanded lecture notes of those tutorials. The topics covered include uncertainty principles for locally compact abelian groups, fundamentals of representations of p-adic groups, the Harish-Chandra-Howe local character expansion, classification of the square-integrable representations modulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur-Weyl-Howe duality.The lecturers include Tomasz Przebinda from the University of Oklahoma, USA; Gordan Savin from the University of Utah, USA; Stephen DeBacker from Harvard University, USA; Marko Tadi? from the University of Zagreb, Croatia; Jing-Song Huang from The Hong Kong University of Science and Technology, Hong Kong; Pavle Pand?i? from the University of Zagreb, Croatia; Chal Benson and Gail Ratcliff from East Carolina University, USA; and Roe Goodman from Rutgers University, USA.
Download or read book Sliding Mode Control In Engineering written by Wilfrid Perruquetti and published by CRC Press. This book was released on 2002-01-29 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equat
Download or read book Mathematics Frontiers and Perspectives written by Vladimir Igorevich Arnolʹd and published by American Mathematical Soc.. This book was released on 2000 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: A celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the book was born as part of the activities of World Mathematical Year 2000. It consists of 28 articles written by influential mathematicians.
Download or read book Selected Papers Of Yu I Manin written by Yu I Manin and published by World Scientific. This book was released on 1996-06-28 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of research and review articles in several areas of modern mathematics and mathematical physics published in the span of three decades. The ICM Kyoto talk “Mathematics as Metaphor” summarises the author's view on mathematics as an outgrowth of natural language.
Download or read book Exactly Solved Models in Statistical Mechanics written by Rodney J. Baxter and published by Elsevier. This book was released on 2016-06-12 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exactly Solved Models in Statistical Mechanics
Download or read book Relative P adic Hodge Theory written by Kiran Sridhara Kedlaya and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors describe a new approach to relative $p$-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of both Berkovich and Huber. They give a thorough development of $\varphi$-modules over a relative Robba ring associated to a perfect Banach ring of characteristic $p$, including the relationship between these objects and etale ${\mathbb Z}_p$-local systems and ${\mathbb Q}_p$-local systems on the algebraic and analytic spaces associated to the base ring, and the relationship between (pro-)etale cohomology and $\varphi$-cohomology. They also make a critical link to mixed characteristic by exhibiting an equivalence of tensor categories between the finite etale algebras over an arbitrary perfect Banach algebra over a nontrivially normed complete field of characteristic $p$ and the finite etale algebras over a corresponding Banach ${\mathbb Q}_p$-algebra. This recovers the homeomorphism between the absolute Galois groups of ${\mathbb F}_{p}((\pi))$ and ${\mathbb Q}_{p}(\mu_{p}\infty)$ given by the field of norms construction of Fontaine and Wintenberger, as well as generalizations considered by Andreatta, Brinon, Faltings, Gabber, Ramero, Scholl, and, most recently, Scholze. Using Huber's formalism of adic spaces and Scholze's formalism of perfectoid spaces, the authors globalize the constructions to give several descriptions of the etale local systems on analytic spaces over $p$-adic fields. One of these descriptions uses a relative version of the Fargues-Fontaine curve.
Download or read book The p adic Simpson Correspondence AM 193 written by Ahmed Abbes and published by Princeton University Press. This book was released on 2016-02-09 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra—namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation. The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos.
