$p$-Adic Analysis, Arithmetic and Singularities

$p$-Adic Analysis, Arithmetic and Singularities
Title $p$-Adic Analysis, Arithmetic and Singularities PDF eBook
Author Carlos Galindo
Publisher American Mathematical Society
Pages 311
Release 2022-05-11
Genre Mathematics
ISBN 1470467798

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This volume contains the proceedings of the 2019 Lluís A. Santaló Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held from June 24–28, 2019, at the Universidad Internacional Menéndez Pelayo, Santander, Spain. The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and Koba-Nielsen-type string amplitudes, among other applications. This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces $p$-adic analysis, the theory of Archimedean, $p$-adic, and motivic zeta functions, singularities of plane curves and their Poincaré series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists. This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics.

P-adic Analysis, Arithmetic and Singularities

P-adic Analysis, Arithmetic and Singularities
Title P-adic Analysis, Arithmetic and Singularities PDF eBook
Author Carlos Galindo
Publisher
Pages
Release 2022
Genre p-adic analysis
ISBN 9781470469764

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p-Adic Analysis

p-Adic Analysis
Title p-Adic Analysis PDF eBook
Author W. A. Zúñiga-Galindo
Publisher Walter de Gruyter GmbH & Co KG
Pages 162
Release 2024-12-02
Genre Mathematics
ISBN 3111578682

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This book is intended to provide a fast, interdisciplinary introduction to the basic results of p-adic analysis and its connections with mathematical physics and applications. The book revolves around three topics: (1) p-adic heat equations and ultradiffusion; (2) fundamental solutions and local zeta functions, Riesz kernels, and quadratic forms; (3) Sobolev-type spaces and pseudo-differential evolution equations. These topics are deeply connected with very relevant current research areas. The book includes numerous examples, exercises, and snapshots of several mathematical theories. This book arose from the need to quickly introduce mathematical audience the basic concepts and techniques to do research in p-adic analysis and its connections with mathematical physics and other areas. The book is addressed to a general mathematical audience, which includes computer scientists, theoretical physicists, and people interested in mathematical analysis, PDEs, etc.

Arithmetic, Geometry, Cryptography, and Coding Theory 2021

Arithmetic, Geometry, Cryptography, and Coding Theory 2021
Title Arithmetic, Geometry, Cryptography, and Coding Theory 2021 PDF eBook
Author Samuele Anni
Publisher American Mathematical Society
Pages 198
Release 2022-07-06
Genre Mathematics
ISBN 1470467941

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This volume contains the proceedings of the 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, held (online) from May 31 to June 4, 2021. For over thirty years, the biennial international conference AGC$^2$T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers together to forge connections between arithmetic geometry and its applications to coding theory and to cryptography. The papers illustrate the fruitful interaction between abstract theory and explicit computations, covering a large range of topics, including Belyi maps, Galois representations attached to elliptic curves, reconstruction of curves from their Jacobians, isogeny graphs of abelian varieties, hypergeometric equations, and Drinfeld modules.

Mathematical Modelling

Mathematical Modelling
Title Mathematical Modelling PDF eBook
Author Hemen Dutta
Publisher American Mathematical Society
Pages 256
Release 2023-06-12
Genre Mathematics
ISBN 1470469642

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This volume is a collection of chapters that present several key principles and theories, as well as their potential uses in the development of mathematical models in areas like waves, thermodynamic, electromagnetics, fluid dynamics, and catastrophes. The techniques and methodologies used in this book, on the other hand, should have a long-term impact and be applicable to a wide range of different topics of study and research. Each chapter should also help readers in gaining a better knowledge of the underlying and connected concepts. The companion volume (Contemporary Mathematics, Volume 787) is devoted to theory and application.

Mathematical Analyses of Decisions, Voting and Games

Mathematical Analyses of Decisions, Voting and Games
Title Mathematical Analyses of Decisions, Voting and Games PDF eBook
Author Michael A. Jones
Publisher American Mathematical Society
Pages 210
Release 2024-03-25
Genre Mathematics
ISBN 1470469782

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This volume contains the proceedings of the virtual AMS Special Session on Mathematics of Decisions, Elections and Games, held on April 8, 2022. Decision theory, voting theory, and game theory are three related areas of mathematics that involve making optimal decisions in different contexts. While these three areas are distinct, much of the recent research in these fields borrows techniques from other branches of mathematics such as algebra, combinatorics, convex geometry, logic, representation theory, etc. The papers in this volume demonstrate how the mathematics of decisions, elections, and games can be used to analyze problems from the social sciences.

The Diverse World of PDEs

The Diverse World of PDEs
Title The Diverse World of PDEs PDF eBook
Author I. S. Krasil′shchik
Publisher American Mathematical Society
Pages 250
Release 2023-08-21
Genre Mathematics
ISBN 1470471477

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This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at the Independent University of Moscow and Moscow State University, Moscow, Russia. The papers are devoted to various interrelations of nonlinear PDEs with geometry and integrable systems. The topics discussed are: gravitational and electromagnetic fields in General Relativity, nonlocal geometry of PDEs, Legendre foliated cocycles on contact manifolds, presymplectic gauge PDEs and Lagrangian BV formalism, jet geometry and high-order phase transitions, bi-Hamiltonian structures of KdV type, bundles of Weyl structures, Lax representations via twisted extensions of Lie algebras, energy functionals and normal forms of knots, and differential invariants of inviscid flows. The companion volume (Contemporary Mathematics, Volume 789) is devoted to Algebraic and Cohomological Aspects of PDEs.