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Noncommutative Geometry, Arithmetic, and Related Topics
Mathematics Institute, these essays collectively provide mathematicians and physicists with a comprehensive resource on the topic.
Spectral Analysis in Geometry and Number Theory
This volume is an outgrowth of an international conference in honor of Toshikazu Sunada on the occasion of his sixtieth birthday. The conference took place at Nagoya University, Japan, in 2007. Sunada's research covers a wide spectrum of spectral analysis, including interactions among geometry, number theory, dynamical systems, probability theory and mathematical physics. Readers will find papers on trace formulae, isospectral problems, zeta functions, quantum ergodicity, random waves, discrete geometric analysis, value distribution, and semiclassical analysis. This volume also contains an article that presents an overview of Sunada's work in mathematics up to the age of sixty.
Women in Numbers 2
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 a...
Far-from-equilibrium Dynamics
When different scales exist in the spatial direction, it produces non- uniformity that is frequently characterized by identifiable patterns. This monograph investigates the dynamics of spatio-temporal patterns created by the coexistence of different scales. Of particular concern is how the loss of uniformity requires the fixing of particular scales that cause the loss of the global picture of the system. Singular perturbation theories are discussed as a way out of that dilemma. Various methodologies for studying dissipative systems from the standpoint of separation and unification of scales are presented. The interface dynamics caused by the difference of spatial scales is also given a prominent place in the discussion. Translated from the 1999 Japanese work Hisenkei mondai. 1, Patan keisei no suri. Annotation copyrighted by Book News, Inc., Portland, OR.
Casimir Force, Casimir Operators and the Riemann Hypothesis
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Introduction to Prehomogeneous Vector Spaces
A textbook for graduate and undergraduate students introducing the classical theory of prehomogeneous vector spaces originated by Mikio Sato in 1961. The original Gaikinshitsu bekutoru kukan was published by Iwanami Shotan, Tokyo, in 1998. The English, translated by M. Nagura and T. Niitani, contains some additional material. Annotation copyrighted by Book News, Inc., Portland, OR
Boolean Functions in Coding Theory and Cryptography
This book offers a systematic presentation of cryptographic and code-theoretic aspects of the theory of Boolean functions. Both classical and recent results are thoroughly presented. Prerequisites for the book include basic knowledge of linear algebra, group theory, theory of finite fields, combinatorics, and probability. The book can be used by research mathematicians and graduate students interested in discrete mathematics, coding theory, and cryptography.
Cohomological Analysis of Partial Differential Equations and Secondary Calculus
This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations. This theory grew up from the classical geometry of PDE's originated by S. Lie and his followers by incorporating some nonclassical ideas from the theory of integrable systems, the formal theory of PDE's in its modern cohomological form given by D. Spencer and H. Goldschmidt and differential calculus over commutative algebras (Primary Calculus). The main result of this synthesis is Secondary Calculus on diffieties, new geometrical objects which are analogs of algebraic varieties in the context of (nonlinear) PDE's. Secondary Calculus surprisin...
LuCaNT: LMFDB, Computation, and Number Theory
This book will be published Open Access with a Creative Commons Attribution 4.0 International License (CC BY 4.0). The eBook can be downloaded electronically for free. This volume contains the proceedings of the LuCaNT (LMFDB, Computation, and Number Theory) conference held from July 10–14, 2023, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island and affiliated with Brown University. This conference provided an opportunity for researchers, scholars, and practitioners to exchange ideas, share advances, and collaborate in the fields of computation, mathematical databases, number theory, and arithmetic geometry. The papers that appear in this volume record recent advances in these areas, with special focus on the LMFDB (the L-Functions and Modular Forms Database), an online resource for mathematical objects arising in the Langlands program and the connections between them.
