Geometry

This monograph presents developments in the abstract theory of topological dynamics, concentrating on the internal structure of minimal flows (actions of groups on compact Hausdorff spaces for which every orbit is dense) and their homomorphisms (continuous equivariant maps).

This monograph summarizes and extends a number of results on the topology of trigonal curves in geometrically ruled surfaces.

This book is a thoroughly revised result, updated to mid-1995, of the NATO Advanced Research Workshop on "e;Intelligent Learning Environments: the case of geometry"e;, held in Grenoble, France, November 13-16, 1989.

This book opens with an axiomatic description of Euclidean and non-Euclidean geometries.

The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications.

Gorenstein homological algebra is an important area of mathematics, with applications in commutative and noncommutative algebra, model category theory, representation theory, and algebraic geometry.

Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter.

In this book the authors study the differential geometry of varieties with degenerate Gauss maps.

Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds.

The first part of this book is a text for graduate courses in topology.

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility.

The textbook provides both beginner and experienced CAD users with the math behind the CAD.

While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory.

The purpose of this monograph is to present the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry.

The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve.

Knot Projections offers a comprehensive overview of the latest methods in the study of this branch of topology, based on current research inspired by Arnold's theory of plane curves, Viro's quantization of the Arnold invariant, and Vassiliev's theory of knots, among others.

This is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand.

This book presents the analytic foundations to the theory of the hypoelliptic Laplacian.

New Developments in Differential Equations

The main goal of the book is to present a proof of the following.

This book studies a category of mathematical objects called Hamiltonians, which are dependent on both time and momenta.

An account of effective methods in transcendental number theory and Diophantine geometry by eminent authors.

For any researcher working in representation theory, algebraic or arithmetic geometry.

The leveraging of artificial intelligence (AI) for model discovery in dynamical systems is cross-fertilizing and revolutionizing both disciplines, heralding a new era of data-driven science.

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds.

Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics.

Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February 2016 conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM).

This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics.

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This book brings together geometric tools and their applications for Information analysis.

An elementary introduction to homology theory suitable for undergraduate courses or for self-study.

A unified account of a powerful classical method, illustrated by applications in number theory.

A NATO Advanced Study Institute entitled "e;Algebraic K-theory and Algebraic Topology"e; was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of 1991.

There is an explosion of interest in dynamical systems in the mathematical community as well as in many areas of science.

Extending Griffiths' classical theory of period mappings for compact Kahler manifolds, this book develops and applies a theory of period mappings of "e;Hodge-de Rham type"e; for families of open complex manifolds.

Riemann introduced the concept of a "e;local system"e; on P1-{a finite set of points} nearly 140 years ago.

This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry.

This book explores various properties of quasimodular forms, especially their connections with Jacobi-like forms and automorphic pseudodifferential operators.

The first part of a two-volume set offering a systematic explanation of symplectic topology.

The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.

Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals.

Experience gained during a ten-year long involvement in modelling, program- ming and application in nonlinear optimization helped me to arrive at the conclusion that in the interest of having successful applications and efficient software production, knowing the structure of the problem to be solved is in- dispensable.

The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS).

Proceedings of the 8th International Conference of Topological Algebras and Their Applications (ICTAA-2014), held on May 26-30, 2014 in Playa de Villas de Mar Beach, dedicated to the memory of Anastasios Mallios (Athens, Greece).

A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.