Mathematical Surveys and Monographs, Volume: 219
2017; 196 pp; Hardcover
ISBN: 978-1-4704-3514-1
This book introduces a simple dynamical model for a planar heat map that is invariant under projective transformations. The map is defined by iterating a polygon map, where one starts with a finite planar N-gon and produces a new N - gon by a prescribed geometric construction. One of the appeals of the topic of this book is the simplicity of the construction that yet leads to deep and far reaching mathematics. To construct the projective heat map, the author modifies the classical affine invariant midpoint map, which takes a polygon to a new polygon whose vertices are the midpoints of the original.
The author provides useful background which makes this book accessible
to a beginning graduate student or advanced undergraduate as well as researchers
approaching this subject from other fields of specialty. The book includes
many illustrations, and there is also a companion computer program.
Undergraduate and graduate students and researchers interested in analysis, geometry, and topology.
Mathematical Surveys and Monographs, Volume: 216
2017; 430 pp; Hardcover
ISBN: 978-0-8218-4360-4
This book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory. It is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its original context with all the necessary background.
This book will be suitable as a textbook for graduate students and researchers interested in beginning to work on mapping theory problems or learning the basics of the geometric approach to quasiconformal mappings. Only a basic background in multidimensional real analysis is assumed.
Graduate students and researchers interested in mapping theory.
Mathematical Surveys and Monographs,Volume: 218
2017; 281 pp; Hardcover
Print ISBN: 978-1-4704-3465
This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.
Graduate students and researchers interested in geometric group theory and Gromov-hyperbolic spaces.
Contemporary Mathematics, Volume: 687
2017; Softcover
Print ISBN: 978-1-4704-2772-6
This volume contains the proceedings of the Workshop on Problems and Recent Methods in Operator Theory, held at the University of Memphis, Memphis, TN, from October 15?16, 2015 and the AMS Special Session on Advances in Operator Theory and Applications, in Memory of James Jamison, held at the University of Memphis, Memphis, TN, from October 17?18, 2015.
Operator theory is at the root of several branches of mathematics and offers a broad range of challenging and interesting research problems. It also provides powerful tools for the development of other areas of science including quantum theory, physics and mechanics. Isometries have applications in solid-state physics. Hermitian operators play an integral role in quantum mechanics very much due to their gniceh spectral properties. These powerful connections demonstrate the impact of operator theory in various branches of science.
The articles in this volume address recent problems and research advances in operator theory. Highlighted topics include spectral, structural and geometric properties of special types of operators on Banach spaces, with emphasis on isometries, weighted composition operators, multi-circular projections on function spaces, as well as vector valued function spaces and spaces of analytic functions.
This volume gives a succinct overview of state-of-the-art techniques from operator theory as well as applications to classical problems and long-standing open questions.
Graduate students and research mathematicians interested in operator theory, functional analysis, geometry of Banach spaces, and complex analysis.
Contemporary Mathematics, Volume: 688
2017; 281 pp; Softcover
Print ISBN: 978-1-4704-2805-1
This volume contains the proceedings of the International Conference on
Groups, Rings, Group Rings, and Hopf Algebras, held October 2-4, 2015 at
Loyola University, Chicago, IL, and the AMS Special Session on Groups,
Rings, Group Rings, and Hopf Algebras, held October 3-4, 2015, at Loyola
University, Chicago, IL. Both conferences were held in honor of Donald
S. Passman's 75th Birthday.
Centered in the area of group rings and algebras, this volume contains a mixture of cutting edge research topics in group theory, ring theory, algebras and their representations, Hopf algebras and quantum groups.
Graduate students and research mathematicians interested in group theory, ring theory, and Hopf algebras.
Student Mathematical Library, Volume: 82
2017; 269 pp; Softcover
ISBN: 978-1-4704-3583-7
This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.
Undergraduate and graduate students interested in teaching and learning undergraduate algebra.