Contemporary Mathematics Volume: 702
2018; 176 pp; Softcover
MSC: Primary 55; 20; 52; 57; 68; 93;
Print ISBN: 978-1-4704-3436-6
This volume contains the proceedings of the mini-workshop on Topological Complexity and Related Topics, held from February 28?March 5, 2016, at the Mathematisches Forschungsinstitut Oberwolfach.
Topological complexity is a numerical homotopy invariant, defined by Farber in the early twenty-first century as part of a topological approach to the motion planning problem in robotics. It continues to be the subject of intensive research by homotopy theorists, partly due to its potential applicability, and partly due to its close relationship to more classical invariants, such as the Lusternik?Schnirelmann category and the Schwarz genus.
This volume contains survey articles and original research papers on topological complexity and its many generalizations and variants, to give a snapshot of contemporary research on this exciting topic at the interface of pure mathematics and engineering.
Graduate students and research mathematicians interested in algebraic topology and its applications, applications of pure mathematics to engineering, and engineers interested in topology and the motion planning problem
Contemporary Mathematics Volume: 703
2018; 222 pp; Softcover
MSC: Primary 11; 14;
Print ISBN: 978-1-4704-2856-3
This volume contains the proceedings of the AMS Special Session on Higher Genus Curves and Fibrations in Mathematical Physics and Arithmetic Geometry, held on January 8, 2016, in Seattle, Washington.
Algebraic curves and their fibrations have played a major role in both mathematical physics and arithmetic geometry. This volume focuses on the role of higher genus curves; in particular, hyperelliptic and superelliptic curves in algebraic geometry and mathematical physics.
The articles in this volume investigate the automorphism groups of curves and superelliptic curves and results regarding integral points on curves and their applications in mirror symmetry. Moreover, geometric subjects are addressed, such as elliptic KK 3 surfaces over the rationals, the birational type of Hurwitz spaces, and links between projective geometry and abelian functions.
Graduate students and research mathematicians interested in superelliptic and hypelliptic curves.
Student Mathematical Library Volume: 85
2018; 248 pp; Softcover
MSC: Primary 46; 45;
Print ISBN: 978-1-4704-4116-6
This book introduces functional analysis to undergraduate mathematics students who possess a basic background in analysis and linear algebra. By studying how the Volterra operator acts on vector spaces of continuous functions, its readers will sharpen their skills, reinterpret what they already know, and learn fundamental Banach-space techniques?all in the pursuit of two celebrated results: the Titchmarsh Convolution Theorem and the Volterra Invariant Subspace Theorem. Exercises throughout the text enhance the material and facilitate interactive study.
Undergraduate students interested in functional analysis and operator theory.
Graduate Studies in Mathematics Volume: 189
2018; 384 pp; Hardcover
MSC: Primary 20;
Print ISBN: 978-1-4704-3485-4
This book, which can be considered as a sequel of the author's famous book Character Theory of Finite Groups, concerns the character theory of finite solvable groups and other groups that have an abundance of normal subgroups.
It is subdivided into three parts: ƒÎƒÎ-theory, character correspondences, and M-groups. The ƒÎƒÎ-theory section contains an exposition of D. Gajendragadkar's ƒÎƒÎ-special characters, and it includes various extensions, generalizations, and applications of his work. The character correspondences section proves the McKay character counting conjecture and the Alperin weight conjecture for solvable groups, and it constructs a canonical McKay bijection for odd-order groups. In addition to a review of some basic material on M-groups, the third section contains an exposition of the use of symplectic modules for studying M-groups. In particular, an accessible presentation of E. C. Dade's deep results on monomial characters of odd prime-power degree is included.
Very little of this material has previously appeared in book form, and much of it is based on the author's research. By reading a clean and accessible presentation written by the leading expert in the field, researchers and graduate students will be inspired to learn and work in this area that has fascinated the author for decades.
Undergraduate and graduate students and researchers interested in solvable groups, character theory, and finite group theory.
University Lecture Series Volume: 70
2018; 184 pp; Softcover
MSC: Primary 37; 20;
Print ISBN: 978-1-4704-4115-9
Within the subject of topological dynamics, there has been considerable recent interest in systems where the underlying topological space is a Cantor set. Such systems have an inherently combinatorial nature, and seminal ideas of Anatoly Vershik allowed for a combinatorial model, called the Bratteli-Vershik model, for such systems with no non-trivial closed invariant subsets. This model led to a construction of an ordered abelian group which is an algebraic invariant of the system providing a complete classification of such systems up to orbit equivalence.
The goal of this book is to give a statement of this classification result and to develop ideas and techniques leading to it. Rather than being a comprehensive treatment of the area, this book is aimed at students and researchers trying to learn about some surprising connections between dynamics and algebra. The only background material needed is a basic course in group theory and a basic course in general topology.
Undergraduate and graduate students and researchers interested in dynamical systems.