Contemporary Mathematics, Volume: 695
2017; 274 pp; Softcover
Print ISBN: 978-1-4704-2666-8
This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14?18, 2015, at the University of Notre Dame, Notre Dame, Indiana.
Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.
Graduate students and research mathematicians interested in representation theory, vertex algebras, conformal field theory and related areas.
Contemporary Mathematics, Volume: 696
2017; 250 pp; Softcover
Print ISBN: 978-1-4704-2651-4
The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmuller theory, hyperbolic geometry, and partial differential equations. Today we see the influence of Ahlfors and Bers on algebraic geometry, mathematical physics, dynamics, probability, geometric group theory, number theory and topology. Recent years have seen a flowering of this legacy with an increased interest in their work.
This current volume contains articles on a wide variety of subjects that
are central to this legacy. These include papers in Kleinian groups, classical
Riemann surface theory, Teichmuller theory, mapping class groups, geometric
group theory, and statistical mechanics
Graduate students and research mathematicians interested in Teichmuller theory, hyperbolic geometry, and geometric function theory.
Graduate Studies in Mathematics Volume: 183
2017; 637 pp; Hardcover
Print ISBN: 978-1-4704-3770-1
This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of etale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups.
The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
Graduate students and researchers interested in algebra.
Part of Cambridge Studies in Advanced Mathematics
Date Published: August 2017
availability: Available
format: Hardback
isbn: 9781108422628
This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether?Lefschetz theorem and Nori's theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Kahler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford?Tate groups and their associated domains, the Mumford?Tate varieties and generalizations of Shimura varieties.
A completely revised and up-to-date new edition, covering all major new developments in the field
Accessible to graduate students with modest backgrounds in algebraic topology and algebra
Begins by providing a comprehensive introduction to the basic theory as developed by Griffiths
October 12, 2017
Textbook - 304 Pages - 306 B/W Illustrations
ISBN 9781138070844
Series: Textbooks in Mathematics
Employs graph theory to teach mathematical reasoning
Expressly written for non-mathematical students
Promotes critical thinking and problem solving
Provides rich examples and clear explanations without using proofs
A Tour Through Graph Theory introduces graph theory to students who are not mathematics majors. Rather than featuring formal mathematical proofs, the book focuses on explanations and logical reasoning. It also includes thoughtful discussions of historical problems and modern questions. The book inspires readers to learn by working through examples, drawing graphs and exploring concepts.
This book distinguishes itself from others covering the same topic. It strikes a balance of focusing on accessible problems for non-mathematical students while providing enough material for a semester-long course.
Instructors
1. Euelrian Tours; 2. Hamiltonian Cycles; 3. Paths; 4. Trees and Networks; 5. Matching; 6. Graph Coloring; 7. Additional Topics; Selected Answers and Solutions
December 27, 2017
Reference - 353 Pages - 102 B/W Illustrations
ISBN 9781498750493 -
Series: Discrete Mathematics and Its Applications
Aimed at graduate students and professionals in both mathematics and computer science
The first book to appear on the topic
Authored by the best known authority
The crossing number is a popular object of study with surprising connections. A rich body of material illustrates a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part deals with the traditional crossing number, crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, the independent odd crossing number, with interesting and non-trivial results. Finally, applications of the crossing number outside topological graph theory are included.
1. Introduction and History
Part I: The Crossing Number
2. Crossing Number
3. Crossing Number and other Parameters
4. Computational Complexity
5. Algorithms
Part II: Crossing Number Variants
6. Rectilinear Crossing Number
7. Local Crossing Number
8. Monotone and Book crossing numbers
9. Pair Crossing Number
10. k-planar Crossing Number
11. Independent Odd Crossing Number
12. Maximum Crossing Numbers
Part III: Applications
13. Crossing Minimization
14. Geometric Configurations
Appendix