IRMA Lectures in Mathematics and Theoretical Physics Vol. 13
ISBN 978-3-03719-055-5
March 2009, 883 pages, hardcover, 17 x 24 cm.
This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The present volume has 19 chapters and is divided into four parts:
The metric and the analytic theory (uniformization, Weil?Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space).
The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups).
Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line).
The Grothendieck?Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the soleniod).
This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.
ISBN: 978-1-57146-107-0
Year Published: 2008
Pages: 124 pages
Binding: Softcover
Description:
Proceedings of the 14th Gokova Geometry-Topology Conference, held on the shores of Gokova Bay, Turkey, in May of 2007.
A question analogous to the flux conjecture concerning Lagrangian submanifolds
K. Ono
Hamiltonian handleslides for Heegard Floer homology
T. Perutz
Construction of symplectic cohomology S2 × S2
A. Akhmedov
Some remarks on cabling, contact structures, and complex curves
M. Hedden
On the Khovanov and knot Floer homologies of quasi-alternating links
C. Manolescu And P. Ozsvath
Tight contact structures on the Weeks manifold
A. I. Stipsicz
Planar Contact Structures with Binding Number Three
M. F. Arikan
ISBN: 978-0-470-05095-8
Hardcover
416 pages
April 2009
Adaptive methods can be found in all fields of statistics. Written by an eminent statistician who has a strong working knowledge of all the key areas in statistics that make use of adaptive designs, this book presents the theory and methodology of stagewise adaptive designs in all applicable fields of statistics. The book includes such novel content as Bayesian dynamic adaptive techniques (for finance), adaptive decision making and sequential analysis (for survey sampling), and adaptive filtering (for engineering). This extensively class-tested text is ideal for researchers, practitioners, and students.
ISBN: 978-0-470-45793-1
Hardcover
928 pages
June 2009
The book begins with an introductory chapter that provides some explanation and examples of what discrete mathematics is about, which is a unique feature to this discrete mathematics text. The formal setting is introduced in Chapter 2 where sets, logic, and Boolean algebra are discussed. Chapter 3 then discusses axiomatic mathematics as a system and subsequently focuses on proof techniques. The proof techniques are extensively illustrated throughout the rest of the book. For example, complete induction with the "optimality of the Deferred Acceptance Algorithm for suitors" in Chapter 3; proof by contradiction with The Halting Problem in Chapter 4; and constructive proofs with "a finite projective plane of order n iff n-1 mutually orthogonal Latin squares of order n" in Chapter 8. Combinatorial proof is introduced in Chapter 5 and used in Chapter 8 to establish the necessary conditions for the existence of a balanced incomplete block design. Technology is introduced when it will enhance understanding. For example, several applications that explore the inner workings of recursion are presented in Chapter 7, a simple perl script (also a web page front-end to that script) that enables students to practice creating regular expressions is discussed in Chapter 9, and a java application that allows students to rubber-band graphs to check for planarity is featured in Chapter 10. Combinatorics receives more coverage than is typical, and additional unique topics include container problems (advanced counting), Latin squares, finite projective planes, balanced incomplete block designs, coding theory, Ramsey numbers, and systems of distinct representatives. Additional topical coverage includes counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions and relations. Several other topics receive more coverage than is typical, including expressing algorithms, Bayes theorem, the Halting problem, and regular expressions.
2009; 547 pp; hardcover
ISBN-13: 978-0-8218-4759-6
Expected publication date is July 19, 2009.
This book surveys matching theory, with an emphasis on connections with other areas of mathematics and on the role matching theory has played, and continues to play, in the development of some of these areas. Besides basic results on the existence of matchings and on the matching structure of graphs, the impact of matching theory is discussed by providing crucial special cases and nontrivial examples on matroid theory, algorithms, and polyhedral combinatorics. The new Appendix outlines how the theory and applications of matching theory have continued to develop since the book was first published in 1986, by launching (among other things) the Markov Chain Monte Carlo method.
Readership
Graduate students and research mathematicians interested in graph theory, combinatorics, combinatorial optimization, or graph algorithms.
Matchings in bipartite graphs
Flow theory
Size and structure of maximum matchings
Bipartite graphs with perfect matchings
General graphs with perfect matchings
Some graph-theoretical problems related to matchings
Matching and linear programming
Determinants and matchings
Matching algorithms
The f-factor problem
Matroid matching
Vertex packing and covering
Appendix: Developments in matching theory since this book was first published
References
Index of terms
Index of symbols
Errata