Series: Abel Symposia , Vol. 3
2008, Approx. 150 p., Hardcover
ISBN: 978-3-540-68848-8
Due: September 24, 2008
The 2006 Abel symposium is focusing on contemporary research involving interaction between computer science, computational science and mathematics. In recent years, computation has been affecting pure mathematics in fundamental ways. Conversely, ideas and methods of pure mathematics are becoming increasingly important within computational and applied mathematics. At the core of computer science is the study of computability and complexity for discrete mathematical structures. Studying the foundations of computational mathematics raises similar questions concerning continuous mathematical structures.
There are several reasons for these developments. The exponential growth of computing power is bringing computational methods into ever new application areas.
Equally important is the advance of software and programming languages, which to an increasing degree allows the representation of abstract mathematical structures in program code. Symbolic computing is bringing algorithms from mathematical analysis into the hands of pure and applied mathematicians, and the combination of symbolic and numerical techniques is becoming increasingly important both in computational science and in areas of pure mathematics.
We are witnessing a development where a focus on computability, computing and algorithms is contributing towards a unification of areas of computer science, applied and pure mathematics. The 2006 Abel symposium brought together some of the leading international researchers working in these areas, presented a snapshot of current state of the art, and raised questions about future research directions.
Researchers and graduate students in mathematics and computer science
Abel symposia
applied mathematics
computational mathematics
computer science
Series: Bolyai Society Mathematical Studies , Vol. 19
2008, Approx. 500 p., Hardcover
ISBN: 978-3-540-85218-6
Due: September 2008
Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is Laszlo Lovasz, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovasz’s 60th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers.
Preface Curriculum Vitae of L. Lovasz.- Publications of Laszlo Lovasz.- I. Barany: On the Power of Linear Dependencies.- J. Beck: Surplus of Graphs and the Lovasz Local Lemma.- A. Bjorner: RandomWalks, Arrangements, Cell Complexes, Greedoids, and Self-organizing Libraries.- A. Blokhuis and F. Mazzocca: The Finite Field Kakeya Problem.- B. Bollobas and V. Nikiforov: An Abstract Szemeredi Regularity Lemma.- U. Feige: Small Linear Dependencies for Binary Vectors of Low Weight.- A. A. Benczur and M. X. Goemans: Deformable Polygon Representation and Near-Mincuts.- A. Schrijver: Graph Invariants in the Edge Model.- J. Nesetril and P. Ossona de Mendez: Structural Properties of Sparse Graphs.- K. Gyarmati, M. Matolcsi and I. Z. Ruzsa: Plunnecke's Inequality for Different Summands.- H. E. Scarf: The Structure of the Complex of Maximal Lattice Free Bodies for a Matrix of Size (n + 1) x n.- J. Solymosi: Incidences and the Spectra of Graphs.- J. Spencer: The Maturation of the Probabilistic Method.- V. Vu: A structural approach to subset-sum problems.
Series: Lecture Notes in Mathematics , Vol. 1954
2008, XI, 457 p. 18 illus., Softcover
ISBN: 978-3-540-69364-2
Due: September 24, 2008
This volume contains the revised and completed notes of lectures given at the school "Quantum Potential Theory: Structure and Applications to Physics," held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald from February 26 to March 10, 2007.
Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction to this theory, concentrating on probabilistic potential theory and it quantum analogs, i.e. quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented.
Potential Theory in Classical Probability, Nicolas Privault.- Introduction to Random Walks on Noncommutative Spaces, Philippe Biane.- Interactions between Qantum Probability and Operator Space Theory, Quanhua Xu.- Dirichlet Forms on Noncommutative Spaces, Fabio Cipriani.- Applications of Controlled Quantum Processes in Quantum Optics, Luc Bouten.- Quantum Walks, Norio Konno
2009, Approx. 350 p., Hardcover
ISBN: 978-3-211-75355-2
Due: October 2008
Trees are a fundamental object in graph theory and combinatorics as well as a basic object for data structures and algorithms in computer science. During the last years research related to (random) trees has been constantly increasing and several asymptotic and probabilistic techniques have been developed in order to describe characteristics of interest of large trees in different settings.
The aim of this book is to provide a thorough introduction into various aspects of trees in random settings and a systematic treatment of the involved mathematical techniques. It should serve as a reference book as well as a basis for future research. One major conceptual aspect is to bridge combinatorial and probabilistic methods that range from counting techniques (generating functions, bijections) over asymptotic methods (saddle point techniques, singularity analysis) to various sophisticated techniques in asymptotic probability (martingales, convergence of stochastic processes, concentration inequalities).
Graduate students and researchers interested in random trees, combinatorics, asymptotic tree statistics, probability theory, and related fields of research
Algorithms
Combinatorics
Probability
Random Trees
Stochastic Processes
Series: Springer Monographs in Mathematics
2009, Approx. 380 p., Hardcover
ISBN: 978-3-540-87524-6
Due: October 22, 2008
The study of hyperbolic systems is one of the core themes of modern dynamical systems. For dynamics on surfaces there is a particularly complete theory where the fine-scale structure of hyperbolic invariant sets and the measures they support can be described in a very complete and elegant way. The present book, written by leading mathematicians in the field, provides a largely self-contained, rigorous description of this theory. It plays an important role in filling a gap in the present literature on hyperbolic dynamics and is highly recommended for all PhD students interested in this field.
1 Introduction.- 2 HR structures.- 3 Solenoid functions.- 4 Self-renomalizable structures.- 5 Rigidity.- 6 Gibbs measures.- 7 Measure scaling functions.- 8 Measure solenoid functions.- 9 Cocycle-gap pairs.- 10 Hausdorff realizations.- 11 Extended Livsic-Sinai eigenvalue formula.- 12 Arc exchange systems and renormalizations.- 13 Golden tiling (in collaboration wtih J.P.Almeida and A.Portela).- 14 Pseudo-Anosov diffeomorphisms in pseudo-surfaces.- Appendix A: Classifying C1+ structures on the real line.- Appendix B: Classifying C1+ structures on Cantor sets.- Appendix C: Expanding dynamics of the circle.- Appendix D: Markov maps on train tracks.- Appendix E: Explosion of smoothness for Markov families.- References.- Index.
Series: Lecture Notes in Mathematics , Vol. 1952
2009, Approx. 410 p., Softcover
ISBN: 978-3-540-85817-1
Due: October 22, 2008
A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series, which consists of the subgroups determined by the augmentation powers, is a challenging task. This monograph presents an exposition of different methods for investigating this relationship. In addition to group theorists, the results are also of interest to topologists and number theorists. The approach is mainly combinatorial and homological. A novel feature is an exposition of simplicial methods for the study of problems in group theory.
Preface.- Lower Central Series.- Dimension Subgroups.- Derived Series.- Augmentation Powers.- Homotopical Aspects.- Miscellanea.- Appendix (Simplicial Methods).- Bibliography.- Index.