Series: Mathematical Sciences Research Institute Publications
Hardback (ISBN-13: 9780521199308)
This book provides an introduction to (1) various zeta functions (for example, Riemann, Hurwitz, Barnes, Epstein, Selberg, and Ruelle), including graph zeta functions; (2) modular forms (Eisenstein series, Hecke and Dirichlet L-functions, Ramanujan's tau function, and cusp forms); and (3) vertex operator algebras (correlation functions, quasimodular forms, modular invariance, rationality, and some current research topics including higher genus conformal field theory). Various concrete applications of the material to physics are presented. These include Kaluza-Klein extra dimensional gravity, Bosonic string calculations, an abstract Cardy formula for black hole entropy, Patterson-Selberg zeta function expression of one-loop quantum field and gravity partition functions, Casimir energy calculations, atomic Schrodinger operators, Bose-Einstein condensation, heat kernel asymptotics, random matrices, quantum chaos, elliptic and theta function solutions of Einstein's equations, a soliton-black hole connection in two-dimensional gravity, and conformal field theory.
* The book consists of lectures that are part of the distinguished series of MSRI Workshops * A serious attempt is made to bridge various gaps between mathematics and physics where, in particular, students and non-experts are targeted * Links and interesting interconnection between seemingly unrelated topics in these fields (mathematics and physics) are consistently explored, with a fair amount of detail and exposition
Part I. Introductory Lectures: 1. Lectures on zeta functions, L-functions and modular forms with some physical applications Floyd L. Williams; 2. Basic zeta functions and some applications in physics Klaus Kirsten; 3. Zeta functions and chaos Audrey Terras; 4. Vertex operators and modular forms Geoffrey Mason and Michael Tuite; Part II. Research Lectures: 5. Applications of elliptic and theta functions to Friedmann*Robertson*Lema*tre*Walker cosmology with cosmological constant Jennie D'Ambroise; 6. Integrable systems and 2D gravitation: How a soliton illuminates a black hole Shabnam Beheshti; 7. Functional determinants in higher dimensions using contour integrals Klaus Kirsten; 8. The role of the Patterson*Selberg zeta function of a hyperbolic cylinder in three-dimensional gravity with a negative cosmological constant Floyd L. Williams.
Series: Mathematical Sciences Research Institute Publications (No. 37)
Paperback (ISBN-13: 9780521153898)
Several Complex Variables is a central area of mathematics with strong interactions with partial differential equations, algebraic geometry, number theory, and differential geometry. The 1995*1996 MSRI program on Several Complex Variables emphasized these interactions and concentrated on developments and problems of interest that capitalize on this interplay of ideas and techniques. This collection provides a remarkably clear and complete picture of the status of research in these overlapping areas and will provide a basis for significant continued contributions from researchers. Several of the articles are expository or have extensive expository sections, making this an excellent introduction for students to the use of techniques from these other areas in several complex variables. Thanks to its distinguished list of contributors this volume provides a representative sample of the work done in Several Complex Variables.
* Many survey articles suitable for graduate students * Explains the connections to many other areas of mathematics * Provides a clear and complete picture of the status of research in these areas
Preface; 1. Local holomorphic equivalence of real analytic submanifolds in CN M. Salah Baouendi and Linda Preiss Rothschild; 2. How to use cycle space in complex geometry Daniel Barlet; 3. Resolution of singularities Edward Bierstone and Pierre D. Milman; 4. Global regularity of the ∂-Neuman problem: a survey of the L2-Sobolev theory Harold P. Boas and Emial J. Straube; 5. Recent developments in the classification theory of compact Kaehler manifolds Frederic Campana and Thomas Peternell; 6. Remarks on global irregularity in the ∂-Neumann problem Michael Christ; 7. Subelliptic estimates and finite type John P. D'Angelo and Joseph J. Kohn; 8. Pseudoconvex-concave duality and regularization of currents Jean-Pierre Demailly; 9. Complex dynamics in higher dimension John Erik Fornaess and Nessim Sibony; 10. Attractors in Ρ2 John Erik Fornaess and Brendan Weickert; 11. Analytic Hilbert quotients Peter Heinzner and Alan Huckleberry; 12. Varieties of minimal rational tangents on uniruled projective manifolds Jun-Muk Hwang and Ngaiming Mok; 13. Recent developments in Seiberg*Witten theory and complex geometry Christian Okonek and Andrei Teleman; 14. Recent techniques in hyperbolicity problems Yum-Tong Siu; 15. Rigidity theorems in Kaehler geometry and fundamental groups of varieties Domingo Toledo; 16. Nevanlinna theory and diophantine approximation Paul Vojta.
Series: London Mathematical Society Lecture Note Series (No. 376)
Paperback (ISBN-13: 9780521728348)
The study of permutation patterns is a thriving area of combinatorics that relates to many other areas of mathematics, including graph theory, enumerative combinatorics, model theory, the theory of automata and languages, and bioinformatics. Arising from the Fifth International Conference on Permutation Patterns, held in St Andrews in June 2007, this volume contains a mixture of survey and research articles by leading experts, and includes the two invited speakers, Martin Klazar and Mike Atkinson. Together, the collected articles cover all the significant strands of current research: structural methods and simple patterns, generalisations of patterns, various enumerative aspects, machines and networks, packing, and more. Specialists in this area and other researchers in combinatorics and related fields will find much of interest in this book. In addition, the volume provides plenty of material accessible to advanced undergraduates and is a suitable reference for projects and dissertations.
* Provides a snapshot of the area’s current state of development * Gives an insight into links with other areas of combinatorics and mathematics * Includes an appendix containing a selection of open problems
Preface; 1. Some general results in combinatorial enumeration Martin Klazar; 2. A survey of simple permutations Robert Brignall; 3. Permuting machines and permutation patterns Mike Atkinson; 4. On three different notions of monotone subsequences Miklos Bona; 5. A survey on partially ordered patterns Sergey Kitaev; 6. Generalized permutation patterns - a short survey Einar Steingrimsson; 7. An introduction to structural methods in permutation patterns Michael Albert; 8. Combinatorial properties of permutation tableaux Alexander Burstein and Niklas Eriksen; 9. Enumeration schemes for words avoiding permutations Lara Pudwell; 10. The lexicographic first occurrence of a I-II-III pattern Torey Burton, Anant P. Godbole and Brett M. Kindle; 11. Enumeration of partitions by rises, levels and descents Toufik Mansour and Augustine O. Munagi; 12. Restricted patience sorting and barred pattern avoidance Alexander Burstein and Isaiah Lankham; 13. Permutations with k-regular descent patterns Anthony Mendes, Jeffrey B. Remmel and Amanda Riehl; 14. Packing rates of measures and a conjecture for the packing density of 2413 Cathleen Battiste Presutti and Walter Stromquist; 15. On the permutational power of token passing networks Michael Albert, Steve Linton and Nik R*skuc; 16. Problems and conjectures.
Paperback (ISBN-13: 9780521159395)
This 1998 text takes a practical, step-by-step approach to algebraic curves and surface interpolation motivated by the understanding of the many practical applications in engineering analysis, approximation, and curve plotting problems. Because of its usefulness for computing, the algebraic approach is the main theme, but a brief discussion of the synthetic approach is also presented as a way of gaining additional insight before proceeding with the algebraic manipulation. The authors start with simple interpolation, including splines, and extend this in an intuitive fashion to the production of conic sections. They then introduce projective co-ordinates as tools for dealing with higher order curves and singular points. They present many applications and concrete examples, including parabolic interpolation, geometric approximation, and the numerical solution of trajectory problems. In the final chapter they apply the basic theory to the construction of finite element basis functions and surface interpolants over non-regular shapes.
* Applications include curve design in the aircraft industry, finite element analysis, computer graphics and curve plotting * Many figures included * Many useful constructions
1. Interpolation; 2. Conic sections; 3. Synthetic geometry; 4. Algebraic projective geometry; 5. Algebraic curves; 6. Examples and applications; 7. Surfaces.
Series: London Mathematical Society Lecture Note Series (No. 378)
Paperback (ISBN-13: 9780521145770)
Focussing on the work of Sir John Kingman, one of the world's leading researchers in probability and mathematical genetics, this book touches on the important areas of these subjects in the last 50 years. Leading authorities give a unique insight into a wide range of currently topical problems. Papers in probability concentrate on combinatorial and structural aspects, in particular exchangeability and regeneration. The Kingman coalescent links probability with mathematical genetics and is fundamental to the study of the latter. This has implications across the whole of genomic modelling including the Human Genome Project. Other papers in mathematical population genetics range from statistical aspects including heterogeneous clustering, to the assessment of molecular variability in cancer genomes. Further papers in statistics are concerned with empirical deconvolution, perfect simulation, and wavelets. This book will be warmly received by established experts as well as their students and others interested in the content.
* Sir John Kingman gives a first-hand account of developments in the 1960s * A state-of-the-art treatment of mathematical genetics, relevant to genomic research * Distinguished authors include 10 Fellows of the Royal Society
Preface; List of contributors; Bibliography of J. F. C. Kingman; 1. A fragment of autobiography, 1957*1967 J. F. C. Kingman; 2. More uses of exchangeability: representations of complex random structures David J. Aldous; 3. Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding G. K. Ambler and B. W. Silverman; 4. Assessing molecular variability in cancer genomes A. D. Barbour and S. Tavare; 5. Branching out J. D. Biggins; 6. Kingman, category and combinatorics N. H. Bingham and A. J. Ostaszewski; 7. Long-range dependence in a Cox process directed by an alternating renewal process D. J. Daley; 8. Kernel methods and minimum contrast estimators for empirical deconvolution Aurore Delaigle and Peter Hall; 9. The coalescent and its descendants Peter Donnelly and Stephen Leslie; 10. Kingman and mathematical population genetics Warren J. Ewens and Geoffrey A. Watterson; 11. Characterizations of exchangeable partitions and random discrete distributions by deletion properties Alexander Gnedin, Chris Haulk and Jim Pitman; 12. Applying coupon-collecting theory to computer-aided assessments C. M. Goldie, R. Cornish and C. L. Robinson; 13. Colouring and breaking sticks: random distributions and heterogeneous clustering Peter J. Green; 14. The associated random walk and martingales in random walks with stationary increments D. R. Grey; 15. Diffusion processes and coalescent trees R. C. Griffiths and D. Spano; 16. Three problems for the clairvoyant demon Geoffrey Grimmett; 17. Homogenization for advection-diffusion in a perforated domain P. H. Haynes, V. H. Hoang, J. R. Norris and K. C. Zygalakis; 18. Heavy traffic on a controlled motorway F. P. Kelly and R. J. Williams; 19. Coupling time distribution asymptotics for some couplings of the Levy stochastic area W. S. Kendall; 20. Queueing with neighbours V. Shcherbakov and S. Volkov; 21. Optimal information feed P. Whittle; 22. A dynamical-system picture of a simple branching-process phase transition David Williams; Index.