T. N. Venkataramana, Tata Institute of Fundamental Research, Mumbai, India
Cohomology of Arithmetic Groups, L-Functions and Automorphic Forms
A publication of the Tata Institute of Fundamental Research.
Description
This collection of papers is based on lectures delivered at the Tata Institute of Fundamental Research (TIFR) as part of a special year on arithmetic groups, L-functions and automorphic forms. The volume opens with an article by Cogdell and Piatetski-Shapiro on Converse Theorems for GL_n and applications to liftings. It ends with some remarks on the Riemann Hypothesis by Ram Murty. Other talks cover topics such as Hecke theory for Jacobi forms, restriction maps and L-values, congruences for Hilbert modular forms, Whittaker models for p-adic GL(4), the Seigel formula, newforms for the Maas Spezialchar, an algebraic Chebotarev density theorem, a converse theorem for Dirichlet series with poles, Kirillov theory for GL_2(mathcal{D}), and the L^2 Euler characteristic of arithmetic quotients. The present volume is the latest in the Tata Institute's tradition of recognized contributions to number theory.
Contents
Cogdell and Piatetski-Shapiro -- Converse theorems for mathrm{GL}_n and their application to liftings
E. Ghate -- Congruences between base-change and non-base-change Hilbert modular forms
C. Khare -- Restriction maps and L-values
M. Manickam -- On Hecke theory for Jacobi forms
A. N. Nair -- The L^2 Euler characteristic of arithmetic quotients
D. Prasad -- The space of degenerate Whittaker models for mathrm{GL}(4) over p-adic fields
S. Raghavan -- The Seigel formula and beyond
R. Raghunathan -- A converse theorem for Dirichlet series with poles
A. Raghuram -- Kirillov theory for mathrm{GL}_2(mathcal{D})
C. S. Rajan -- An algebraic Chebotarev density theorem
B. Ramakrishnan -- Theory of newforms for the Maas Spezialschar
M. R. Murty -- Some remarks on the Riemann hypothesis
D. Prasad and N. Sanat -- On the restriction of cuspidal representations to unipotent elements
W. Kohnen and J. Sengupta -- Nonvanishing of symmetric square L-functions of cusp forms inside the critical strip
H. H. Kim and F. Shahidi -- Symmetric cube for mathrm{GL}_2
D. S. Thakur -- L-functions and modular forms in finite characteristic
T. C. Vasudevan -- Automorphic forms for Siegel and Jacobi modular groups
T. N. Venkataramana -- Restriction maps between cohomology of locally symmetric varieties
Details:
Publisher: Tata Institute of Fundamental Research
Distributor: American Mathematical Society
Series: Tata Institute of Fundamental Research
Publication Year: 2001
ISBN: 81-7319-421-1
Paging: 251 pp.
Binding: Softcover
Seiichi Kamada, Osaka City University, Japan
Braid and Knot Theory in Dimension Four
Expected publication date is June 15, 2002
Description
Braid theory and knot theory are related via two famous results due to Alexander and Markov. Alexander's theorem states that any knot or link can be put into braid form. Markov's theorem gives necessary and sufficient conditions to conclude that two braids represent the same knot or link. Thus, one can use braid theory to study knot theory and vice versa.
In this book, the author generalizes braid theory to dimension four. He develops the theory of surface braids and applies it to study surface links. In particular, the generalized Alexander and Markov theorems in dimension four are given. This book is the first to contain a complete proof of the generalized Markov theorem.
Surface links are studied via the motion picture method, and some important techniques of this method are studied. For surface braids, various methods to describe them are introduced and developed: the motion picture method, the chart description, the braid monodromy, and the braid system. These tools are fundamental to understanding and computing invariants of surface braids and surface links.
Included is a table of knotted surfaces with a computation of Alexander polynomials. Braid techniques are extended to represent link homotopy classes. The book is geared toward a wide audience, from graduate students to specialists. It would make a suitable text for a graduate course and a valuable resource for researchers.
Contents
Basic notions and notation
Classical braids and links
Braids
Braid automorphisms
Classical links
Braid presentation of links
Deformation chain and Markov's theorem
Surface knots and links
Surface links
Surface link diagrams
Motion pictures
Normal forms of surface links
Examples (Spinning)
Ribbon surface links
Presentations of surface link groups
Surface braids
Branched coverings
Surface braids
Products of surface braids
Braided surfaces
Braid monodromy
Chart descriptions
Non-simple surface braids
1-handle surgery on surface braids
Braid presentation of surface links
The normal braid presentation
Braiding ribbon surface links
Alexander's theorem in dimension four
Split union and connected sum
Markov's theorem in dimension four
Proof of Markov's theorem in dimension four
Surface braids and surface links
Knot groups
Unknotted surface braids and surface links
Ribbon surface braids and surface links
3-braid 2-knots
Unknotting surface braids and surface links
Seifert algorithm for surface braids
Basic symmetries in chart descriptions
Singular surface braids and surface links
Bibliography
Index
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Mathematical Surveys and Monographs, ISSN: 0076-5376
Volume: 95
Publication Year: 2002
ISBN: 0-8218-2969-6
Paging: 305 pp.
Binding: Hardcover
Stephen Gaukroger
Descartes' System of Natural Philosophy
Description
Towards the end of his life, Descartes published the first four parts of a projected six-part work, The Principles of Philosophy. This was intended to be the definitive statement of his complete system of philosophy, dealing with everything from cosmology to the nature of human happiness. Stephen Gaukroger examines the whole system, and reconstructs the last two parts, 前n Living Things・and 前n Man・ from Descartes・other writings. He relates the work to the tradition of late Scholastic textbooks which it follows, and also to Descartes・other philosophical writings, and he examines the ways in which Descartes transformed not only the practice of natural philosophy but also our understanding of what it is to be a philosopher. His book is the first comprehensive examination of Descartes・complete philosophical system.
Chapter Contents
Introduction; 1. Before the Principia; 2. The scholastic textbook tradition; 3. Part I: The principles of knowledge; 4. Part II: The principles of material objects; 5. Part III: The visible universe; 6. Part IV: The earth; 7. Part V: Living things; 8. Part VI: Man.
ISBN: 0-521-00525-6
Binding: Paperback
ISBN: 0-521-80897-9
Binding: Hardback
Size: 229 x 153 mm
Pages: 266
Weight: 0.434kg
Figures: 27 line diagrams
Published: 21 March 2002
GONZALO NAVARRO / University of Chile
AND MATHIEU RAFFINOT / CNRS Equipe Genome et Informatique, Evry, France
Flexible Pattern Matching in Strings
Practical On-Line Search Algorithms for Texts and Biological Sequences
Description: String matching problems range from the relatively simple task of searching a single text for a string of characters to searching a database for approximate occurrences of a complex pattern. Recent years have witnessed a dramatic increase of interest in sophisticated string matching problems, especially in information retrieval and computational biology. This book presents a practical approach to string matching problems, focusing on the algorithms and implementations that perform best in practice. It covers searching for simple, multiple and extended strings, as well as regular expressions, and exact and approximate searching. It includes all the most significant new developments in complex pattern searching. The clear explanations, step-by-step examples, algorithm pseudocode, and implementation efficiency maps will enable researchers, professionals and students in bioinformatics, computer science, and software engineering to choose the most appropriate algorithms for their applications.
Contents: 1. Introduction; 2. String matching; 3. Multiple string matching; 4. Extended string matching; 5. Regular expression matching; 6. Approximate matching; 7. Conclusion.
ISBN, Binding, Price: 0-521-81307-7 Hardback
Approximate Publication Date: c.01/07/2002
Main Subject Category: Theory of computation, data
Market (Subject)
information retrieval, bioinformatics, computer science, software engineering
Level
academic researchers, professionals, graduate students, undergraduate students
Bibliographic Details
90 line diagrams
Comparable titles: GUSFIELD/Algorithms on Strings, Trees, and Sequences/1997/0521 585198
Kulenovic Mustafa R. S. University of Rhode Island, Kingston, Rhode Island, USA
Merino Orlando University of Rhode Island, Kingston, Rhode Island, USA
Discrete "Dynamical" Systems and Difference Equations
with Mathematica
ISBN: 1-58488-287-5 No. of Pages: 360
Publication date: 2/19/2002
Description
Following the work of Yorke and Li in 1975, the theory of discrete dynamical systems and difference equations developed rapidly. The applications of difference equations also grew rapidly, especially with the introduction of graphical-interface software that can plot trajectories, calculate Lyapunov exponents, plot bifurcation diagrams, and find basins of attraction.
Modern computer algebra systems have opened the door to the use of symbolic calculation for studying difference equations. This book offers an introduction to discrete dynamical systems and difference equations and presents the Dynamica software. Developed by the authors and based on Mathematica, Dynamica provides an easy-to-use collection of algebraic, numerical, and graphical tools and techniques that allow users to quickly gain the ability to:
Find and classify the stability character of equilibrium and periodic points
Perform semicycle analysis of solutions
Calculate and visualize invariants
Calculate and visualize Lyapunov functions and numbers
Plot bifurcation diagrams
Visualize stable and unstable manifolds
Calculate Box Dimension
While presenting the essential theoretical concepts and results, the emphasis is on using the software. The authors present two sets of Dynamica sessions: one that serves as a tutorial of the different techniques, the other features case studies of well-known difference equations. Dynamica and notebooks corresponding to particular chapters are available for download from the Internet.
Garroni Maria Giovanna Universita di Roma, 'Lasapienza'
Menaldi Jose Luis Wayne State University, Detroit, Michigan, USA
Second Order Elliptic Integro-Differential Problems
ISBN: 1-58488-200-X No. of Pages: 240
Publication date: 2/15/2002
Chapman & Hall/CRC Research Notes in Mathematics.
Description
The Green function has played a key role in the analytical approach that in recent years has led to important developments in the study of stochastic processes with jumps. In this Research Note, the authors-both regarded as leading experts in the field- collect several useful results derived from the construction of the Green function and its estimates.
The first three chapters form the foundation for the rest of the book, presenting key results and background in integro-differential operators, and integro-differential equations. After a summary of the properties relative to the Green function for second-order parabolic integro-differential operators, the authors explore important applications, paying particular attention to integro-differential problems with oblique boundary conditions. They show the existence and uniqueness of the invariant measure by means of the Green function, which then allows a detailed study of ergodic stopping time and control problems.