Vol. I: Plenary Lectures and Ceremonies
Vols. II-IV: Invited Lectures
Hyderabad, India, 19?27 August 2010
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Volume II:
The Proper Forcing Axiom (J T Moore)
Tensor Triangular Geometry (P Balmer)
The Emerging p-adic Langlands Programme (C Breuil)
The Tangent Space to an Enumerative Problem (P Belkale)
Scalar Curvature, Conformal Geometry, and the Ricci Flow with Surgery (F C Marques)
Fukaya Categories and Bordered Heegaard-Floer Homology (D Auroux)
Volume III:
Quasi-isometric Rigidity of Solvable Groups (A Eskin & D Fisher)
Differentiability of Lipschitz Functions, Structure of Null Sets, and Other Problems(M Csornyei et al.)
Group Actions on Operator Algebras (M Izumi)
Green Bundles and Related Topics (M-C Arnaud)
A Hyperbolic Dispersion Estimate, with Applications to the Linear Schrodinger Equation (N Anantharaman et al.)
Topological Field Theory, Higher Categories, and Their Applications (A Kapustin)
Volume IV:
Random Planar Metrics (I Benjamini)
Flag Enumeration in Polytopes, Eulerian Partially Ordered Sets and Coxeter Groups (L J Billera)
Smoothed Analysis of Condition Numbers (P Burgisser)
The Hybridizable Discontinuous Galerkin Methods (B Cockburn)
Optimal Control under State Constraints (H Frankowska)
Deterministic and Stochastic Aspects of Single-crossover Recombination (E Baake)
Professional Knowledge Matters in Mathematics Teaching (J Adler)
History of Convexity and Mathematical Programming: Connections and Relationships in Two Episodes of Research in Pure and Applied Mathematics of the 20th Century (T H Kjeldsen)
and other papers
Set
4000pp (approx.) Pub. date: Sep 2010
ISBN: 978-981-4324-30-4
20% Discount Until 31 October 2010
This textbook introduces the theory of complex variables at undergraduate level. A good collection of problems is provided in the second part of the book. The book is written in a user-friendly style that presents important fundamentals a beginner needs to master the technical details of the subject. The organization of problems into focused sets is an important feature of the book and the teachers may adopt this book for a course on complex variables and for mining problems.
Complex Numbers
Elementary Functions and Differentiation
Functions with Branch Point Singularity
Integration in Complex Plane
Cauchy Integral Formula
Residue Theorem
Contour Integration
Asymptotic Expansion
Conformal Mappings
Physical Applications of Conformal Mappings
500pp (approx.) Pub. date: Oct 2010
ISBN: 978-981-4313-52-0
ISBN: 978-981-4313-53-7(pbk)
Classical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. Volume 2 begins with analytic continuation. The Riemann mapping theorem is proved and used in solving Dirichlet's problem for an open disk and, hence, a class of general domains via Perron's method. Finally, proof of the uniformization theorem of Riemann surfaces is given.
The book is rich in contents, figures, examples and exercises. It is self-contained and is designed for a variety of usages and motivations concerning advanced studies. It can be used both as a textbook for undergraduate and graduate students, and as a reference book in general.
Fundamental Theory: Sequences, Series and Infinite Products
Conformal Mapping and Dirichlet's Problem
Riemann Surfaces
900pp (approx.) Pub. date: Sep 2010
ISBN: 978-981-4271-28-8
ISBN: 978-981-4271-29-5(pbk)
The Maxwell, Einstein, Schrodinger and Dirac equations are considered the most important equations in all of physics. This volume aims to provide new eight- and twelve-dimensional complex solutions to these equations for the first time in order to reveal their richness and continued importance for advancing fundamental Physics. If M-Theory is to keep its promise of defining the ultimate structure of matter and spacetime, it is only through the topological configurations of additional dimensionality (or degrees of freedom) that this will be possible. Stretching the exploration of complex space through all of the main equations of Physics should help tighten the noose on gtheh fundamental theory. This kind of exploration of higher dimensional spacetime has for the most part been neglected by M-theorists and physicists in general and is taken to its penultimate form here.
Orbiting the Moons of Pluto
Formalism for Complexification of Maxwell's Equations
Relativistic Formulation of Maxwell's Equations in Complex Form
Solutions to the Schrodinger Equation in Complex 8-Space
Sub- and Superluminal Transformations of the Complex Vector Potential
The Dirac Equation: Spinors, Twistors and Quaternions in Complex Space
Complex Unified Geometrodynamics
The Arrow of Time and the Nature of Reality
Synopticon of the Plenum and the Structure of Matter
A New Medical Modality: A Revolution in Biological Science
Immanent FTL Warp Drive Technology from Extended Geometrodynamics
and other chapters
350pp (approx.) Pub. date: Scheduled Summer 2011
ISBN: 978-981-4324-24-3
A publication of the Tata Institute of Fundamental Research.
2010; 103 pp; softcover
ISBN-13: 978-81-8487-023-7
Expected date of availability is August 30, 2010.
The genesis of these notes was a series of four lectures given by the first author at the Tata Institute of Fundamental Research. It evolved into a joint project and contains many improvements and extensions on the material covered in the original lectures.
Let F be a finite extension of q, and E an elliptic curve defined over F. The fundamental idea of the Iwasawa theory of elliptic curves, which grew out of Iwasawa's basic work on the ideal class groups of cyclotomic fields, is to study deep arithmetic questions about E over F via the study of coarser questions about the arithmetic of E over various infinite extensions of F. At present, we only know how to formulate this Iwasawa theory when the infinite extension is a p-adic Lie extension for a fixed prime number p. These notes will mainly discuss the simplest non-trivial example of the Iwasawa theory of E over the cyclotomic zp-extension of F. However, the authors also make some comments about the Iwasawa theory of E over the field obtained by adjoining all p-power division points on E to F. They discuss in detail a number of numerical examples, which illustrate the general theory beautifully. In addition, they outline some of the basic results in Galois cohomology which are used repeatedly in the study of the relevant Iwasawa modules.
The only changes made to the original notes: The authors take modest account of the considerable progress which has been made in non-commutative Iwasawa theory in the intervening years. They also include a short section on the deep theorems of Kato on the cyclotomic Iwasawa theory of elliptic curves.
A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka.
Mathematicians interested in algebraic number theory.
*Notation
*Basic results from Galois cohomology
*The Iwasawa theory of the Selmer group
*The Euler characteristic formula
*Numerical examples over the cyclotomic Zp-extension of Q
*Numerical examples over Q(\mu p)
*Appendix
*Bibliography