From August 29 to September 7, 2006, a large group of distinguished lecturers and young physicists coming from various countries around the world met in Erice, Italy, at the Ettore Majorana Foundation and Centre for Scientific Culture (EMFCSC) for the 44th course of the International School of Subnuclear Physics: 典he Logic of Nature, Complexity and New Physics: From Quark-Gluon Plasma to Superstrings, Quantum Gravity and Beyond・
This book is a collection of lectures given during the course, covering the most recent advances in theoretical physics and the latest results from current experimental facilities. Following one of the aims of the School, which is to encourage and promote young physicists to achieve recognition at an international level, the students who have distinguished themselves for their excellence in research have been given the opportunity to publish their presentations in this volume.
Complexity and Landscape in String Theory (F Denef & M R Douglas)
Black Holes, Qubits and the Fano Plane (M J Duff & S Ferrara)
Complexity at the Fundamental Level: Consequences for LHC (A Zichichi)
Evidence for a Quark-Gluon Plasma at RHIC (J W Harris)
International Linear Collider (N S Lockyer)
How to Detect Extra-dimensions (I Antoniadis)
Dick Dalitz: Examples of His Contributions to Particle Physics (G R Goldstein)
Analog Models Beyond Kinematics (S Fagnocchi)
Complexity in Cosmic Structures (F S Labini)
Mapping the Transverse Size of the Proton (O Smith)
On the Precision of a Length Measurement (X Calmet)
and other papers
Readership: Students, researchers and academics in the field of subnuclear physics.
688pp Pub. date: Jul 2008
ISBN 978-981-283-245-0
This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.
The volume includes works on picture (2+1)-TQFTs and their applications to quantum computing, Berry phase and Yang烹axterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, Gromov妨itten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flow, Calabi忘au problems for CR manifolds, Milnor痴 conjecture on volume of simplexes, Heegaard genera of 3-manifolds, and the (A,B)-slice problem. It also includes five unpublished papers of Xiao-Song Lin and various speeches related to the memorial conference.
On Picture (2+1)-TQFTs (M Freedman et al.)
Generalized Ricci Flow I: Local Existence and Uniqueness (C-L He et al.)
Unitary Representations of the Artin Braid Groups and Quantum Algorithms for Colored Jones Polynomials and the Witten乏eshetikhin Invariant (L H Kauffman & S J Lomonaco Jr.)
A New Approach to Deriving Recursion Relations for the Gromov妨itten Theory (Y-S Kim & K Liu)
Twisted L2泡lexander砲onway Invariants for Knots (W Li & W Zhang)
Existence of Knots of Minimum Energy and Topological Growth Laws in the Faddeev Model (F Lin & Y Yang)
Additional Gradings in Khovanov Homology (V O Manturov)
and other papers
Readership: Graduate students and researchers in mathematics and physics.
400pp (approx.) Pub. date: Scheduled Fall 2008
ISBN 978-981-281-910-9
Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations.
These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.
Painlev・Equations
Hopf Algebra of Trees
Picard坊essiot Closure
Model Theory and Differential Galois Theory
Frobenius Structures in Differential Algebra
Computability and Differential Fields
Jacobi痴 Bound and Normal Forms Computations
Linear Differential Equations and Lie Algebras
Readership: Researchers in mathematics, especially those interested in the theory of differential equations from an algebraic viewpoint and relations between differential algebra and Galois theory, model theory, combinatorics, computability and symbolic computations.
150pp (approx.) Pub. date: Scheduled Fall 2008
ISBN 978-981-283-371-6
This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quadratic forms, the proof of Fermat痴 last theorem and the approximation of pi. It provides a balanced overview of both the theoretical and computational sides of the subject, allowing a variety of courses to be taught from it.
Historical Overview
Introduction to Modular Forms
Arithmetic of Modular Forms
Applications of Modular Forms
Mod p Modular Forms
p-adic Modular Forms
Computing with Modular Forms
Appendices on MAGMA Code for Classical Modular Forms
SAGE Code for Classical Modular Forms
Hints and Answers to the Exercises
Readership: Academics, researchers and graduate students in number theory and computational mathematics.
200pp (approx.) Pub. date: Scheduled Fall 2008
ISBN 978-1-84816-213-6
1-84816-213-8 US