This proceedings volume covers the main fields of mathematics: analysis, algebra and number theory, geometry and topology, combinatorics and graphs, applied mathematics, numerical analysis and computer mathematics, probability and statistics, teaching and popularization of mathematics.

This volume presents introductory lectures on the Standard Model and Higgs physics, as well as QCD. These lectures provided the particle physics background for the main topics of the school: astroparticle physics and modern cosmology.

The NATO Advanced Study Institute 2000 was held in Cascais, a small town located in a renowned beach resort area, near Lisbon. The aim of the Meeting was to provide an overview and to cover the recent devel opments in some of the most important topics in Particle Physics and Cosmology, including Neutrino Physics, CP violation, B-Physics, Baryo genesis, Dark Matter, Inflation, Supersymmetry, Unified Theories, Large Extra-Di~ensions and M-theory. In the NATO ASI 2000, we had the priv ilege to have among the lecturers, some of the most prominent physicists working in the fields of Particle Physics and Cosmology. Furthermore, there was a strong participation by a large number of young scientists, including graduate students and post-docs who had an opportunity to learn about the latest developments in the field and discuss the various topics with lec turers and other participants. The enthusiasm of the young participants, the generosity of the lecturers in giving their time to participate in open discussions and debates, together with the social events and the pleasant environment of Cascais, all contributed to the great success of the Meeting. We are very grateful to Camara Municipal de Cascais for their support and organization of the reception in the beautiful Palace Condes Castro de Guimaraes and we are also specially grateful to colonel Eugenio de Oliveira for his support, to commander A. Monteiro de Macedo and to Mr.

The topic of the CVIII session of the Ecole de Physique des Houches, held in July 2017, was Effective Field Theory in Particle Physics and Cosmology. Effective Field Theory (EFT) is a general method for describing quantum systems with multiple length scales in a tractable fashion. It allows to perform precise calculations in established models (such as the Standard Models of particle physics and cosmology), as well as to concisely parametrise possible effects from physics beyond the Standard Models. The goal of this school was to offer a broad introduction to the foundations and modern applications of Effective Field Theory in many of its incarnations. This is all the more important as there are preciously few textbooks covering the subject, none of them in a complete way. In this book, the lecturers present the concepts in a pedagogical way so that readers can adapt some of the latest developments to their own problems. The chapters cover almost all the lectures given at the school and will serve as an introduction to the topic and as a reference manual to students and researchers.

The 16 articles presented here are based on lectures given at the Winter School on Mirror Symmetry held at Harvard University in January 1999. They represent recent progress and new directions in the field. Specific topics include Floer homology and mirror symmetry, special Lagrange fibrations, special Lagrangian submanifolds, and local mirror symmetry at higher genus. Other topics include homological mirror symmetry with higher products, categorical mirror symmetry in the elliptic curve, Lagrangian torus fibration of quintic hypersurfaces, mirror symmetry and T-duality, and mirror symmetry and actions of Braid groups on derived categories. This work lacks a subject index. c. Book News Inc.

This book is a collection of lectures given in August 2006 at the Les Houches Summer School on "Particle Physics and Cosmology: the Fabric of Spacetime. It provides a pedagogical introduction to the various aspects of both particle physics beyond the Standard Model and Cosmology of the Early Universe, covering each topic from the basics to the most recent developments.· Provides a pedagogical introduction to topics at the interface of particle physics and cosmology· Addresses each topic from the basis to the most recent developments· Provides necessary tools to build new theoretical models addressing various issues both in cosmology and particle physics· Covers the lectures by internationally-renowned and leading experts· Faces the predictions of theoretical models against collider experimental data as well as from cosmological observations

It is generally felt in the cosmology and particle astrophysics community that we have just entered an era which later can only be looked back upon as a golden age. Thanks to the rapid technical development, with powerful new telescopes and other detectors taken into operation at an impressive rate, and the accompanying advancement of theoretical ideas, the picture of the past, present and future Universe is getting ever clearer. Some of the most exciting new findings and expected future developments are discussed in this invaluable volume. The topics covered include the physics of the early Universe and ultra-high energy processes. Emphasis is also put on neutrino physics and astrophysics, with the evidence for non-zero neutrino masses emerging from both solar neutrinos and atmospheric neutrinos covered in great depth. Another field with interesting new results concerns the basic cosmological parameters, where both traditional methods and the potential of new ones, like deep supernova surveys and acoustic peak detections in the cosmic microwave background, are thoroughly discussed. Various aspects of the dark matter problem, such as gravitational lensing estimates of galaxy masses, cluster evolution and hot cluster electron distortions of the thermal microwave background spectrum, are also discussed, as are particle physics candidates of dark matter and methods to detect them. Cosmic rays of matter and antimatter are included as a topic, and so is the problem of the enigmatic dark energy of the vacuum.

A unified perspective on new and advanced mathematical techniques used in string theory research for graduate students and researchers.

In this third volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This volume presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, supergraphs, non-perturbative results, theories of supersymmetry in higher dimensions, and supergravity. A thorough review is given of the phenomenological implications of supersymmetry, including theories of both gauge and gravitationally-mediated supersymmetry breaking. Also provided is an introduction to mathematical techniques, based on holomorphy and duality, that have proved so fruitful in recent developments. This book contains much material not found in other books on supersymmetry, including previously unpublished results. Exercises are included.

This volume contains the proceedings of an NSF-CBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18-22, 2009. The papers, written especially for this volume by well-known mathematicians and mathematical physicists, are an outgrowth of the talks presented at the conference. Topics examined are highly interdisciplinary and include, among many other things, recent results on D-brane charges in $K$-homology and twisted $K$-homology, Yang-Mills gauge theory and connections with non-commutative geometry, Landau-Ginzburg models, $C^*$-algebraic non-commutative geometry and ties to quantum physics and topology, the rational homotopy type of the group of unitary elements in an Azumaya algebra, and functoriality properties in the theory of $C^*$-crossed products and fixed point algebras for proper actions. An introduction, written by Jonathan Rosenberg, provides an instructive overview describing common themes and how the various papers in the volume are interrelated and fit together. The rich diversity of papers appearing in the volume demonstrates the current interplay between superstring theory, geometry/topology, and non-commutative geometry. The book will be of interest to graduate students, mathematicians, mathematical physicists, and researchers working in these areas.