This eighteenth volume in the Poincare Seminar Series provides a thorough description of Information Theory and some of its most active areas, in particular, its relation to thermodynamics at the nanoscale and the Maxwell Demon, and the emergence of quantum computation and of its counterpart, quantum verification. It also includes two introductory tutorials, one on the fundamental relation between thermodynamics and information theory, and a primer on Shannon's entropy and information theory. The book offers a unique and manifold perspective on recent mathematical and physical developments in this field.

This volume provides a detailed description of some of the most active areas in astrophysics from the largest scales probed by the Planck satellite to massive black holes that lie at the heart of galaxies and up to the much awaited but stunning discovery of thousands of exoplanets. It contains the following chapters: * Jean-Philippe UZAN, The Big-Bang Theory: Construction, Evolution and Status * Jean-Loup PUGET, The Planck Mission and the Cosmic Microwave Background * Reinhard GENZEL, Massive Black Holes: Evidence, Demographics and Cosmic Evolution * Arnaud CASSAN, New Worlds Ahead: The Discovery of Exoplanets Reinhard Genzel and Andrea Ghez shared the 2020 Nobel Prize in Physics "for the discovery of a supermassive compact object at the centre of our galaxy'", alongside Roger Penrose "for the discovery that black hole formation is a robust prediction of the general theory of relativity". The book corresponds to the twentieth Poincare Seminar, held on November 21, 2015, at Institut Henri Poincare in Paris. Originally written as lectures to a broad scientific audience, these four chapters are of high value and will be of general interest to astrophysicists, physicists, mathematicians and historians.

This eighteenth volume in the Poincare Seminar Series provides a thorough description of Information Theory and some of its most active areas, in particular, its relation to thermodynamics at the nanoscale and the Maxwell Demon, and the emergence of quantum computation and of its counterpart, quantum verification. It also includes two introductory tutorials, one on the fundamental relation between thermodynamics and information theory, and a primer on Shannon's entropy and information theory. The book offers a unique and manifold perspective on recent mathematical and physical developments in this field.

This volume provides a detailed description of some of the most active areas in astrophysics from the largest scales probed by the Planck satellite to massive black holes that lie at the heart of galaxies and up to the much awaited but stunning discovery of thousands of exoplanets. It contains the following chapters: * Jean-Philippe UZAN, The Big-Bang Theory: Construction, Evolution and Status * Jean-Loup PUGET, The Planck Mission and the Cosmic Microwave Background * Reinhard GENZEL, Massive Black Holes: Evidence, Demographics and Cosmic Evolution * Arnaud CASSAN, New Worlds Ahead: The Discovery of Exoplanets Reinhard Genzel and Andrea Ghez shared the 2020 Nobel Prize in Physics "for the discovery of a supermassive compact object at the centre of our galaxy'", alongside Roger Penrose "for the discovery that black hole formation is a robust prediction of the general theory of relativity". The book corresponds to the twentieth Poincare Seminar, held on November 21, 2015, at Institut Henri Poincare in Paris. Originally written as lectures to a broad scientific audience, these four chapters are of high value and will be of general interest to astrophysicists, physicists, mathematicians and historians.

This fifteenth volume of the Poincare Seminar Series, Dirac Matter, describes the surprising resurgence, as a low-energy effective theory of conducting electrons in many condensed matter systems, including graphene and topological insulators, of the famous equation originally invented by P.A.M. Dirac for relativistic quantum mechanics. In five highly pedagogical articles, as befits their origin in lectures to a broad scientific audience, this book explains why Dirac matters. Highlights include the detailed "Graphene and Relativistic Quantum Physics", written by the experimental pioneer, Philip Kim, and devoted to graphene, a form of carbon crystallized in a two-dimensional hexagonal lattice, from its discovery in 2004-2005 by the future Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum Hall effect; the review entitled "Dirac Fermions in Condensed Matter and Beyond", written by two prominent theoreticians, Mark Goerbig and Gilles Montambaux, who consider many other materials than graphene, collectively known as "Dirac matter", and offer a thorough description of the merging transition of Dirac cones that occurs in the energy spectrum, in various experiments involving stretching of the microscopic hexagonal lattice; the third contribution, entitled "Quantum Transport in Graphene: Impurity Scattering as a Probe of the Dirac Spectrum", given by Helene Bouchiat, a leading experimentalist in mesoscopic physics, with Sophie Gueron and Chuan Li, shows how measuring electrical transport, in particular magneto-transport in real graphene devices - contaminated by impurities and hence exhibiting a diffusive regime - allows one to deeply probe the Dirac nature of electrons. The last two contributions focus on topological insulators; in the authoritative "Experimental Signatures of Topological Insulators", Laurent Levy reviews recent experimental progress in the physics of mercury-telluride samples under strain, which demonstrates that the surface of a three-dimensional topological insulator hosts a two-dimensional massless Dirac metal; the illuminating final contribution by David Carpentier, entitled "Topology of Bands in Solids: From Insulators to Dirac Matter", provides a geometric description of Bloch wave functions in terms of Berry phases and parallel transport, and of their topological classification in terms of invariants such as Chern numbers, and ends with a perspective on three-dimensional semi-metals as described by the Weyl equation. This book will be of broad general interest to physicists, mathematicians, and historians of science.

This volume provides a detailed description of the seminal theoretical construction in 1964, independently by Robert Brout and Francois Englert, and by Peter W. Higgs, of a mechanism for short-range fundamental interactions, now called the Brout-Englert-Higgs (BEH) mechanism. It accounts for the non-zero mass of elementary particles and predicts the existence of a new particle - an elementary massive scalar boson. In addition to this the book describes the experimental discovery of this fundamental missing element in the Standard Model of particle physics. The H Boson, also called the Higgs Boson, was produced and detected in the Large Hadron Collider (LHC) of CERN near Geneva by two large experimental collaborations, ATLAS and CMS, which announced its discovery on the 4th of July 2012.This new volume of the Poincare Seminar Series, The H Boson, corresponds to the nineteenth seminar, held on November 29, 2014, at Institut Henri Poincare in Paris.

This volume provides a detailed description of the seminal theoretical construction in 1964, independently by Robert Brout and Francois Englert, and by Peter W. Higgs, of a mechanism for short-range fundamental interactions, now called the Brout-Englert-Higgs (BEH) mechanism. It accounts for the non-zero mass of elementary particles and predicts the existence of a new particle - an elementary massive scalar boson. In addition to this the book describes the experimental discovery of this fundamental missing element in the Standard Model of particle physics. The H Boson, also called the Higgs Boson, was produced and detected in the Large Hadron Collider (LHC) of CERN near Geneva by two large experimental collaborations, ATLAS and CMS, which announced its discovery on the 4th of July 2012.This new volume of the Poincare Seminar Series, The H Boson, corresponds to the nineteenth seminar, held on November 29, 2014, at Institut Henri Poincare in Paris.

This fifteenth volume of the Poincare Seminar Series, Dirac Matter, describes the surprising resurgence, as a low-energy effective theory of conducting electrons in many condensed matter systems, including graphene and topological insulators, of the famous equation originally invented by P.A.M. Dirac for relativistic quantum mechanics. In five highly pedagogical articles, as befits their origin in lectures to a broad scientific audience, this book explains why Dirac matters. Highlights include the detailed "Graphene and Relativistic Quantum Physics", written by the experimental pioneer, Philip Kim, and devoted to graphene, a form of carbon crystallized in a two-dimensional hexagonal lattice, from its discovery in 2004-2005 by the future Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum Hall effect; the review entitled "Dirac Fermions in Condensed Matter and Beyond", written by two prominent theoreticians, Mark Goerbig and Gilles Montambaux, who consider many other materials than graphene, collectively known as "Dirac matter", and offer a thorough description of the merging transition of Dirac cones that occurs in the energy spectrum, in various experiments involving stretching of the microscopic hexagonal lattice; the third contribution, entitled "Quantum Transport in Graphene: Impurity Scattering as a Probe of the Dirac Spectrum", given by Helene Bouchiat, a leading experimentalist in mesoscopic physics, with Sophie Gueron and Chuan Li, shows how measuring electrical transport, in particular magneto-transport in real graphene devices - contaminated by impurities and hence exhibiting a diffusive regime - allows one to deeply probe the Dirac nature of electrons. The last two contributions focus on topological insulators; in the authoritative "Experimental Signatures of Topological Insulators", Laurent Levy reviews recent experimental progress in the physics of mercury-telluride samples under strain, which demonstrates that the surface of a three-dimensional topological insulator hosts a two-dimensional massless Dirac metal; the illuminating final contribution by David Carpentier, entitled "Topology of Bands in Solids: From Insulators to Dirac Matter", provides a geometric description of Bloch wave functions in terms of Berry phases and parallel transport, and of their topological classification in terms of invariants such as Chern numbers, and ends with a perspective on three-dimensional semi-metals as described by the Weyl equation. This book will be of broad general interest to physicists, mathematicians, and historians of science.

This thirteenth volume of the Poincare Seminar Series, Henri Poincare, 1912-2012, is published on the occasion of the centennial of the death of Henri Poincare in 1912. It presents a scholarly approach to Poincare's genius and creativity in mathematical physics and mathematics. Its five articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include "Poincare's Light" by Olivier Darrigol, a leading historian of science, who uses light as a guiding thread through much of Poincare 's physics and philosophy, from the application of his superior mathematical skills and the theory of diffraction to his subsequent reflections on the foundations of electromagnetism and the electrodynamics of moving bodies; the authoritative "Poincare and the Three-Body Problem" by Alain Chenciner, who offers an exquisitely detailed, hundred-page perspective, peppered with vivid excerpts from citations, on the monumental work of Poincare on this subject, from the famous (King Oscar's) 1889 memoir to the foundations of the modern theory of chaos in "Les methodes nouvelles de la mecanique celeste." A profoundly original and scholarly presentation of the work by Poincare on probability theory is given by Laurent Mazliak in "Poincare's Odds," from the incidental first appearance of the word "probability" in Poincare's famous 1890 theorem of recurrence for dynamical systems, to his later acceptance of the unavoidability of probability calculus in Science, as developed to a great extent by Emile Borel, Poincare's main direct disciple; the article by Francois Beguin, "Henri Poincare and the Uniformization of Riemann Surfaces," takes us on a fascinating journey through the six successive versions in twenty-six years of the celebrated uniformization theorem, which exemplifies the Master's distinctive signature in the foundational fusion of mathematics and physics, on which conformal field theory, string theory and quantum gravity so much depend nowadays; the final chapter, "Harmony and Chaos, On the Figure of Henri Poincare" by the filmmaker Philippe Worms, describes the homonymous poetical film in which eminent scientists, through mathematical scenes and physical experiments, display their emotional relationship to the often elusive scientific truth and universal "harmony and chaos" in Poincare's legacy. This book will be of broad general interest to physicists, mathematicians, philosophers of science and historians.

This tenth volume in the Poincare Seminar Series describes recent developments at one of the most challenging frontiers in statistical physics - the deeply related fields of glassy dynamics, especially near the glass transition, and of the statics and dynamics of granular systems. These fields are marked by a vigorous interchange between experiment, theory, and numerical studies, all of which are well represented by the leading experts who have contributed articles to this volume. These articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a Galilean dialogue on the mean field and competing theories of the glass transition, a wide-ranging survey of colloidal glasses, and experimental as well as theoretical treatments of the relatively new field of dense granular flows. This book should be of broad general interest to both physicists and mathematicians.

Addressing graduate students and researchers in physics and mathematics, this book fills a gap in the literature. It is an introduction into modern constructive physics, field theory and statistical mechanics and a survey on the most recent research in this field. It presents the main technical tools such as cluster expansion and their implementation in the rigorous renormalization group, and studies physical models in some detail. The reader will find a study of the ultraviolet limit of the Gross-Neveu model, of continuous symmetry breaking and of self-avoiding random walks in statistical mechanics, as well as applications to solid-state physics. Mathematicians will find constructive methods useful for studies in partial differential equations.

This new volume in the Poincare Seminar Series, describing recent developments at the interface between physics and biology, is directed towards a broad audience of physicists, biologists, and mathematicians. Both the theoretical and experimental aspects are covered, and particular care is devoted to the pedagogical nature of the presentations. The first survey article, by Jean-Francois Joanny and Jacques Prost, describes the theoretical advances made in the study of "active gels," with applications to liquid crystals and cell motility. Jasper van der Gucht and Cecile Sykes then report on recent advances made with biomimetic model systems in the understanding of cytokinesis. The next article, by Jonathon Howard, presents several molecular models for motor proteins, which are compared with experimental results for kinesin. David Lacoste and Kirone Mallick then show theoretically that similar ratchet models of motor proteins naturally satisfy a fundamental time-reversal symmetry, the Gallavotti-Cohen fluctuation relation. Jean-Francois Allemand, David Bensimon and Vincent Croquette and their coauthors describe the latest advances made in the real-time single molecule study of the enzymes involved in DNA replication. Raymond E. Goldstein addresses the problem of understanding, from a physics perspective, the driving forces behind the biological evolution of multicellularity, using Volvocine algae as model organisms. Stanislas Dehaene finally addresses the major challenge of understanding the neuronal mechanism of consciousness, and speculates on the possible theoretical explanations of MRI experiments.

The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.

This tenth volume in the Poincare Seminar Series describes recent developments at one of the most challenging frontiers in statistical physics - the deeply related fields of glassy dynamics, especially near the glass transition, and of the statics and dynamics of granular systems. These fields are marked by a vigorous interchange between experiment, theory, and numerical studies, all of which are well represented by the leading experts who have contributed articles to this volume. These articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a Galilean dialogue on the mean field and competing theories of the glass transition, a wide-ranging survey of colloidal glasses, and experimental as well as theoretical treatments of the relatively new field of dense granular flows. This book should be of broad general interest to both physicists and mathematicians.

This new volume in the Poincare Seminar Series, describing recent developments at the interface between physics and biology, is directed towards a broad audience of physicists, biologists, and mathematicians. Both the theoretical and experimental aspects are covered, and particular care is devoted to the pedagogical nature of the presentations. The first survey article, by Jean-Francois Joanny and Jacques Prost, describes the theoretical advances made in the study of "active gels," with applications to liquid crystals and cell motility. Jasper van der Gucht and Cecile Sykes then report on recent advances made with biomimetic model systems in the understanding of cytokinesis. The next article, by Jonathon Howard, presents several molecular models for motor proteins, which are compared with experimental results for kinesin. David Lacoste and Kirone Mallick then show theoretically that similar ratchet models of motor proteins naturally satisfy a fundamental time-reversal symmetry, the Gallavotti-Cohen fluctuation relation. Jean-Francois Allemand, David Bensimon and Vincent Croquette and their coauthors describe the latest advances made in the real-time single molecule study of the enzymes involved in DNA replication. Raymond E. Goldstein addresses the problem of understanding, from a physics perspective, the driving forces behind the biological evolution of multicellularity, using Volvocine algae as model organisms. Stanislas Dehaene finally addresses the major challenge of understanding the neuronal mechanism of consciousness, and speculates on the possible theoretical explanations of MRI experiments.

This book is the eighth in a series of Proceedings for the S eminaire Poincar e, which is directed towards a large audience of physicists and of mathematicians. The goal of this seminar is to provide up to date information about general topics of great interest in physics. Both the theoretical and experimental aspects are covered, with some historical background. Inspired by the Bourbaki seminar in mathematics in its organization, hence nicknamed "Bourbaphy", this Poincar e SeminarisheldattheInstitutHenriPoincar einParis,withcontributionsprepared inadvance.Particularcareisdevotedtothepedagogicalnatureofthepresentation so as to ful?ll the goal of being readable by a large audience of scientists. This new volume of the Poincar e Seminar series "The Spin" corresponds to the eleventh such Seminar, held on December 8, 2007. It describes how this once mysterious quantum reality called spin has become ubiquitous in modern physics from the most theoretical aspects down to the most practical applications of miniaturizing electronic and computer devices or helping medical diagnosis.

This book confirms noncommutative geometry as an increasingly useful tool for the description of intricate condensed matter phenomena. It describes the striking progress recently made in gathering all the interactions and fields of the standard model into a non-commutative geometry on a simple internal space. Coverage also details the very recent technique of renormalization of quantum field theories on non-commutative space-time.

This book offers a detailed, pedagogical introduction to general relativity. It includes a review of what may lie beyond and collects up-to-date essays on the experimental tests of this theory, including the precise timing of the double pulsar J0737-3039. Coverage also details the recent results of the Gravity Probe B mission.

This volume is devoted to Quantum Decoherence with lectures from the Seminaire Poincare, held in November 2005 at the Institute Henri Poincare Paris. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental results are covered, with some historical background. Particular care is devoted to the pedagogical nature of the presentation.

This book is the fourth in a series of lectures of the S eminaire Poincar e, whichis directed towards a large audience of physicists and of mathematicians. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental aspects are covered, with some historical background. Inspired by the Bourbaki seminar in mathematics in its organization, hence nicknamed "Bourbaphi," the Poincar e Seminar is held twice a year at the Institut Henri Poincar e in Paris, with cont- butions prepared in advance. Particular care is devoted to the pedagogical nature of the presentations so as to ful?ll the goal of being readable by a large audience of scientists. This volume contains the seventh such Seminar, held in 2005. It is devoted to Einstein's 1905 papers and their legacy. After a presentation of Einstein's ep- temological approach to physics, and the genesis of special relativity, a cen- nary perspective is o?ered. The geometry of relativistic spacetime is explained in detail. Single photon experiments are presented, as a spectacular realization of Einstein's light quanta hypothesis. A previously unpublished lecture by Einstein, which presents an illuminating point of view on statistical physics in 1910, at the dawn of quantum mechanics, is reproduced. The volume ends with an essay on the historical, physical and mathematical aspects of Brownian motion. We hopethatthe publicationofthis serieswill servethe community ofphy- cists and mathematicians at the graduate student or professional level."

This book is the third in a series of lectures of the S' eminaire Poincar' e,whichis directed towards a large audience of physicists and of mathematicians. The goal of this seminar is to provide up to date information about general topics of great interest in physics. Both the theoretical and experimental aspects are covered, with some historical background. Inspired by the Bourbaki seminar in mathematics in its organization, hence nicknamed "Bourbaphi", this Poincar' e Seminar is held twice a year at the Institut Henri Poincar' ein Paris,with contri- tions prepared in advance. A particular care is devoted to the pedagogical nature of the presentation so as to ful?ll the goal of being readable by a large audience of scientists. ThisvolumecontainsthesixthsuchSeminar,heldin2004.Itisdevotedtothe Quantum Hall E?ect. After a historical and general presentation by Nobel prize Klaus von Klitzing, discoverer of this e?ect, the volume proceeds with reviews on the mathematics and physics of both the integer and fractional case, and includes up to date presentations of the tunneling and metrology experiments related to the Quantum Hall E?ect. We hopethat the publicationof this serieswill servethe community of phy- cists and mathematicians at professional or graduate student level. ' We thank the Commissariat 'al'Energie Atomique (Division des Sciences de laMati' ere),theCentreNationaldelaRechercheScienti?que(SciencesPhysiqueet Math' ematiques), and the Daniel Iagolnitzer Foundation for sponsoring the Se- nar. Special thanks are due to Chantal Delongeas for the preparation of the m- uscript.

This volume contains the third and fourth Poincare Seminar, both held in 2003. The third one is devoted to Bose-Einstein Condensation: it covers the physics of superfluid liquid helium as well as the recently discovered atomic Bose-Einstein condensates. Major experimental results are presented, together with relevant theoretical approaches and remaining open questions. The fourth one is devoted to Entropy, giving a comprehensive account of the history and various realizations of this concept, from thermodynamics to black holes, and includes theoretical and experimental discussions of the corresponding fluctuations for mesoscopic systems near equilibrium."

This volume contains the third and fourth Poincare Seminar, both held in 2003. The third one is devoted to Bose-Einstein Condensation: it covers the physics of superfluid liquid helium as well as the recently discovered atomic Bose-Einstein condensates. Major experimental results are presented, together with relevant theoretical approaches and remaining open questions. The fourth one is devoted to Entropy, giving a comprehensive account of the history and various realizations of this concept, from thermodynamics to black holes, and includes theoretical and experimental discussions of the corresponding fluctuations for mesoscopic systems near equilibrium."

The Poincare Seminar is held twice a year at the Institut Henri Poincare in Paris. This volume contains the lectures of the 2002 seminars. The main topic of the first one was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The second one concentrated on renormalization, giving a comprehensive account of its mathematical structure and applications to high energy physics, statistical mechanics and classical mechanics.
Students will find excellent introductions to the subjects with further lectures leading to the frontiers of experimental and theoretical research, scientists will profit from contributions by outstanding experts."

The Poincare Seminar is held twice a year at the Institut Henri Poincare in Paris. This volume contains the lectures of the 2002 seminars. The main topic of the first one was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The second one concentrated on renormalization, giving a comprehensive account of its mathematical structure and applications to high energy physics, statistical mechanics and classical mechanics.
Students will find excellent introductions to the subjects with further lectures leading to the frontiers of experimental and theoretical research, scientists will profit from contributions by outstanding experts."