Series:De Gruyter Proceedings in Mathematics
Hardcover ISBN 978-3-11-061818-1
Publication Date: 2019To be published: July 2019
A collection of surveys and research articles on mean curvature flow
With key contributions by leading experts in the area
Of interest to researchers and graduate students working in partial differential equations and differential geometry
With contributions by leading experts in geometric analysis, this volume is documenting the material presented in the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, on May 29 - June 1, 2018. The central topic of the 2018 lectures was mean curvature flow, and the material in this volume covers all recent developments in this vibrant area that combines partial differential equations with differential geometry.
24.0 x 17.0 cmApprox. xii, 220 pages 10 Fig. Language: EnglishType of Publication: MonographKeyword(s):
Subjects
Mathematics > Analysis
Mathematics > Differential Equations and Dynamical Systems
Mathematics > Geometry and Topology
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A publication of the Societe Mathematique de France.
ISBN: 978-2-85629-903-6
Series, Volume: Asterisque, Number 409
Bibliographic Information: Published: 15 May 2019; Copyright Year:
2019; Pages: 226; Softcover;
Subject Classification
Analysis
Number Theory
Readership: Graduate students and research mathematicians.
The authors prove a numerical form of a Jacquet-Langlands correspondence for torsion
classes on arithmetic hyperbolic 3-manifolds.
Information for our distributors: A publication of the Societe Mathematique de France,
Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other
countries should be sent to the SMF. AMS individual members receive a 10% discount and
members of the SMF receive a 30% discount from list. No other discounts apply.
A publication of the Societe Mathematique de France.
ISBN: 978-2-85629-900-5
Series, Volume: Asterisque, Number 408
Bibliographic Information: Published: 15 April 2019; Copyright Year:
2019; Pages: 212; Softcover;
Subject Classification
Algebra and Algebraic Geometry
Readership: Graduate students and research mathematicians.
In this paper, the authors study the classical and quantum equivariant cohomology
of Nakajima quiver varieties for a general quiver Q . Using a geometric R -matrix formalism,
they construct a Hopf algebra YQ , the Yangian of Q , acting on the cohomology of these varieties,
and show several results about their basic structure theory. The authors prove a formula for
quantum multiplication by divisors in terms of this Yangian action. The quantum connection
can be identified with the trigonometric Casimir connection for YQ ; equivalently, the divisor
operators correspond to certain elements of Baxter subalgebras of YQ . A key role is played by
geometric shift operators which can be identified with the quantum KZ difference connection.
In the second part, the authors give an extended example of the general theory for moduli
spaces of sheaves on C2 , framed at infinity. Here, the Yangian action is analyzed explicitly in
terms of a free field realization; the corresponding R -matrix is closely related to the reflection
operator in Liouville field theory. The authors show that divisor operators generate the quantum
ring, which is identified with the full Baxter subalgebras. As a corollary of our construction,
the authors obtain an action of the W-algebra W (gl(r )) on the equivariant cohomology
of rank r moduli spaces, which implies certain conjectures of Alday, Gaiotto, and Tachikawa.
Information for our distributors: A publication of the Societe Mathematique de France,
Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other
countries should be sent to the SMF. AMS individual members receive a 10% discount and
members of the SMF receive a 30% discount from list. No other discounts apply.
Oxford Master Series in Physics
Complete overview of the "Standard Model" of particle physics
Detailed discussion of the most important particle physics experiments
Simplified but precise treatment of the theory
Modern approach, including discussion of CP violation, neutrino mass, and the Higgs boson
Illustrative and challenging problems at the end of each chapter
The purpose of this textbook is to explain the Standard Model of particle physics to a student with an undergraduate preparation in physics. Today we can claim to have a fundamental picture of the strong and weak subnuclear forces. Through an interplay between theory and experiment, we have learned the basic equations through which these forces operate, and we have tested these equations against observations at particle accelerators. The story is beautiful and full of surprises. Using a simplified presentation that does not assume prior knowledge of quantum field theory, this book begins from basic concepts of special relativity and quantum mechanics, describes the key experiments that have clarified the structure of elementary particle interactions, introduces the crucial theoretical concepts, and builds up to the full description of elementary particle interactions as we know them today.
I Preliminaries and Tools
1: Introduction
2: Symmetries of Space-Time
3: Relativistic Wave Equations
4: The Hydrogen Atom and Positronium
5: The Quark Model
6: Detectors of Elementary Particles
7: Tools for Calculation
II The Strong Interaction
8: Electron-Positron Annihilation
9: Deep Inelastic Electron Scattering
10: The Gluon
11: Quantum Chromodynamics
12: Partons and Jets
13: QCD at Hadron Colliders
14: Chiral Symmetry
III The Weak Interaction
15: The Current-Current Model of the Weak Interaction
16: Gauge Theories with Spontaneous Symmetry Breaking
17: The W and Z Bosons
18: Quark Mixing Angles and Weak Decays
19: CP Violation
20: Neutrino Masses and Mixings
21: The Higgs Boson
22: Epilogue
The most beautiful theorem in mathematics
Introduces perhaps the most beautiful of equations in pure mathematics which connects five of the most important numbers in mathematics
Its simplicity and profundity have been compared to a Shakespearian sonnet
Discusses each of the elements of the equation in turn, explaining why they are so significant
Concludes with an analysis of the equation itself, its discovery and significance
Combines historical elements with lucid, step-by-step mathematical explanation
In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence".
What is it that makes Euler's identity, eiƒÎ + 1 = 0, so special?
In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; ƒÎ an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.
Introduction
1: 1
2: 0
3: ƒÎ
4: e
5: i
6: eiƒÎ + 1 = 0
Further Reading
Index
Oxford Graduate Texts
Logical rather than historical interpretation to allow phenomena to speak for themselves
Broad coverage, including both technological applications and foundational implications
A thorough introduction to a foundation of quantum technology and quantum information science science
Includes exercises at chapter ends
The development of quantum technologies has seen a tremendous upsurge in recent years, and the theory of Bell nonlocality has been key in making these technologies possible. Bell nonlocality is one of the most striking discoveries triggered by quantum theory. It states that in some situations, measurements of physical systems do not reveal pre-existing properties; rather, the property is created by the measurement itself. In 1964, John Bell demonstrated that the predictions of quantum theory are incompatible with the assumption that outcomes are predetermined. This phenomenon has been observed beyond any doubt in the last decades. It is an observation that is here to stay, even if quantum theory were to be replaced in the future. Besides having fundamental implications, nonlocality is so specific that it can be used to develop and certify reliable quantum devices.
This book is a logical, rather than historical, presentation of nonlocality and its applications. Part 1 opens with a survey of the meaning of Bell nonlocality and its interpretations, then delves into the mathematical formalisation of this phenomenon, and finally into its manifestations in quantum theory. Part 2 is devoted to the possibility of using the evidence of nonlocality for certification of devices for quantum technologies. Part 3 explores some of the extensions and consequences of nonlocality for the foundations of physics.
I Classical Bell Nonlocality
1: First Encounter with Bell Nonlocality
2: Formalising Bell Nonlocality
3: Bell Nonlocality in Quantum Theory
4: Review of Bipartite Bell Scenarios
5: Multipartite Bell Nonlocality
II Nonlocality as a Tool for Certification
6: The Set of Quantum Behaviors
7: Device-independent Self-Testing
8: Certifying Randomness
III Foundational Insights from Nonlocality
9: Nolocality in the No-signaling Framework
10: The Quest for Device-Independent Quantum Principles
11: Signaling and Measurement Dependence
12: Epilogue
Appendix A: History Museum
Appendix B: Experimental Platforms: A Reading Guide
Appendix C: Notions of Quantum Theory Used in This Book
Appendix D: LV Models for Single Systems
Appendix E: Basic Notions of Convex Optimisation
Appendix F: Device-Independent Certification: History and Review
Appendix G: Repository of Technicalities