Courant Lecture Notes, Volume: 25
2014; 145 pp; softcover
ISBN-13: 978-1-4704-1711-6
Expected publication date is December 31, 2014.
This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on conservation laws. Particularly striking features of the book include: (a) a mathematically rigorous derivation of the interaction of electromagnetic waves with matter, (b) a straightforward explanation of how to use variational principles to solve problems in electro- and magnetostatics, and (c) a thorough discussion of the central importance of the conservation of charge. It is suitable for advanced undergraduate students in mathematics and physics with a background in advanced calculus and linear algebra, as well as mechanics and electromagnetics at an undergraduate level. Apart from minor corrections to the text, the notation was updated in this edition to follow the conventions of modern vector calculus.
Undergraduate students, graduate students, and research mathematicians interested in electromagnetics.
Preliminaries
Electrostatics
Currents and Ohm's law
Magnetostatics
Electromagnetic fields changing in time
Transmission lines. Method of the Laplace transformation
Electromagnetodynamics of moving bodies and the principle of relativity
Electromagnetic wave propagation
The scattering problem
References
Student Mathematical Library, Volume: 73
2014; 384 pp; softcover
ISBN-13: 978-0-8218-9867-3
Expected publication date is December 22, 2014.
Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems.
For this new edition, several sections have been added and others have been significantly updated. Among the newly introduced topics are: rainbow Ramsey theory, an "inequality" version of Schur's theorem, monochromatic solutions of recurrence relations, Ramsey results involving both sums and products, monochromatic sets avoiding certain differences, Ramsey properties for polynomial progressions, generalizations of the Erd?s-Ginzberg-Ziv theorem, and the number of arithmetic progressions under arbitrary colorings. Many new results and proofs have been added, most of which were not known when the first edition was published. Furthermore, the book's tables, exercises, lists of open research problems, and bibliography have all been significantly updated.
This innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subject. This breakthrough book will engage students, teachers, and researchers alike.
Undergraduate and graduate students interested in combinatorics, number theory, and Ramsey theory.
Preliminaries
Van der Waerden's theorem
Supersets of AP
Subsets of AP
Other generalizations of w(k;r)
Arithmetic progressions (modm)
Other variations on van der Waerden's theorem
Schur's theorem
Rado's theorem
Other topics
Notation
Bibliography
Index
Mathematical Surveys and Monographs, Volume: 199
2014; 183 pp; hardcover
ISBN-13: 978-1-4704-1697-3
Expected publication date is December 15, 2014.
In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions.
Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, quantum control.
Graduate students interested in noncommutative analysis.
Mathematical Surveys and Monographs, Volume: 201
2014; 315 pp; hardcover
ISBN-13: 978-1-4704-1884-7
Expected publication date is December 29, 2014.
The theory of topological modular forms (tmf) is a new area of mathematics originated in the early 2000s. It ties together several previously unrelated mathematical disciplines, such as the theory of algebraic modular forms, formal groups, multiplicative homotopy theory, stacks, Quillen cohomology, and others. In 2003, Michael Hopkins taught a course at MIT about this new theory, and the editors of this book were among the listeners. Their attempts to understand the course material lasted several years and culminated in the so-called 2007 Talbot Workshop. The first draft of this book was produced based on talks at this workshop.
The book consists of 12 chapters, each devoted to a particular aspect of the theory of topological modular forms. There are also three sets of previously unpublished notes from Hopkins痴 lectures, retyped and edited for this book. Finally, the book includes a chapter on the history of tmf, glossary, and literature guide.
Graduate students and research mathematicians interested in algebraic topology and algebraic geometry.
C. Redden -- Elliptic genera and elliptic cohomology
C. Mautner -- Ellliptic curves and modular forms
A. Henriques -- The moduli stack of elliptic curves
H. Hohnhold -- The Landweber exact functor theorem
C. L. Douglas -- Sheaves in homotopy theory
T. Bauer -- Bousfield localization and the Hasse square
J. Lurie -- The local structure of the moduli stack of formal groups
V. Angeltveit -- Goerss-Hopkins obstruction theory
M. Hopkins -- From spectra to stacks
M. Hopkins -- The string orientation
M. Hopkins -- The sheaf of E∞ ring spectra
M. Behrens -- The construction of tmf
A. Henriques -- The homotopy groups of tmf and of its localizations
M. J. Hopkins and H. R. Miller -- Ellitpic curves and stable homotopy I
M. Hopkins and M. Mahowald -- From elliptic curves to homotopy theory
M. J. Hopkins -- K(1)-local E∞ ring spectra
C. L. Douglas, J. Francis, A. G. Henriques, and M. A. Hill -- Glossary
IAS/Park City Mathematics Series, Volume: 21
2014; 405 pp; hardcover
ISBN-13: 978-1-4704-1227-2
Expected publication date is January 9, 2015.
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution.
The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups.
This book is a valuable resource for graduate students and researchers interested in geometric group theory.
Graduate students and research mathematicians interested in geometric group theory.
M. Sageev -- CAT(0) cube complexes and groups
V. Guirardel -- Geometric small cancellation
P.-E. Caprace -- Lectures on proper CAT(0) spaces and their isometry groups
M. Kapovich -- Lectures on quasi-isometric rigidity
M. Bestvina -- Geometry of outer space
D. W. Morris -- Some arithmetic groups that do not act on the circle
T. Gelander -- Lectures on lattices and locally symmetric spaces
A. Wilkinson -- Lectures on marked length spectrum rigidity
E. Breuillard -- Expander graphs, property (τ) and approximate groups
M. R. Bridson -- Cube complexes, subgroups of mapping class groups, and nilpotent genus
Proceedings of Symposia in Pure Mathematics, Volume: 88
2014; 370 pp; hardcover
ISBN-13: 978-1-4704-1051-3
Expected publication date is January 9, 2015.
This volume contains the proceedings of the conference `String-Math 2013' which was held June 17-21, 2013 at the Simons Center for Geometry and Physics at Stony Brook University. This was the third in a series of annual meetings devoted to the interface of mathematics and string theory.
Topics include the latest developments in supersymmetric and topological field theory, localization techniques, the mathematics of quantum field theory, superstring compactification and duality, scattering amplitudes and their relation to Hodge theory, mirror symmetry and two-dimensional conformal field theory, and many more.
This book will be important reading for researchers and students in the area, and for all mathematicians and string theorists who want to update themselves on developments in the math-string interface.
Graduate students and research mathematicians interested in mathematical aspects of quantum field theory, in particular string theory.
Plenary talks
K. Costello -- Integrable lattice models from four-dimensional field theories
D. S. Freed -- Anomalies and invertible field theories
L. Katzarkov and Y. Liu -- Categorical base loci and spectral gaps, via Okounkov bodies and Nevanlinna theory
B. Pioline -- Rankin-Selberg methods for closed string amplitudes
S. Schafer-Nameki -- Singular fibers and Coulomb phases
P. Vanhove -- The physics and the mixed Hodge structure of Feynman integrals
Contributed talks
M. Alim -- Polynomial rings and topological strings
L. B. Anderson -- Exploring novel geometry in heterotic/F-theory dual pairs
M. Bertolini, I. V. Melnikov, and M. R. Plesser -- Massless spectrum for hybrid CFTs
I. Brunner, N. Carqueville, and D. Plencner -- A quick guide to defect orbifolds
C. Daenzer -- Geometric t-dualization
A. Dey -- Mirror symmetry in flavored affine D-type quivers
T. Dimofte -- Duality domain walls in class S[A1]
J. Gray, A. Haupt, and A. Lukas -- Calabi-Yau fourfolds in products of projective space
T. Johnson-Freyd -- Poisson AKSZ theories and their quantizations
C. A. Keller -- Modularity, Calabi-Yau geometry and 2d CFTs
P. Koroteev -- Three dimensional mirror symmetry and integrability
A. Lai -- Strict deformation quantisation of the G-connections via Lie groupoid
T. Okazaki and S. Yamaguchi -- Supersymmetric boundary conditions in 3d N=2 theories
C. Papageorgakis and A. B. Royston -- Instanton-soliton loops in 5D super-Yang-Mills
C. Y. Park -- 2d SCFT from M-branes and its spectral network