A publication of the Societe Mathematique de France
AstAcrisque Volume: 425
2021; 208 pp; Softcover
MSC: Primary 14; 19;
Print ISBN: 978-2-85629-939-5
If f:S′→S is a finite locally free morphism of schemes, the authors construct a symmetric monoidal “norm” functor f?:H?(S′)→H?(S), where H?(S) is the pointed unstable motivic homotopy category over S. If f is finite etale, the authors show that it stabilizes to a functor f?:SH(S′)→SH(S), where SH(S) is the P1-stable motivic homotopy category over S.
Using these norm functors, the authors define the notion of a normed motivic spectrum, which is an enhancement of a motivic E∞-ring spectrum. The main content of this text is a detailed study of the norm functors and of normed motivic spectra, and the construction of examples. In particular: the authors investigate the interaction of norms with Grothendieck's Galois theory, with Betti realization, and with Voevodsky's slice filtration; they prove that the norm functors categorify Rost's multiplicative transfers on Grothendieck-Witt rings; and they construct normed spectrum structures on the motivic cohomology spectrumHZ, the homotopy K-theory spectrum KGL, and the algebraic cobordism spectrum MGL. The normed spectrum structure on HZ is a common refinement of Fulton and MacPherson's mutliplicative transfers on Chow groups and of Voevodsky's power operations in motivic cohomology.
Simplifies the approach to birational properties of connections, based on a
formal analysis of singularities at infinity
Features a discussion on the stability of properties of connections based on
higher direct images under a smooth morphism, only using basic tools of coherent cohomology
Presents a unified approach to GAGA-type theorems in De Rham cohomology
covering both complex and $p$-adic analytifications
This is the revised second edition of the well-received book by the first two authors. It offers a
systematic treatment of the theory of vector bundles with integrable connection on smooth
algebraic varieties over a field of characteristic 0. Special attention is paid to singularities along
divisors at infinity, and to the corresponding distinction between regular and irregular
singularities. The topic is first discussed in detail in dimension 1, with a wealth of examples,
and then in higher dimension using the method of restriction to transversal curves. The
authors develop a new approach to classical algebraic/analytic comparison theorems in De
Rham cohomology, and provide a unified discussion of the complex and the p-adic situations
while avoiding the resolution of singularities. They conclude with a proof of a conjecture by
Baldassarri to the effect that algebraic and p-adic analytic De Rham cohomologies coincide,
under an arithmetic condition on exponents. As used in this text, the term “De Rham
cohomology” refers to the hypercohomology of the De Rham complex of a connection with
respect to a smooth morphism of algebraic varieties, equipped with the Gauss-Manin
connection. This simplified approach suffices to establish the stability of crucial properties of
connections based on higher direct images.
2nd ed. 2020, XIV, 241 p.
Hardcover
ISBN 978-3-030-39718-0
Product category : Monograph
Series : Progress in Mathematics
Mathematics : Algebraic Geometry
Addresses several important classes of nonlinear PDEs
Adapts as a textbook for advanced graduate courses in dissipative dynamics
Appeals to both mathematicians interested in synchronization theory as well
as physicists and engineers interested in mathematical background and
methods for the asymptotic analysis of infinite-dimensional dissipative
systems
Uniquely presents synchronization theory in the infinite-dimensional case at
the monograph level
Remains accessible to advanced students and scientific professionals without
deep knowledge of Sobolev theory and functional spaces
The main goal of this book is to systematically address the mathematical methods that are
applied in the study of synchronization of infinite-dimensional evolutionary dissipative or
partially dissipative systems. It bases its unique monograph presentation on both general and
abstract models and covers several important classes of coupled nonlinear deterministic and
stochastic PDEs which generate infinite-dimensional dissipative systems. This text, which adapts
readily to advanced graduate coursework in dissipative dynamics, requires some background
knowledge in evolutionary equations and introductory functional analysis as well as a basic
understanding of PDEs and the theory of random processes. Suitable for researchers in
synchronization theory, the book is also relevant to physicists and engineers interested in both
the mathematical background and the methods for the asymptotic analysis of coupled
infinitedimensional dissipative systems that arise in continuum mechanics
1st ed. 2020, XIX, 329 p.
Hardcover
ISBN 978-3-030-47090-6
Product category : Monograph
Series : Applied Mathematical Sciences
Mathematics : Dynamical Systems and Ergodic Theory
Provides an accessible introduction to basic results and notions of unbounded
representation theory
Contains an extensive study of representations of the Weyl algebra and the
commutation relation of quantum mechanics
Treats many topics in unbounded representation theory in book form for the
first time
This textbook provides an introduction to representations of general -algebras by unbounded
operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far
only been properly treated in advanced monographs aimed at researchers. The book covers
both the general theory of unbounded representation theory on Hilbert space as well as
representations of important special classes of -algebra, such as the Weyl algebra and
enveloping algebras associated to unitary representations of Lie groups. A broad scope of
topics are treated in book form for the first time, including group graded -algebras, the
transition probability of states, Archimedean quadratic modules, noncommutative
Positivstellensatze, induced representations, well-behaved representations and representations
on rigged modules. Making advanced material accessible to graduate students, this book will
appeal to students and researchers interested in advanced functional analysis and
mathematical physics, and with many exercises it can be used for courses on the
representation theory of Lie groups and its application to quantum physics. A rich selection of
material and bibliographic notes also make it a valuable reference.
1st ed. 2020, XVIII, 381 p.
Hardcover
ISBN 978-3-030-46365-6
Product category : Graduate/advanced undergraduate textbook
Series : Graduate Texts in Mathematics
Mathematics : Operator Theory
First systematic and comprehensive introductory book on inverse problems
for differential equations
Self-contained and accessible also to beginning graduate students
Can be used as a backbone for a lecture on inverse and ill-posed problems for
partial differential equations
This book presents a systematic exposition of the main ideas and methods in treating inverse
problems for PDEs arising in basic mathematical models, though it makes no claim to being
exhaustive. Mathematical models of most physical phenomena are governed by initial and
boundary value problems for PDEs, and inverse problems governed by these equations arise
naturally in nearly all branches of science and engineering. The book’s content, especially in
the Introduction and Part I, is self-contained and is intended to also be accessible for
beginning graduate students, whose mathematical background includes only basic courses in
advanced calculus, PDEs and functional analysis. Further, the book can be used as the
backbone for a lecture course on inverse and ill-posed problems for partial differential
equations. In turn, the second part of the book consists of six nearly-independent chapters.
The choice of these chapters was motivated by the fact that the inverse coefficient and source
problems considered here are based on the basic and commonly used mathematical models
governed by PDEs. These chapters describe not only these inverse problems, but also main
inversion methods and techniques. Since the most distinctive features of any inverse problems
related to PDEs are hidden in the properties of the corresponding solutions to direct problems,
special attention is paid to the investigation of these properties. For the second edition, the
authors have added two new chapters focusing on real-world applications of inverse problems
arising in wave and vibration phenomena.They have also revised the whole text of the first
edition.
2nd ed. 2021, XVII, 515 p. 28 illus., 5 illus. in color.
Hardcover
ISBN 978-3-030-79426-2
Product category : Monograph
Mathematics : Partial Differential Equations
Uses a wide diversity of methods reflecting the Rademacher system in various
areas of mathematics
Includes Appendices explaining the prerequisites needed
Collects material available only scattered through journal articles so far
This book presents a systematic treatment of the Rademacher system, one of the most
important unifying concepts in mathematics, and includes a number of recent important and
beautiful results related to the Rademacher functions. The book discusses the relationship
between the properties of the Rademacher system and geometry of some function spaces. It
consists of three parts, in which thissystem is considered respectively in Lp-spaces, in general
symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey).
The presentation is clear and transparent, providing all main results with detailed proofs.
Moreover, literary and historical comments are given at the end of each chapter. This book will
be suitable for graduate students and researchers interested in functional analysis, theory of
functions and geometry of Banach spaces.
1st ed. 2020, XX, 559 p. 2 illus., 1 illus. in color.
Hardcover
ISBN 978-3-030-47889-6
Product category : Monograph
Mathematics : Functional Analysis
Provides the first systematic account of the theory of zero product
determined algebras
Presents applications to various problems in algebra and functional analysis
Discusses a wide variety of mathematical topics in an accessible manner
This book provides a concise survey of the theory of zero product-determined algebras, which
has been developed over the last 15 years. It is divided into three parts. The first part presents
the purely algebraic branch of the theory, the second part presents the functional analytic
branch, and the third part discusses various applications. The book is intended for researchers
and graduate students in ring theory, Banach algebra theory, and nonassociative algebra.
Due 2021-09-24
1st ed. 2021, VIII, 185 p.
Softcover
ISBN 978-3-030-80241-7
Product category : Monograph
Series : Frontiers in Mathematics
Mathematics : Algebra
Nominated as an outstanding Ph.D. thesis by the Osaka University, Osaka,
Japan
Offer a frontier research on constructing S-matrix without infrared divergence
Provides reviews of basics of asymptotic symmetry, infrared divergence and Smatrix in QED
This book presents the better understanding of infrared structures of particle scattering
processes in quantum electrodynamics (QED) in four-dimensional spacetime. An S-matrix is the
fundamental quantity in scattering theory. However, if a theory involves massless particles, such
as QED and gravity, the conventional S-matrix has not been well defined due to the infrared
divergence, and infrared dynamics thus needs to be understood in-depth to figure out the Smatrix.
The book begins with introducing fundamental nature of the charge conservation law
associated with asymptotic symmetry, and explaining its relations to soft theorems and
memory effect. Subsequently it looks into an appropriate asymptotic state of the S-matrix
without infrared divergences. The Faddeev-Kulish dressed state is known as a candidate of
such a state, and its gauge invariant condition and its relation to the asymptotic symmetry are
discussed. It offers an important building blocks for constructing the S-matrix without infrared
divergences.
1st ed. 2021, XIII, 127 p. 5 illus., 4 illus. in color.
Hardcover
ISBN 978-981-16-3044-6
Product category : Monograph
Series : Springer Theses
Physics : Elementary Particles, Quantum Field Theory