Download or read book The B pseudodifferential Calculus on Galois Coverings and a Higher Atiyah Patodi Singer Index Theorem written by Eric Leichtnam and published by . This book was released on 1997 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $\Gamma \rightarrow \tilde M \rightarrow M$ be a Galois covering with boundary. In this book, the authors develop a $b$-pseudodifferential calculus on the noncompact manifold $\tilde M$. The main application is the proof of a higher Atiyah-Patodi-Singer index formula for a generalized Dirac operator $\tilde D$ on $\tilde M$, under the assumption that the group $\Gamma$ is of polynomial growth with respect to a word metric and that the $L^2$-spectrum of the boundary operator $\tilde D_0$ has a gap at zero. Results extend the work of Atiyah-Patodi-Singer, Connes-Moscovici, and Lott.
Download or read book Noncommutative Geometry and Global Analysis written by Henri Moscovici and published by American Mathematical Soc.. This book was released on 2011 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the proceedings of the conference on Noncommutative Geometric Methods in Global Analysis, held in honor of Henri Moscovici, from June 29-July 4, 2009, in Bonn, Germany. Henri Moscovici has made a number of major contributions to noncommutative geometry, global analysis, and representation theory. This volume, which includes articles by some of the leading experts in these fields, provides a panoramic view of the interactions of noncommutative geometry with a variety of areas of mathematics. It focuses on geometry, analysis and topology of manifolds and singular spaces, index theory, group representation theory, connections of noncommutative geometry with number theory and arithmetic geometry, Hopf algebras and their cyclic cohomology.
Download or read book Cyclic Cohomology and Noncommutative Geometry written by Joachim J. R. Cuntz and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry is a new field that is among the great challenges of present-day mathematics. Its methods allow one to treat noncommutative algebras - such as algebras of pseudodifferential operators, group algebras, or algebras arising from quantum field theory - on the same footing as commutative algebras, that is, as spaces. Applications range over many fields of mathematics and mathematical physics. This volume contains the proceedings of the workshop on "Cyclic Cohomology and Noncommutative Geometry" held at The Fields Institute (Waterloo, ON) in June 1995. The workshop was part of the program for the special year on operator algebras and its applications.
Download or read book Noncommutative Maslov Index and Eta Forms written by Charlotte Wahl and published by American Mathematical Soc.. This book was released on 2007 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a $C *$-algebra $\mathcal{A}$, is an element in $K_0(\mathcal{A})$. The generalized formula calculates its Chern character in the de Rham homology of certain dense subalgebras of $\mathcal{A}$. The proof is a noncommutative Atiyah-Patodi-Singer index theorem for a particular Dirac operator twisted by an $\mathcal{A}$-vector bundle. The author develops an analytic framework for this type of index problem.
Download or read book Cyclic Cohomology at 40 Achievements and Future Prospects written by A. Connes and published by American Mathematical Society. This book was released on 2023-02-23 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27–October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada. Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory. The reader will find survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc., in which cyclic homology plays the role of a unifying theme. The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.
Download or read book Featured Reviews in Mathematical Reviews 1997 1999 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on 2000-05-05 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.
Download or read book Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds written by Gerd Grubb and published by American Mathematical Soc.. This book was released on 2005 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.
Download or read book Mathematical Study of the Betaplane Model written by Isabelle Gallagher and published by . This book was released on 2006 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors are interested in a model of rotating fluids, describing the motion of the ocean in the equatorial zone. This model is known as the Saint-Venant, or shallow-water type system, to which a rotation term is added whose amplitude is linear with respect to the latitude; in particular it vanishes at the equator. After a physical introduction to the model, the authors describe the various waves involved and study in detail the resonances associated to those waves. They then exhibit the formal limit system (as the rotation becomes large), obtained as usual by filtering out the waves, and prove its wellposedness. Finally they prove three types of convergence results: a weak convergence result towards a linear, geostrophic equation, a strong convergence result of the filtered solutions towards the unique strong solution to the limit system, and a ``hybrid'' strong convergence result of the filtered solutions towards a weak solution to the limit system. In particular the authors obtain that there are no confined equatorial waves in the mean motion as the rotation becomes large.
Download or read book The Wave Diffracted by a Wedge with Mixed Boundary Conditions written by Olivier Lafitte and published by . This book was released on 2002 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies the diffraction of a wave by a curved wedge on the plane in the case where each side of the wedge is characterized by a mixed boundary condition of impedance type. This book is suitable for graduate students and researchers interested in partial differential equations, in particular in diffraction theory and its applications to problems in physics.
Download or read book Spectral Properties of Self similar Lattices and Iteration of Rational Maps written by Christophe Sabot and published by . This book was released on 2003 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the author considers discrete Laplace operators defined on lattices based on finitely ramified self-similar sets and their continuous analogs defined on the self-similar sets. He focuses on the spectral properties of these operators. The basic example is the lattice based on the Sierpinski gasket. He introduces a new renormalization map that appears to be a rational map defined on a smooth projective variety. (More precisely, this variety is isomorphic to a product of three types of Grassmannians: complex Grassmannians, Lagrangian Grassmannian, and orthogonal Grassmannians.) He relates some characteristics of the dynamics of its iterates with some characteristics of the spectrum of the operator. Specifically, he gives an explicit formula for the density of states in terms of the Green current of the map, and he relates the indeterminacy points of the map with the so-called Neumann-Dirichlet eigenvalues which lead to eigenfunctions with compact support on the unbounded lattice. Depending on the asymptotic degree of the map, he can prove drastically different spectral properties of the operators. The formalism is valid for the general class of finitely ramified self-similar sets.
Download or read book On Mapping Properties of the General Relativistic Constraints Operator in Weighted Function Spaces with Applications written by Piotr T. Chruściel and published by . This book was released on 2003 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors prove perturbation and gluing results for solutions of the general relativistic constraints with controlled boundary behavior or asymptotic behavior. This is obtained by a study of the linearized equation in weighted spaces a la Corvino-Schoen. Among other methods, this can be used to prove existence of non-trivial asymptotically simple vacuum space-times. The book is suitable for graduate students and research mathematicians interested in analysis.
Download or read book Strichartz Estimates for Schr dinger Equations with Variable Coefficients written by Luc Robbiano and published by . This book was released on 2005 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove the (local in time) Stricharz estimates (for the full range of parameters given by the scaling unless the end point) for asymptotically flat and non trapping perturbations of the flat Laplacian in $\mathbb {R} ^n$, $n\geq 2$. The main point of the proof, namely the dispersion estimate, is obtained in constructing a parametrix. The main tool for this construction is the use of the Fourier-Bros-Iagolnitzer (FBI) transform.
Download or read book Annales Scientifiques de L cole Normale Sup rieure written by École normale supérieure (France) and published by . This book was released on 2012 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Cohomology of Shimura Varieties III written by Michael Harris and published by . This book was released on 2001 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors complete the verification of the following fact: The nerve spectral sequence for the cohomology of the Borel-Serre boundary of a Shimura variety $\mathrm{Sh}$ is a spectral sequence of mixed Hodge-de Rham structures over the field of definition of its canonical model. To achieve that, they develop the machinery of automorphic vector bundles on mixed Shimura varieties, for the latter enter in the boundary of the toroidal compactifications of $\mathrm{Sh}$; and study the nerve spectral sequence for the automorphic vector bundles and the toroidal boundary. They also extend the technique of averting issues of base-change by taking cohomology with growth conditions. They give and apply formulas for the Hodge gradation of the cohomology of both $\mathrm{Sh}$ and its Borel-Serre boundary.
Download or read book Coefficient Systems and Supersingular Representations of GL2 F written by Vytautas Paskunas and published by . This book was released on 2004 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $F$ be a non-Archimedean local field with the residual characteristic $p$. The author constructs a good number of smooth irreducible $\overline {\mathbf {F}}_p$-representations of $\mathrm {GL}_2(F)$, which are supersingular in the sense of Barthel and Livne. If $F=\mathbf {Q}_p$ then results of Breuil imply that our construction gives all the supersingular representations up to the twist by an unramified quasi-character. The author conjectures that this is true for an arbitrary $F$. The book is suitable for graduate students and research mathematicians interested in algebra and algebraic geometry.
Download or read book M moire written by and published by . This book was released on 2006 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Global Solutions for Small Nonlinear Long Range Perturbations of Two Dimensional Schr dinger Equations written by Jean-Marc Delort and published by . This book was released on 2002 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here the author presents the following: Let $Q_1, Q_2$ be two quadratic forms, and $u$ a local solution of the two-dimensional Schrodinger equation $(i\partial _t + \Delta )u = Q_1(u,\nabla _x u) + Q_2(\bar {u},\nabla _x \bar {u})$. He proves that if $Q_1$ and $Q_2$ do depend on the derivatives of $u$, and if the Cauchy datum is small enough and decaying enough at infinity, the solution exists for all times. The difficulty of the problem originates in the fact that the nonlinear perturbation is a long range one: This means that it can be written as the product of (a derivative of) $u$ and of a potential whose $L^\infty$ space-norm is not time integrable at infinity.
