Download or read book Hypoelliptic Laplacian and Orbital Integrals written by Jean-Michel Bismut and published by Princeton University Press. This book was released on 2011-08-08 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof.
Download or read book Hypoelliptic Laplacian and Bott Chern Cohomology written by Jean-Michel Bismut and published by Springer Science & Business Media. This book was released on 2013-05-23 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann–Roch–Grothendieck for proper submersions. It gives an equality of cohomology classes in Bott–Chern cohomology, which is a refinement for complex manifolds of de Rham cohomology. When the manifolds are Kähler, our main result is known. A proof can be given using the elliptic Hodge theory of the fibres, its deformation via Quillen's superconnections, and a version in families of the 'fantastic cancellations' of McKean–Singer in local index theory. In the general case, this approach breaks down because the cancellations do not occur any more. One tool used in the book is a deformation of the Hodge theory of the fibres to a hypoelliptic Hodge theory, in such a way that the relevant cohomological information is preserved, and 'fantastic cancellations' do occur for the deformation. The deformed hypoelliptic Laplacian acts on the total space of the relative tangent bundle of the fibres. While the original hypoelliptic Laplacian discovered by the author can be described in terms of the harmonic oscillator along the tangent bundle and of the geodesic flow, here, the harmonic oscillator has to be replaced by a quartic oscillator. Another idea developed in the book is that while classical elliptic Hodge theory is based on the Hermitian product on forms, the hypoelliptic theory involves a Hermitian pairing which is a mild modification of intersection pairing. Probabilistic considerations play an important role, either as a motivation of some constructions, or in the proofs themselves.
Download or read book Metric and Differential Geometry written by Xianzhe Dai and published by Springer Science & Business Media. This book was released on 2012-06-01 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric and Differential Geometry grew out of a similarly named conference held at Chern Institute of Mathematics, Tianjin and Capital Normal University, Beijing. The various contributions to this volume cover a broad range of topics in metric and differential geometry, including metric spaces, Ricci flow, Einstein manifolds, Kähler geometry, index theory, hypoelliptic Laplacian and analytic torsion. It offers the most recent advances as well as surveys the new developments. Contributors: M.T. Anderson J.-M. Bismut X. Chen X. Dai R. Harvey P. Koskela B. Lawson X. Ma R. Melrose W. Müller A. Naor J. Simons C. Sormani D. Sullivan S. Sun G. Tian K. Wildrick W. Zhang
Download or read book Arithmetic L Functions and Differential Geometric Methods written by Pierre Charollois and published by Springer Nature. This book was released on 2021-05-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outgrowth of the conference “Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods” that was held in Paris in May 2016. Gathering contributions by leading experts in the field ranging from original surveys to pure research articles, this volume provides comprehensive coverage of the front most developments in the field of regulator maps. Key topics covered are: • Additive polylogarithms • Analytic torsions • Chabauty-Kim theory • Local Grothendieck-Riemann-Roch theorems • Periods • Syntomic regulator The book contains contributions by M. Asakura, J. Balakrishnan, A. Besser, A. Best, F. Bianchi, O. Gregory, A. Langer, B. Lawrence, X. Ma, S. Müller, N. Otsubo, J. Raimbault, W. Raskin, D. Rössler, S. Shen, N. Triantafi llou, S. Ünver and J. Vonk.
Download or read book Variational Methods written by Maïtine Bergounioux and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-01-11 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase・amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index
Download or read book Annals of Mathematics Studies written by Jean-Michel Bismut and published by . This book was released on 1940 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convolution and Equidistribution written by Nicholas M. Katz and published by . This book was released on 1940 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Problems of Unlikely Intersections in Arithmetic and Geometry written by Umberto Zannier and published by . This book was released on 1940 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Decomposition of Global Conformal Invariants written by Spyros Alexakis and published by . This book was released on 1940 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fr chet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces written by Joram Lindenstrauss and published by . This book was released on 1940 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spaces of PL Manifolds and Categories of Simple Maps written by Friedhelm Waldhausen and published by . This book was released on 1940 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Degenerate Diffusion Operators Arising in Population Biology written by Charles L. Epstein and published by . This book was released on 1940 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book S minaire Bourbaki written by Société mathématique de France and published by . This book was released on 2019 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This 69th volume of the Bourbaki Seminar contains the texts of the fifteen survey lectures done during the year 2016/2017. Topics addressed covered Langlands correspondence, NIP property in model theory, Navier-Stokes equation, algebraic and complex analytic geometry, algorithmic and geometric questions in knot theory, analytic number theory formal moduli problems, general relativity, sofic entropy, sphere packings, subriemannian geometry." -- Prové de l'editor.
Download or read book Mathematical Theory of Scattering Resonances written by Semyon Dyatlov and published by American Mathematical Soc.. This book was released on 2019-09-10 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Download or read book Oculofacial Orbital and Lacrimal Surgery written by Adam J. Cohen and published by Springer Nature. This book was released on 2019-08-30 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive text covers both core and advanced principles within oculofacial, orbital, and lacrimal surgery with extensive detail not found in any other current book on the subject. Richly illustrated with hundreds of images,Oculofacial, Orbital, and Lacrimal Surgery: A Compendium is written and edited by international leaders in fields spanning ophthalmology, otolaryngology, oral and maxillofacial surgery, and plastic surgery. Covering topics such as embryology, anatomy, and physiology of the lacrimal system, imaging for orbital diseases and thyroid-related ophthalmology, and flap geometry and planning, this book is an excellent resource for those in training, as well as seasoned clinicians looking to stay current. This book is divided into five sections: Eyelid, Oculofacial, Lacrimal, Orbit, and Socket, with each section containing detailed chapters addressing evaluation, imaging, and various surgical approaches and management. Designed to not only provide an anatomical and surgical guide for all three types of surgeries, but to help physicians avoid mistakes and correct complications of patients referred to them, Oculofacial, Orbital, and Lacrimal Surgery: A Compendium is the definitive, authoritative reference on this complex field.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Laplacian Eigenvectors of Graphs written by Türker Biyikoglu and published by Springer. This book was released on 2007-07-07 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fascinating volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, and graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology. Eigenvectors of graph Laplacians may seem a surprising topic for a book, but the authors show that there are subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs.
