Category: Differential Geometry

By Maurice A. de Gosson

The target of this publication is to provide a rigorous and whole therapy of assorted issues from harmonic research with a powerful emphasis on symplectic invariance houses, that are usually overlooked or underestimated within the time-frequency literature. the themes which are addressed comprise (but usually are not restricted to) the idea of the Wigner remodel, the uncertainty precept (from the viewpoint of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s worldwide idea of pseudo-differential operators, and Feichtinger’s concept of modulation areas. a number of purposes to time-frequency research and quantum mechanics are given, a lot of them concurrent with ongoing examine. for example, a non-standard pseudo-differential calculus on part house is brought and studied, the place the most position is performed by means of “Bopp operators” (also referred to as “Landau operators” within the literature). This calculus is heavily on the topic of either the Landau challenge and to the deformation quantization concept of Flato and Sternheimer, of which it offers an easy pseudo-differential formula the place Feichtinger’s modulation areas are key actors.

This ebook is essentially directed in the direction of scholars or researchers in harmonic research (in the huge feel) and in the direction of mathematical physicists operating in quantum mechanics. it may well even be learn with revenue by means of researchers in time-frequency research, offering a useful supplement to the prevailing literature at the subject. a undeniable familiarity with Fourier research (in the wide experience) and introductory useful research (e.g. the effortless concept of distributions) is thought. another way, the ebook is basically self-contained and comprises an in depth checklist of references.

By Yau S.-T. (ed.)

The Surveys in Differential Geometry are supplementations to the magazine of Differential Geometry, that are released by way of overseas Press. They contain major invited papers combining unique study and overviews of the most up-tp-date examine in particular components of curiosity to the becoming magazine of Differential Geometry group. The survey volumes function carrying on with references, inspirations for brand spanking new learn, and introductions to the range of subject matters of curiosity to differential geometers. those vitamins are released every year on account that 1999. This quantity arises out of the convention backed through the magazine of Differential Geometry and held at Harvard collage to honor the 4 mathematicians who based Index idea. a number of geometers collected for this historical social gathering which incorporated various tributes and memories so as to be released in a separate quantity. The 4 founders of the Index idea - Michael Atiyah, Raoul Bott, Frederich Hirzebruch, and Isadore Singer - are assets of notion, mentors and lecturers for the opposite audio system and individuals on the convention. The larger-than-usual dimension of this quantity derives at once from the great recognize and admiration for the honorees. desk of Contents: 1. Projective planes, Severi types and spheres - M. Atiyah and J. Berndt 2. Degeneration of Einstein metrics and metrics with distinctive holonomy - J. Cheeger three. The min-max building of minimum surfaces - T. H. Colding and C. De Lellis four. common quantity bounds in Riemannian manifolds - C. B. Croke and M. Katz five. A Kawamata-Viehweg vanishing theorem on compact Kahler manifolds - J.-P. Demailly and T. Peternell 6. second maps in differential geometry - S. okay. Donaldson 7. neighborhood pressure for cocycles - D. Fisher and G. A. Margulis eight. Einstein metrics, four-manifolds, and differential topology - C. LeBrun nine. Topological quantum box idea for Calabi-Yau threefolds and $G_2$-manifold - N. C. Leung 10. Geometric leads to classical minimum floor conception - W. H. Meeks III eleven. On international life of wave maps with severe regularity - A. Nahmod 12. Discreteness of minimum types of Kodaira measurement 0 and subvarieties of moduli stacks - E. Viehweg and ok. Zuo thirteen. Geometry of the Weil-Petersson crowning glory of Teichmüller house - S. A. Wolpert

By Lee J.M.

By Yuri I. Manin

This is often the 1st monograph devoted to the systematic exposition of the entire number of subject matters regarding quantum cohomology. the topic first originated in theoretical physics (quantum string concept) and has persevered to enhance greatly over the past decade. The author's method of quantum cohomology relies at the concept of the Frobenius manifold. the 1st a part of the publication is dedicated to this suggestion and its wide interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. within the moment a part of the booklet, the writer describes the development of quantum cohomology and experiences the algebraic geometry mechanisms thinking about this building (intersection and deformation idea of Deligne-Artin and Mumford stacks). Yuri Manin is presently the director of the Max-Planck-Institut f?r Mathematik in Bonn, Germany. He has authored and coauthored 10 monographs and nearly two hundred examine articles in algebraic geometry, quantity concept, mathematical physics, background of tradition, and psycholinguistics. Manin's books, resembling Cubic kinds: Algebra, Geometry, and mathematics (1974), A path in Mathematical common sense (1977), Gauge box idea and complicated Geometry (1988), undemanding debris: arithmetic, Physics and Philosophy (1989, with I. Yu. Kobzarev), themes in Non-commutative Geometry (1991), and techniques of Homological Algebra (1996, with S. I. Gelfand), secured for him stable acceptance as an exceptional expositor. definitely the current booklet will serve mathematicians for a few years to come back.

By M. Boucetta, J.M. Morvan

The purpose of this quantity is to offer an advent and evaluation to differential topology, differential geometry and computational geometry with an emphasis on a few interconnections among those 3 domain names of arithmetic. The chapters provide the history required to start learn in those fields or at their interfaces. They introduce new learn domain names and either outdated and new conjectures in those diversified matters express a few interplay among different sciences with reference to arithmetic. issues mentioned are; the foundation of differential topology and combinatorial topology, the hyperlink among differential geometry and topology, Riemanian geometry (Levi-Civita connextion, curvature tensor, geodesic, completeness and curvature tensor), attribute periods (to affiliate each fibre package with isomorphic fiber bundles), the hyperlink among differential geometry and the geometry of non delicate items, computational geometry and urban purposes reminiscent of structural geology and graphism.

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By Tristan Hubsch

Calabi-Yau areas are used to build in all probability real looking (super)string types and are therefore being studied vigorously within the contemporary physics literature. typically a part of this ebook, the authors gather and overview the suitable effects on (1) numerous significant development concepts, (2) computation of bodily proper amounts corresponding to massless box spectra and the Yukawa interactions, (3) stringy corrections, (4) moduli house and its geometry. moreover, a initial dialogue of the conjectured common moduli area and similar open difficulties are incorporated. The authors additionally comprise numerous specific types to exemplify the innovations and the overall dialogue. this can be most likely to be the 1st systematic exposition in e-book kind of the fabric on Calabi-Yau areas, differently scattered via convention court cases and journals.

By Bennett Chow

This is often effectively the easiest booklet at the Ricci circulate that i've got ever encountered. this is often the one e-book at the Ricci move that i've got ever encountered. i feel that its worth to the advance and alertness of geometric research for the learn of manifolds is incalculable (no pun intended). i need to say, i have not noticeable nicer services or such more desirable metrics. i'm fairly inspired by means of via the skills of the second one writer, Dr. Dan Knopf, as displayed during this wonderful e-book. His commanding grab of the fabric, lucid and thought-provoking presentation, and high-quality expository kind are not anything in need of breathtaking. i'm happy to suggest this glorious paintings.

By Lee J.M.

By Katharina Habermann

One of the elemental rules in differential geometry is that the examine of analytic homes of convinced differential operators performing on sections of vector bundles yields geometric and topological homes of the underlying base manifold. Symplectic spinor fields are sections in an L^2-Hilbert house package over a symplectic manifold and symplectic Dirac operators, performing on symplectic spinor fields, are linked to the symplectic manifold in a really traditional method. accordingly they are anticipated to offer attention-grabbing functions in symplectic geometry and symplectic topology. those symplectic Dirac operators are known as Dirac operators, given that they're outlined in an identical approach because the classical Riemannian Dirac operator recognized from Riemannian spin geometry. they're referred to as symplectic simply because they're built by means of use of the symplectic atmosphere of the underlying symplectic manifold. This quantity is the 1st one who offers a scientific and self-contained creation to the speculation of symplectic Dirac operators and displays the present country of the topic. even as, it really is meant to set up the concept symplectic spin geometry and symplectic Dirac operators can provide precious instruments in symplectic geometry and symplectic topology, that have turn into vital fields and extremely energetic parts of mathematical research.

By Ren De-Lin

Necessities of the indispensable geometry in a homogenous house are offered and the point of interest is at the easy effects and purposes. This publication offers the readers with new findings, a few being released for the 1st time.