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Compact Quotients of Cahen-Wallach Spaces

2020-02-13 Education
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Release : 2020-02-13
Genre : Education
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Book Rating : 039/5 ( reviews)

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Book Synopsis Compact Quotients of Cahen-Wallach Spaces by : Ines Kath

Download or read book Compact Quotients of Cahen-Wallach Spaces written by Ines Kath. This book was released on 2020-02-13. Available in PDF, EPUB and Kindle. Book excerpt: Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. The authors derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.

Space – Time – Matter

2018-04-09 Mathematics
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Release : 2018-04-09
Genre : Mathematics
Kind : eBook
Book Rating : 530/5 ( reviews)

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Book Synopsis Space – Time – Matter by : Jochen Brüning

Download or read book Space – Time – Matter written by Jochen Brüning. This book was released on 2018-04-09. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data

2020-05-13 Education
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Release : 2020-05-13
Genre : Education
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Book Rating : 11X/5 ( reviews)

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Book Synopsis Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data by : Cristian Gavrus

Download or read book Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data written by Cristian Gavrus. This book was released on 2020-05-13. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors prove global well-posedness of the massless Maxwell–Dirac equation in the Coulomb gauge on R1+d(d≥4) for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions. Main components of the authors' proof are A) uncovering null structure of Maxwell–Dirac in the Coulomb gauge, and B) proving solvability of the underlying covariant Dirac equation. A key step for achieving both is to exploit (and justify) a deep analogy between Maxwell–Dirac and Maxwell-Klein-Gordon (for which an analogous result was proved earlier by Krieger-Sterbenz-Tataru, which says that the most difficult part of Maxwell–Dirac takes essentially the same form as Maxwell-Klein-Gordon.

Subgroup Decomposition in Out(Fn)

2020-05-13 Education
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Release : 2020-05-13
Genre : Education
Kind : eBook
Book Rating : 136/5 ( reviews)

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Book Synopsis Subgroup Decomposition in Out(Fn) by : Michael Handel

Download or read book Subgroup Decomposition in Out(Fn) written by Michael Handel. This book was released on 2020-05-13. Available in PDF, EPUB and Kindle. Book excerpt: In this work the authors develop a decomposition theory for subgroups of Out(Fn) which generalizes the decomposition theory for individual elements of Out(Fn) found in the work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in the work of Ivanov.

The Triangle-Free Process and the Ramsey Number R(3,k)

2020-04-03 Education
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Release : 2020-04-03
Genre : Education
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Book Rating : 717/5 ( reviews)

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Book Synopsis The Triangle-Free Process and the Ramsey Number R(3,k) by : Gonzalo Fiz Pontiveros

Download or read book The Triangle-Free Process and the Ramsey Number R(3,k) written by Gonzalo Fiz Pontiveros. This book was released on 2020-04-03. Available in PDF, EPUB and Kindle. Book excerpt: The areas of Ramsey theory and random graphs have been closely linked ever since Erdős's famous proof in 1947 that the “diagonal” Ramsey numbers R(k) grow exponentially in k. In the early 1990s, the triangle-free process was introduced as a model which might potentially provide good lower bounds for the “off-diagonal” Ramsey numbers R(3,k). In this model, edges of Kn are introduced one-by-one at random and added to the graph if they do not create a triangle; the resulting final (random) graph is denoted Gn,△. In 2009, Bohman succeeded in following this process for a positive fraction of its duration, and thus obtained a second proof of Kim's celebrated result that R(3,k)=Θ(k2/logk). In this paper the authors improve the results of both Bohman and Kim and follow the triangle-free process all the way to its asymptotic end.

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