The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a ...major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
If X is a manifold then the \mathbb R-algebra C^\infty (X) of smooth functions c:X\rightarrow \mathbb R is a C^\infty -ring. That is, for each smooth function f:\mathbb R^n\rightarrow \mathbb R there ...is an n-fold operation \Phi _f:C^\infty (X)^n\rightarrow C^\infty (X) acting by \Phi _f:(c_1,\ldots ,c_n)\mapsto f(c_1,\ldots ,c_n), and these operations \Phi _f satisfy many natural identities. Thus, C^\infty (X) actually has a far richer structure than the obvious \mathbb R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C^\infty -rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C^\infty -schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C^\infty -schemes, and C^\infty -stacks, in particular Deligne-Mumford C^\infty-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C^\infty-rings and C^\infty -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, "derived" versions of manifolds and orbifolds related to Spivak's "derived manifolds".
In this paper, we classified the paracontact metric κ,μ-manifold satisfying the Miao-Tam critical equation with κ>−1. We proved that it is locally isometric to the product of a flat n+1-dimensional ...manifold and an n-dimensional manifold of negative constant curvature −4.
This volume contains the proceedings of the conference on tropical geometry and integrable systems, held July 3-8, 2011, at the University of Glasgow, United Kingdom. One of the aims of this ...conference was to bring together researchers in the field of tropical geometry and its applications, from apparently disparate ends of the spectrum, to foster a mutual understanding and establish a common language which will encourage further developments of the area. This aim is reflected in these articles, which cover areas from automata, through cluster algebras, to enumerative geometry. In addition, two survey articles are included which introduce ideas from researchers on one end of this spectrum to researchers on the other. This book is intended for graduate students and researchers interested in tropical geometry and integrable systems and the developing links between these two areas.
This volume contains the proceedings of the conference Local and Global Methods in Algebraic Geometry, held from May 12-15, 2016, at the University of Illinois at Chicago, in honor of Lawrence Ein's ...60th birthday. The articles cover a broad range of topics in algebraic geometry and related fields, including birational geometry and moduli theory, analytic and positive characteristic methods, geometry of surfaces, singularity theory, hyper-Kähler geometry, rational points, and rational curves.
We revisit the famous Buffon’s needle problem, one of the first problems in geometric probability. Only now, the plane upon which we toss our needles is not Euclidean, as it was for Buffon, but ...instead has the simple but fascinating taxicab geometry. We find that we get the exact same solution as Buffon did, except that now π = 4! As a bonus, we get nice introductions to basic probability theory and geometry.
The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many ...important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.
Using Dwork's theory, the authors prove a broad generalization of his famous p-adic formal congruences theorem. This enables them to prove certain p-adic congruences for the generalized ...hypergeometric series with rational parameters; in particular, they hold for any prime number p and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the "Eisenstein constant" of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement "on average" of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases.
The ambient metric Fefferman, Charles; Graham, C. Robin
2012., 20111114, 2011, 2012-01-01, Letnik:
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eBook
This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient ...metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics.
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