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Author : M. J. Shai Haran
Publisher :
ISBN 13 : 9781470436414
Total Pages : 200 pages
Book Rating : 4.4/5 (364 download)
Download or read book New Foundations for Geometry written by M. J. Shai Haran and published by . This book was released on 2017 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shai M. J. Haran
Publisher : American Mathematical Soc.
ISBN 13 : 147042312X
Total Pages : 216 pages
Book Rating : 4.4/5 (74 download)
Download or read book New Foundations for Geometry: Two Non-Additive Languages for Arithmetical Geometry written by Shai M. J. Haran and published by American Mathematical Soc.. This book was released on 2017-02-20 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: To view the abstract go to http://www.ams.org/books/memo/1166.
Author : Robert G. Niemeyer
Publisher : American Mathematical Soc.
ISBN 13 : 1470435810
Total Pages : 302 pages
Book Rating : 4.4/5 (74 download)
Download or read book Horizons of Fractal Geometry and Complex Dimensions written by Robert G. Niemeyer and published by American Mathematical Soc.. This book was released on 2019-06-26 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, in celebration of Michel L. Lapidus's 60th birthday, held from June 21–29, 2016, at California Polytechnic State University, San Luis Obispo, California. The theme of the contributions is fractals and dynamics and content is split into four parts, centered around the following themes: Dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings).
Author : Bo’az Klartag
Publisher : American Mathematical Soc.
ISBN 13 : 1470425424
Total Pages : 90 pages
Book Rating : 4.4/5 (74 download)
Download or read book Needle Decompositions in Riemannian Geometry written by Bo’az Klartag and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Author : Nicola Gigli
Publisher : American Mathematical Soc.
ISBN 13 : 1470427656
Total Pages : 174 pages
Book Rating : 4.4/5 (74 download)
Download or read book Nonsmooth Differential Geometry-An Approach Tailored for Spaces with Ricci Curvature Bounded from Below written by Nicola Gigli and published by American Mathematical Soc.. This book was released on 2018-02-23 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.
Author : Igor Burban
Publisher : American Mathematical Soc.
ISBN 13 : 1470425378
Total Pages : 134 pages
Book Rating : 4.4/5 (74 download)
Download or read book Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems written by Igor Burban and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article the authors develop a new method to deal with maximal Cohen–Macaulay modules over non–isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen–Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen–Macaulay representation type. The authors' approach is illustrated on the case of k as well as several other rings. This study of maximal Cohen–Macaulay modules over non–isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.
Author : H. Hofer
Publisher : American Mathematical Soc.
ISBN 13 : 1470422034
Total Pages : 230 pages
Book Rating : 4.4/5 (74 download)
Download or read book Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory written by H. Hofer and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyfold theory the authors use the results of the present paper to describe an alternative construction of the Gromov-Witten invariants for general compact symplectic manifolds.
Author : Akihito Ebisu
Publisher : American Mathematical Soc.
ISBN 13 : 1470425335
Total Pages : 108 pages
Book Rating : 4.4/5 (74 download)
Download or read book Special Values of the Hypergeometric Series written by Akihito Ebisu and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the author presents a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Appell-Lauricella hypergeometric series. Furthermore, using this method, the author gets identities for the hypergeometric series and shows that values of at some points can be expressed in terms of gamma functions, together with certain elementary functions. The author tabulates the values of that can be obtained with this method and finds that this set includes almost all previously known values and many previously unknown values.
Author : Akinari Hoshi
Publisher : American Mathematical Soc.
ISBN 13 : 1470424096
Total Pages : 228 pages
Book Rating : 4.4/5 (74 download)
Download or read book Rationality Problem for Algebraic Tori written by Akinari Hoshi and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give the complete stably rational classification of algebraic tori of dimensions and over a field . In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank and is given. The authors show that there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension , and there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension . The authors make a procedure to compute a flabby resolution of a -lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a -lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby -lattices of rank up to and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for -lattices holds when the rank , and fails when the rank is ...
Author : Stefano Bianchini
Publisher : American Mathematical Soc.
ISBN 13 : 1470427664
Total Pages : 124 pages
Book Rating : 4.4/5 (74 download)
Download or read book On Sudakov's Type Decomposition of Transference Plans with Norm Costs written by Stefano Bianchini and published by American Mathematical Soc.. This book was released on 2018-02-23 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost with , probability measures in and absolutely continuous w.r.t. . The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in , where are disjoint regions such that the construction of an optimal map is simpler than in the original problem, and then to obtain by piecing together the maps . When the norm is strictly convex, the sets are a family of -dimensional segments determined by the Kantorovich potential called optimal rays, while the existence of the map is straightforward provided one can show that the disintegration of (and thus of ) on such segments is absolutely continuous w.r.t. the -dimensional Hausdorff measure. When the norm is not strictly convex, the main problems in this kind of approach are two: first, to identify a suitable family of regions on which the transport problem decomposes into simpler ones, and then to prove the existence of optimal maps. In this paper the authors show how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented. The results yield a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the Monge problem in each set and then in . The strategy is sufficiently powerful to be applied to other optimal transportation problems.
Author : Pablo Shmerkin
Publisher : American Mathematical Soc.
ISBN 13 : 1470426889
Total Pages : 114 pages
Book Rating : 4.4/5 (74 download)
Download or read book Spatially Independent Martingales, Intersections, and Applications written by Pablo Shmerkin and published by American Mathematical Soc.. This book was released on 2018-02-22 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors define a class of random measures, spatially independent martingales, which we view as a natural generalization of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian cut-outs. The authors pair the random measures with deterministic families of parametrized measures , and show that under some natural checkable conditions, a.s. the mass of the intersections is Hölder continuous as a function of . This continuity phenomenon turns out to underpin a large amount of geometric information about these measures, allowing us to unify and substantially generalize a large number of existing results on the geometry of random Cantor sets and measures, as well as obtaining many new ones. Among other things, for large classes of random fractals they establish (a) very strong versions of the Marstrand-Mattila projection and slicing results, as well as dimension conservation, (b) slicing results with respect to algebraic curves and self-similar sets, (c) smoothness of convolutions of measures, including self-convolutions, and nonempty interior for sumsets, and (d) rapid Fourier decay. Among other applications, the authors obtain an answer to a question of I. Łaba in connection to the restriction problem for fractal measures.
Author : Colette Moeglin
Publisher : American Mathematical Soc.
ISBN 13 : 1470427710
Total Pages : 196 pages
Book Rating : 4.4/5 (74 download)
Download or read book La Formule des Traces Locale Tordue written by Colette Moeglin and published by American Mathematical Soc.. This book was released on 2018-02-23 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: A note to readers: This book is in French. The text has two chapters. The first one, written by Waldspurger, proves a twisted version of the local trace formula of Arthur over a local field. This formula is an equality between two expressions, one involving weighted orbital integrals, the other one involving weighted characters. The authors follow Arthur's proof, but the treatement of the spectral side is more complicated in the twisted situation. They need to use the combinatorics of the “Morning Seminar”. The authors' local trace formula has the same consequences as in Arthur's paper on elliptic characters. The second chapter, written by Moeglin, gives a symmetric form of the local trace formula as in Arthur's paper on Fourier Transform of Orbital integral and describes any twisted orbital integral, in the p-adic case, as integral of characters.
Author : Ramon Antoine
Publisher : American Mathematical Soc.
ISBN 13 : 1470427974
Total Pages : 206 pages
Book Rating : 4.4/5 (74 download)
Download or read book Tensor Products and Regularity Properties of Cuntz Semigroups written by Ramon Antoine and published by American Mathematical Soc.. This book was released on 2018-02-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cuntz semigroup of a -algebra is an important invariant in the structure and classification theory of -algebras. It captures more information than -theory but is often more delicate to handle. The authors systematically study the lattice and category theoretic aspects of Cuntz semigroups. Given a -algebra , its (concrete) Cuntz semigroup is an object in the category of (abstract) Cuntz semigroups, as introduced by Coward, Elliott and Ivanescu. To clarify the distinction between concrete and abstract Cuntz semigroups, the authors call the latter -semigroups. The authors establish the existence of tensor products in the category and study the basic properties of this construction. They show that is a symmetric, monoidal category and relate with for certain classes of -algebras. As a main tool for their approach the authors introduce the category of pre-completed Cuntz semigroups. They show that is a full, reflective subcategory of . One can then easily deduce properties of from respective properties of , for example the existence of tensor products and inductive limits. The advantage is that constructions in are much easier since the objects are purely algebraic.
Author : A. M. Mason
Publisher : American Mathematical Soc.
ISBN 13 : 1470426854
Total Pages : 106 pages
Book Rating : 4.4/5 (74 download)
Download or read book Orthogonal and Symplectic $n$-level Densities written by A. M. Mason and published by American Mathematical Soc.. This book was released on 2018-02-23 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors apply to the zeros of families of -functions with orthogonal or symplectic symmetry the method that Conrey and Snaith (Correlations of eigenvalues and Riemann zeros, 2008) used to calculate the -correlation of the zeros of the Riemann zeta function. This method uses the Ratios Conjectures (Conrey, Farmer, and Zimbauer, 2008) for averages of ratios of zeta or -functions. Katz and Sarnak (Zeroes of zeta functions and symmetry, 1999) conjecture that the zero statistics of families of -functions have an underlying symmetry relating to one of the classical compact groups , and . Here the authors complete the work already done with (Conrey and Snaith, Correlations of eigenvalues and Riemann zeros, 2008) to show how new methods for calculating the -level densities of eigenangles of random orthogonal or symplectic matrices can be used to create explicit conjectures for the -level densities of zeros of -functions with orthogonal or symplectic symmetry, including all the lower order terms. They show how the method used here results in formulae that are easily modified when the test function used has a restricted range of support, and this will facilitate comparison with rigorous number theoretic -level density results.
Author : John McCuan
Publisher : American Mathematical Soc.
ISBN 13 : 1470409380
Total Pages : 122 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Stability of Cylindrical Pendant Drops written by John McCuan and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author considers the stability of certain liquid drops in a gravity field satisfying a mixed boundary condition. He also considers as special cases portions of cylinders that model either the zero gravity case or soap films with the same kind of boundary behavior.
Author : Aaron Hoffman
Publisher : American Mathematical Soc.
ISBN 13 : 1470422018
Total Pages : 132 pages
Book Rating : 4.4/5 (74 download)
Download or read book Entire Solutions for Bistable Lattice Differential Equations with Obstacles written by Aaron Hoffman and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions they show that wave-like solutions exist when obstacles (characterized by “holes”) are present in the lattice. Their work generalizes to the discrete spatial setting the results obtained in Berestycki, Hamel, and Matuno (2009) for the propagation of waves around obstacles in continuous spatial domains. The analysis hinges upon the development of sub and super-solutions for a class of discrete bistable reaction-diffusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.
Author : R. Lawther
Publisher : American Mathematical Soc.
ISBN 13 : 147042679X
Total Pages : 234 pages
Book Rating : 4.4/5 (74 download)
Download or read book Maximal Abelian Sets of Roots written by R. Lawther and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work the author lets be an irreducible root system, with Coxeter group . He considers subsets of which are abelian, meaning that no two roots in the set have sum in . He classifies all maximal abelian sets (i.e., abelian sets properly contained in no other) up to the action of : for each -orbit of maximal abelian sets we provide an explicit representative , identify the (setwise) stabilizer of in , and decompose into -orbits. Abelian sets of roots are closely related to abelian unipotent subgroups of simple algebraic groups, and thus to abelian -subgroups of finite groups of Lie type over fields of characteristic . Parts of the work presented here have been used to confirm the -rank of , and (somewhat unexpectedly) to obtain for the first time the -ranks of the Monster and Baby Monster sporadic groups, together with the double cover of the latter. Root systems of classical type are dealt with quickly here; the vast majority of the present work concerns those of exceptional type. In these root systems the author introduces the notion of a radical set; such a set corresponds to a subgroup of a simple algebraic group lying in the unipotent radical of a certain maximal parabolic subgroup. The classification of radical maximal abelian sets for the larger root systems of exceptional type presents an interesting challenge; it is accomplished by converting the problem to that of classifying certain graphs modulo a particular equivalence relation.
