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On Dworks P Adic Formal Congruences Theorem And Hypergeometric Mirror Maps
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Book Synopsis On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps by : E. Delaygue
Download or read book On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps written by E. Delaygue and published by American Mathematical Soc.. This book was released on 2017-02-20 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using Dwork's theory, the authors prove a broad generalization of his famous -adic formal congruences theorem. This enables them to prove certain -adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number 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.
Download or read book 2017 MATRIX Annals written by Jan de Gier and published by Springer. This book was released on 2019-03-13 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in its second year, 2017: - Hypergeometric Motives and Calabi–Yau Differential Equations - Computational Inverse Problems - Integrability in Low-Dimensional Quantum Systems - Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book - Combinatorics, Statistical Mechanics, and Conformal Field Theory - Mathematics of Risk - Tutte Centenary Retreat - Geometric R-Matrices: from Geometry to Probability The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Book Synopsis Special Values of the Hypergeometric Series by : Akihito Ebisu
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.
Book Synopsis Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem by : Denis R. Hirschfeldt
Download or read book Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem written by Denis R. Hirschfeldt and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of . Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.
Book Synopsis Knot Invariants and Higher Representation Theory by : Ben Webster
Download or read book Knot Invariants and Higher Representation Theory written by Ben Webster and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for sl and sl and by Mazorchuk-Stroppel and Sussan for sl . The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is sl , the author shows that these categories agree with certain subcategories of parabolic category for gl .
Book Synopsis Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory by : H. Hofer
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.
Book Synopsis The Stability of Cylindrical Pendant Drops by : John McCuan
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.
Book Synopsis On Sudakov's Type Decomposition of Transference Plans with Norm Costs by : Stefano Bianchini
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.
Book Synopsis Entire Solutions for Bistable Lattice Differential Equations with Obstacles by : Aaron Hoffman
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.
Book Synopsis Spatially Independent Martingales, Intersections, and Applications by : Pablo Shmerkin
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.
Book Synopsis La Formule des Traces Locale Tordue by : Colette Moeglin
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.
Book Synopsis Maximal Abelian Sets of Roots by : R. Lawther
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.
Book Synopsis Tensor Products and Regularity Properties of Cuntz Semigroups by : Ramon Antoine
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.
Book Synopsis Medial/Skeletal Linking Structures for Multi-Region Configurations by : James Damon
Download or read book Medial/Skeletal Linking Structures for Multi-Region Configurations written by James Damon and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider a generic configuration of regions, consisting of a collection of distinct compact regions in which may be either regions with smooth boundaries disjoint from the others or regions which meet on their piecewise smooth boundaries in a generic way. They introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions' individual shapes and geometric properties as well as the “positional geometry” of the collection. The linking structure extends in a minimal way the individual “skeletal structures” on each of the regions. This allows the authors to significantly extend the mathematical methods introduced for single regions to the configuration of regions.
Book Synopsis Nonsmooth Differential Geometry-An Approach Tailored for Spaces with Ricci Curvature Bounded from Below by : Nicola Gigli
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.
Book Synopsis The Planar Cubic Cayley Graphs by : Agelos Georgakopoulos
Download or read book The Planar Cubic Cayley Graphs written by Agelos Georgakopoulos and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Book Synopsis Property ($T$) for Groups Graded by Root Systems by : Mikhail Ershov
Download or read book Property ($T$) for Groups Graded by Root Systems written by Mikhail Ershov and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.
