Download or read book Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees written by Rodney G. Downey and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.
Download or read book Art And Practice Of Mathematics The Interviews At The Institute For Mathematical Sciences National University Of Singapore 2010 2020 written by Yu Kiang Leong and published by World Scientific. This book was released on 2021-06-23 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the second volume of interviews with prominent mathematicians and mathematical scientists who visited the Institute for Mathematical Sciences, National University of Singapore. First published in the Institute's newsletter Imprints during the period 2010-2020, they offer glimpses of an esoteric universe as viewed and experienced by some of the leading and creative practitioners of the craft of mathematics.The topics covered in this volume are wide-ranging, running from pure mathematics (logic, number theory, algebraic geometry) to applied mathematics (mathematical modeling, fluid dynamics) through probability and statistics, mathematical physics, theoretical computer science and financial mathematics. This eclectic mix of the abstract and the concrete should interest those who are enthralled by the mystique and power of mathematics, whether they are students, researchers or the non-specialists.By briefly tracing the paths traveled by the pioneers of different national backgrounds, the interviews attempt to put a cultural face to an intellectual endeavor that is often perceived as dry and austere by the uninitiated. They should also interest those who are intrigued by the influence of the environment on the creative spirit, and, in particular, those who are interested in the psychology and history of ideas.
Download or read book Algorithmic Randomness and Complexity written by Rodney G. Downey and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 883 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.
Download or read book Differential Function Spectra the Differential Becker Gottlieb Transfer and Applications to Differential Algebraic K Theory written by Ulrich Bunke and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.
Download or read book Operator Theory on One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus and Spectral Operators written by Jonathan Gantner and published by American Mathematical Society. This book was released on 2021-02-10 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.
Download or read book ojasiewicz Simon Gradient Inequalities for Coupled Yang Mills Energy Functionals written by Paul M Feehan and published by American Mathematical Society. This book was released on 2021-02-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors' primary goal in this monograph is to prove Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections.
Download or read book Theory of Fundamental Bessel Functions of High Rank written by Zhi Qi and published by American Mathematical Society. This book was released on 2021-02-10 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
Download or read book Gromov Witten Theory of Quotients of Fermat Calabi Yau Varieties written by Hiroshi Iritani and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gromov-Witten theory started as an attempt to provide a rigorous mathematical foundation for the so-called A-model topological string theory of Calabi-Yau varieties. Even though it can be defined for all the Kähler/symplectic manifolds, the theory on Calabi-Yau varieties remains the most difficult one. In fact, a great deal of techniques were developed for non-Calabi-Yau varieties during the last twenty years. These techniques have only limited bearing on the Calabi-Yau cases. In a certain sense, Calabi-Yau cases are very special too. There are two outstanding problems for the Gromov-Witten theory of Calabi-Yau varieties and they are the focus of our investigation.
Download or read book Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms written by Kazuyuki Hatada and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Resolvent Heat Kernel and Torsion under Degeneration to Fibered Cusps written by Pierre Albin and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.
Download or read book Local Well Posedness and Break Down Criterion of the Incompressible Euler Equations with Free Boundary written by Chao Wang and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschitz function and the free surface belongs to C 3 2 +ε. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.
Download or read book Traffic Distributions and Independence Permutation Invariant Random Matrices and the Three Notions of Independence written by Camille Male and published by American Mathematical Society. This book was released on 2021-02-10 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by permutation matrices. This fact leads naturally to an extension of free probability, formalized under the notions of traffic probability. The author first establishes this construction for random matrices and then defines the traffic distribution of random matrices, which is richer than the $^*$-distribution of free probability. The knowledge of the individual traffic distributions of independent permutation invariant families of matrices is sufficient to compute the limiting distribution of the join family. Under a factorization assumption, the author calls traffic independence the asymptotic rule that plays the role of independence with respect to traffic distributions. Wigner matrices, Haar unitary matrices and uniform permutation matrices converge in traffic distributions, a fact which yields new results on the limiting $^*$-distributions of several matrices the author can construct from them. Then the author defines the abstract traffic spaces as non commutative probability spaces with more structure. She proves that at an algebraic level, traffic independence in some sense unifies the three canonical notions of tensor, free and Boolean independence. A central limiting theorem is stated in this context, interpolating between the tensor, free and Boolean central limit theorems.
Download or read book C Projective Geometry written by David M Calderbank and published by American Mathematical Society. This book was released on 2021-02-10 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kähler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kähler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kähler manifolds: if such a manifold admits a one parameter group of c-projective transformations that are not affine, then it is complex projective space, equipped with a multiple of the Fubini-Study metric.
Download or read book Paley Wiener Theorems for a p Adic Spherical Variety written by Patrick Delorme and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let C pXq be the space of Harish-Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley–Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers — rings of multipliers for SpXq and C pXq.WhenX “ a reductive group, our theorem for C pXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step — enough to recover the structure of the Bern-stein center — towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01].
Download or read book Bounded Littlewood Identities written by Eric M. Rains and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe a method, based on the theory of Macdonald–Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald’s partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R, S) in terms of ordinary Macdonald polynomials, are q, t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups. In the classical limit, our method implies that MacMahon’s famous ex-conjecture for the generating function of symmetric plane partitions in a box follows from the identification of GL(n, R), O(n) as a Gelfand pair. As further applications, we obtain combinatorial formulas for characters of affine Lie algebras; Rogers–Ramanujan identities for affine Lie algebras, complementing recent results of Griffin et al.; and quadratic transformation formulas for Kaneko–Macdonald-type basic hypergeometric series.
Download or read book The Irreducible Subgroups of Exceptional Algebraic Groups written by Adam R. Thomas and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is a contribution to the study of the subgroup structure of excep-tional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we com-plete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected sub-group X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G.
Download or read book Linear Dynamical Systems on Hilbert Spaces Typical Properties and Explicit Examples written by S. Grivaux and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigen-values and admits no non-trivial invariant measure, but is densely distri-butionally chaotic. (ii) A typical upper-triangular operator with coefficients of modulus 1 on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form “diagonal with coefficients of modulus 1 on the diagonal plus backward unilateral weighted shift” is ergodic but has only countably many unimodular eigenvalues; in particular, it is ergodic but not ergodic in the Gaussian sense. (iii) There exist Hilbert space operators which are chaotic and U-frequently hypercyclic but not frequently hypercyclic, Hilbert space operators which are chaotic and frequently hypercyclic but not ergodic, and Hilbert space operators which are chaotic and topologically mixing but not U-frequently hypercyclic. We complement our results by investigating the descriptive complexity of some natural classes of operators defined by dynamical properties.
