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Author : Rod G. Downey,Keng Meng Ng,Reed Solomon
Publisher : Unknown
Page : 90 pages
File Size : 42,6 Mb
Release : 2020
Category : Computable functions
ISBN : 1470461374
Author : Rodney G. Downey,Keng Meng Ng,Reed Solomon
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 53,7 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470441623
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.
Author : Yu Kiang Leong
Publisher : World Scientific
Page : 442 pages
File Size : 45,9 Mb
Release : 2021-06-23
Category : Mathematics
ISBN : 9789811219603
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.
Author : Rodney G. Downey,Denis R. Hirschfeldt
Publisher : Springer Science & Business Media
Page : 855 pages
File Size : 48,5 Mb
Release : 2010-10-29
Category : Computers
ISBN : 9780387684413
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.
Author : Ulrich Bunke,David Gepner
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 54,5 Mb
Release : 2021-06-21
Category : Education
ISBN : 9781470446857
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.
Author : Jonathan Gantner
Publisher : American Mathematical Society
Page : 114 pages
File Size : 40,9 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470442385
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.
Author : Paul M Feehan,Manousos Maridakis
Publisher : American Mathematical Society
Page : 138 pages
File Size : 54,9 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470443023
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.
Author : Zhi Qi
Publisher : American Mathematical Society
Page : 123 pages
File Size : 42,6 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470443252
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.
Author : Hiroshi Iritani,Todor Milanov,Yongbin Ruan, Yefeng Shen
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 44,5 Mb
Release : 2021-06-21
Category : Education
ISBN : 9781470443634
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.
Author : Kazuyuki Hatada
Publisher : American Mathematical Soc.
Page : 165 pages
File Size : 49,6 Mb
Release : 2021-06-18
Category : Education
ISBN : 9781470443344
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Author : Pierre Albin,Frédéric Rochon,David Sher
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 53,7 Mb
Release : 2021-06-21
Category : Education
ISBN : 9781470444228
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.
Author : Chao Wang
Publisher : American Mathematical Soc.
Page : 119 pages
File Size : 43,7 Mb
Release : 2021-07-21
Category : Education
ISBN : 9781470446895
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.
Author : Camille Male
Publisher : American Mathematical Society
Page : 88 pages
File Size : 45,8 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470442989
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.
Author : David M Calderbank,Michael G. Eastwood,Vladimir S. Matveev,Katharina Neusser
Publisher : American Mathematical Society
Page : 137 pages
File Size : 53,5 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470443009
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.
Author : Patrick Delorme,Pascale Harinck,Yiannis Sakellaridis
Publisher : American Mathematical Soc.
Page : 102 pages
File Size : 40,6 Mb
Release : 2021-06-21
Category : Education
ISBN : 9781470444020
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].