Generalized Descriptive Set Theory and Classification Theory
Generalized Descriptive Set Theory and Classification Theory

Author: Sy-David Friedman

Publisher: American Mathematical Soc.

Published: 2014-06-05

Total Pages: 92

ISBN-13: 0821894757

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Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Generalized Descriptive Set Theory and Classification Theory
Generalized Descriptive Set Theory and Classification Theory

Author: Sy D. Friedman

Publisher:

Published: 2014-10-03

Total Pages: 92

ISBN-13: 9781470416713

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Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

A Homology Theory for Smale Spaces
A Homology Theory for Smale Spaces

Author: Ian F. Putnam

Publisher: American Mathematical Soc.

Published: 2014-09-29

Total Pages: 136

ISBN-13: 1470409097

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The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.

Local Entropy Theory of a Random Dynamical System
Local Entropy Theory of a Random Dynamical System

Author: Anthony H. Dooley

Publisher: American Mathematical Soc.

Published: 2014-12-20

Total Pages: 118

ISBN-13: 1470410559

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In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.

Analysis of the Hodge Laplacian on the Heisenberg Group
Analysis of the Hodge Laplacian on the Heisenberg Group

Author: Detlef Muller

Publisher: American Mathematical Soc.

Published: 2014-12-20

Total Pages: 104

ISBN-13: 1470409399

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The authors consider the Hodge Laplacian \Delta on the Heisenberg group H_n, endowed with a left-invariant and U(n)-invariant Riemannian metric. For 0\le k\le 2n+1, let \Delta_k denote the Hodge Laplacian restricted to k-forms. In this paper they address three main, related questions: (1) whether the L^2 and L^p-Hodge decompositions, 1

Pursuit of the Universal
Pursuit of the Universal

Author: Arnold Beckmann

Publisher: Springer

Published: 2016-06-13

Total Pages: 388

ISBN-13: 3319401890

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This book constitutes the refereed proceedings of the 12th Conference on Computability in Europe, CiE 2016, held in Paris, France, in June/July 2016. The 18 revised full papers and 19 invited papers and invited extended abstracts were carefully reviewed and selected from 40 submissions. The conference CiE 2016 has six special sessions – two sessions, cryptography and information theory and symbolic dynamics, are organized for the first time in the conference series. In addition to this new developments in areas frequently covered in the CiE conference series were addressed in the following sessions: computable and constructive analysis; computation in biological systems; history and philosophy of computing; weak arithmetic.

Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk
Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk

Author: A. Rod Gover

Publisher: American Mathematical Soc.

Published: 2015-04-09

Total Pages: 108

ISBN-13: 1470410923

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The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.

Locally AH-Algebras
Locally AH-Algebras

Author: Huaxin Lin

Publisher: American Mathematical Soc.

Published: 2015-04-09

Total Pages: 122

ISBN-13: 147041466X

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A unital separable -algebra, is said to be locally AH with no dimension growth if there is an integer satisfying the following: for any and any compact subset there is a unital -subalgebra, of with the form , where is a compact metric space with covering dimension no more than and is a projection, such that The authors prove that the class of unital separable simple -algebras which are locally AH with no dimension growth can be classified up to isomorphism by their Elliott invariant. As a consequence unital separable simple -algebras which are locally AH with no dimension growth are isomorphic to a unital simple AH-algebra with no dimension growth.

Spectral Means of Central Values of Automorphic L-Functions for GL(2)
Spectral Means of Central Values of Automorphic L-Functions for GL(2)

Author: Masao Tsuzuki

Publisher: American Mathematical Soc.

Published: 2015-04-09

Total Pages: 144

ISBN-13: 1470410192

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Starting with Green's functions on adele points of considered over a totally real number field, the author elaborates an explicit version of the relative trace formula, whose spectral side encodes the informaton on period integrals of cuspidal waveforms along a maximal split torus. As an application, he proves two kinds of asymptotic mean formula for certain central -values attached to cuspidal waveforms with square-free level.

Transfer of Siegel Cusp Forms of Degree 2
Transfer of Siegel Cusp Forms of Degree 2

Author: Ameya Pitale

Publisher: American Mathematical Soc.

Published: 2014-09-29

Total Pages: 120

ISBN-13: 0821898566

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Let be the automorphic representation of generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of . Using Furusawa's integral representation for combined with a pullback formula involving the unitary group , the authors prove that the -functions are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functorial lifting to a cuspidal representation of . Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of . As an application, the authors obtain analytic properties of various -functions related to full level Siegel cusp forms. They also obtain special value results for and