Structural Ramsey Theory Of Metric Spaces And Topological Dynamics Of Isometry Groups
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Structural Ramsey Theory of Metric Spaces and Topological Dynamics of Isometry Groups
Author: L. Nguyen Van Th
language: en
Publisher: American Mathematical Soc.
Release Date: 2010-06-11
In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces--called ultrahomogeneous--is closely related to the combinatorial behavior of the class of their finite metric spaces. The purpose of the present paper is to explore different aspects of this connection.
Asymptotic Geometric Analysis
Author: Monika Ludwig
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-27
Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as the dimension tends to infinity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in the Fall of 2010 continued an established tradition of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces * Concentration of measure and isoperimetric inequalities, optimal transportation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Random matrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working in a wide range of mathematical sciences—in particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science.
$C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics
Author: Klaus Thomsen
language: en
Publisher: American Mathematical Soc.
Release Date: 2010-06-11
The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.