Related papers: Dynamical simplices and minimal homeomorphisms

A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of G are perturbable to genuine representations in the point-norm topology. For large classes of groups G, we show that…

We prove that the Cuntz-Pimsner algebra associated to any surjective aperiodic one-sided subshift with finitely many left special elements has finite nuclear dimension, which is especially the case for every surjective aperiodic subshift…

The higher characteristics w_m(G) for a finite abstract simplicial complex G are topological invariants that satisfy k-point Green function identities and can be computed in terms of Euler characteristic in the case of closed manifolds,…

Let $k$ be a field of characteristic two. We prove that a non constant monic polynomial $f\in k[X]$ of degree $n$ is the minimal/characteristic polynomial of a symmetric matrix with entries in $k$ if and only if it is not the product of…

Let X be a h-homogeneous zero-dimensional compact Hausdorff space, i.e. X is a Stone dual of a homogeneous Boolean algebra. Using the dual Ramsey theorem and a detailed combinatorial analysis of what we call stable collections of subsets of…

We prove that any absolutely continuous probability measure on a high-dimensional linear space has low-dimensional marginals that are approximately spherically-symmetric.

A dynamical system is a pair $(X,G)$, where $X$ is a compact metrizable space and $G$ is a countable group acting by homeomorphisms of $X$. An endomorphism of $(X,G)$ is a continuous selfmap of $X$ which commutes with the action of $G$. One…

Let X be a zero-dimensional compact space such that all non-empty clopen subsets of X are homeomorphic to each other, and let H(X) be the group of all self-homeomorphisms of X with the compact-open topology. We prove that the Roelcke…

A well-known consequence of the ergodic decomposition theorem is that the space of invariant probability measures of a topological dynamical system, endowed with the weak$^*$ topology, is a non-empty metrizable Choquet simplex. We show that…

We study criteria for the existence of a dense or comeager conjugacy class in the automorphism group of a given measure on the Cantor space. We concentrate on good measures, defined by Akin [\emph{Trans.\ Amer.\ Math.\ Soc.} \textbf{357}…

Let $M$ be a compact manifold of dimension at least 2. If $M$ admits a minimal homeomorphism then $M$ admits a minimal noninvertible map.

For a given graph G and an associated class of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in G, the collection of all possible spectra for such matrices is considered. Building on the pioneering work…

Let $G$ be a split simply-connected group of type $D$ or $E$. The minimal automorphic representation $\Pi$ of $G(\mathbb A)$ admits a realization on a space of functions $\mathcal S(X(\mathbb A))$ for a variety $X$. In this paper we write…

We use weighted polynomial approximation to prove the existence of a compact set K with non-empty interior and a function f is dense in the space A(K) of all continuous functions on K that are holomorphic in the interior of K, endowed with…

The principal aim of this paper is to give a dynamical presentation of the Jiang-Su algebra. Originally constructed as an inductive limit of prime dimension drop algebras, the Jiang-Su algebra has gone from being a poorly understood oddity…

We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kahler potentials on a compact Kahler manifold thus confirming a conjecture of Chen and give some applications in Kahler geometry, including a…

We show that given a compact minimal system $(X,g)$ and an element $h$ of the topological full group $\tau[g]$ of $g$, then the infinite orbits of $h$ admit a locally constant orientation with respect to the orbits of $g$. We use this to…

We study lower and upper bounds of the Hausdorff dimension for sets which are wiggly at scales of positive density. The main technical ingredient is a construction, for every continuum K, of a Borel probabilistic measure \mu with the…

Let U denote a simply connected compact Lie group, let K denote the fixed point set for an involutive automorphism of U, and let m denote the U-invariant probability measure on the symmetric space U/K. Consider the geodesic embedding U/K…

The deck, $\mathcal{D}(X)$, of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}]\colon x \in X\}$, where $[Y]$ denotes the homeomorphism class of $Y$. A space $X$ is (topologically) reconstructible if whenever…