Related papers: URP, comparison, mean dimension, and sharp shift e…

Let $G$ be a group and let ${\mathcal G}$ be a free factor system of $G$, namely a free splitting of $G$ as $G=G_1*\dots*G_k*F_r$. In this paper, we study the set of train track points for ${\mathcal G}$-irreducible automorphisms $\phi$…

Let $X$ be a rational homogeneous space and let $QH^*(X)_{loc}^\times$ be the group of invertible elements in the small quantum cohomology ring of $X$ localised in the quantum parameters. We generalise results of arXiv:math/0609796 and…

We generalize Renault's notion of measurewise amenability to actions of second countable, Hausdorff, \'etale groupoids on separable $C^*$-algebras and show that measurewise amenability characterizes nuclearity of the crossed product…

Let $R\to U$ be an associative ring epimorphism such that $U$ is a flat left $R$-module. Assume that the related Gabriel topology $\mathbb G$ of right ideals in $R$ has a countable base. Then we show that the left $R$-module $U$ has…

Let G be one of the local gauge groups C(X,U(n)), C^\infty(X,U(n)), C(X,SU(n)) or C^\infty(X,SU(n)) where X is a compact Riemannian manifold. We observe that G has a nontrivial group topology, coarser than its natural topology, w.r.t. which…

Let $G$ be a countable discrete amenable group, ${\cal M}$ a McDuff factor von Neumann algebra, and $A$ a separable nuclear weakly dense C$^*$-subalgebra of ${\cal M}$. We show that if two centrally free actions of $G$ on ${\cal M}$ differ…

We resolve key open questions regarding approximation properties and their permanence for Fell bundles over locally compact groups. Specifically, we establish the equivalence between the B\'edos--Conti approximation property (BCAP) and the…

We introduce the notion of proper proximality for finite von Neumann algebras, which naturally extends the notion of proper proximality for groups. Apart from the group von Neumann algebras of properly proximal groups, we provide a number…

We show that for every finite subgroup $G$ of $Aut(F_n)$, the fixed point subcomplex $X_n^G$ is contractible, where $F_n$ is the free group on $n$ letters and $X_n$ is the spine of ``auter space'' constructed by Hatcher and Vogtmann. In…

There has been much interest in generalizing Kesten's criterion for amenability in terms of a random walk to other contexts, such as determining amenability of a deck covering group by the bottom of the spectrum of the Laplacian or entropy…

We consider the moduli spaces of flat $SL(n, C)$-bundles on Riemann surfaces with one puncture when we fix the conjugacy class ${\cal C}$ of the monodromy transformation around the puncture. We show that under a certain condition on the…

We develop a relative boundary theory for actions of discrete groups on compact spaces and use it to derive rigidity results for reduced crossed products. For a discrete group $\Gamma$ acting on a compact space $X$ and a subgroup $H$, we…

We undertake a systematic study of irreducible affine isometric actions of locally compact groups on Hilbert spaces. It turns out that, while that are a few parallels of this study to the by now classical theory of irreducible unitary…

It is shown that, for an arbitrary free and minimal $\mathbb Z^n$-action on a compact Hausdorff space $X$, the crossed product C*-algebra $\mathrm{C}(X)\rtimes\mathbb Z^n$ always has stable rank one, i.e., invertible elements are dense.…

It is well known that a dense subgroup $G$ of the complex unitary group $U(d)$ cannot be amenable as a discrete group when $d>1$. When $d$ is large enough we give quantitative versions of this phenomenon in connection with certain estimates…

Let $G$ be a discrete countable group and $C$ its central subgroup with $G/C$ treeable. We show that for any treeable action of $G/C$ on a standard probability space $X$, the groupoid $G\ltimes X$ is isomorphic to the direct product of $C$…

Sharp comparison theorems are derived for all eigenvalues of the (weighted) Laplacian, for various classes of weighted-manifolds (i.e. Riemannian manifolds endowed with a smooth positive density). Examples include Euclidean space endowed…

Let $E$ be a number field and $X$ a smooth geometrically connected variety defined over a characteristic $p$ finite field. Given an $n$-dimensional pure $E$-compatible system of semisimple $\lambda$-adic representations of the \'etale…

A new concept of (asymptotic) qualitative robustness for plug-in estimators based on identically distributed possibly dependent observations is introduced, and it is shown that Hampel's theorem for general metrics $d$ still holds. Since…

Let $G$ be a countable infinite discrete amenable group.It should be noted that a $G$-system $(X,G)$ naturally induces a $G$-system $(\mathcal{M}(X),G)$, where $\mathcal{M}(X)$ denotes the space of Borel probability measures on the compact…