Related papers: An improved proof of the Almost Stability Theorem

We consider dynamical semigroups with unbounded Kossakowski-Lindblad-Davies generators which are related to evolution of an open system with a tuned repeated harmonic perturbation. Our main result is the proof of existence of uniquely…

We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability.…

Let G be a finite graph with the non-k-order property (essentially, a uniform finite bound on the size of an induced sub-half-graph). A major result of the paper applies model-theoretic arguments to obtain a stronger version of…

We prove that if $G$ is a finitely generated group and $Z$ is a uniformly recurrent subgroup of $G$ then there exists a minimal system $(X,G)$ with $Z$ as its stability system. This answers a query of Glasner and Weiss \cite{GW} in the case…

A countable discrete group $\Gamma$ is said to be Frobenius stable if a function from the group that is "almost multiplicative" in the point Frobenius norm topology is "close" to a genuine unitary representation in the same topology. The…

We give new information about the relationship between the low-dimensional homology of a group and its derived series. This yields information about how the low-dimensional homology of a topological space constrains its fundamental group.…

We prove a pointwise ergodic theorem for quasi-probability-measure-preserving (quasi-pmp) locally countable measurable graphs, equivalently, Schreier graphs of quasi-pmp actions of countable groups. For ergodic graphs, the theorem gives an…

Using the calculus of variations, we prove that a Euclidean set of fixed Gaussian measure that nearly maximizes Gaussian noise stability is close to a half space. The main result proves a modification of a conjecture of Eldan from 2013: a…

We show that a relatively ergodic extension of measure-preserving dynamical systems has relative discrete spectrum if and only if it can be represented as a skew-product by a bundle of compact homogeneous spaces. Our result holds without…

This paper is the 10th in a sequence on the structure of sets of solutions to systems of equations over groups, projections of such sets (Diophantine sets), and the structure of definable sets over few classes of groups. In the 10th paper…

If $X$ is a smooth manifold and ${\mathcal{G}}$ is a subgroup of $Diff(X)$ we say that $(X,{\mathcal{G}})$ has the almost fixed point property if there exists a number $C$ such that for any finite subgroup $G\leq{\mathcal{G}}$ there is some…

We determine when two almost automorphisms of a regular tree are conjugate. This is done by combining the classification of conjugacy classes in the automorphism group of a level-homogeneous tree by Gawron, Nekrashevych and Sushchansky and…

We prove a criterion for the geometric and algebraic finiteness properties of vertex stabilisers of $G$-CW-complexes, given the finiteness properties of the group $G$ and of the stabilisers of positive dimensional cells. This generalises a…

We introduce a concept of tree-graded metric space and we use it to show quasi-isometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic…

We show that in closed string topology and in open-closed string topology with one $D$-brane, higher genus stable string operations are trivial. This is a consequence of Harer's stability theorem and related stability results on the…

We investigate properties of closed approximate subgroups of locally compact groups, with a particular interest for approximate lattices i.e. those approximate subgroups that are discrete and have finite co-volume. We prove an approximate…

We study manifolds endowed with an (almost) even Clifford (hermitian) structure and admitting a large automorphism group. We classify them when they are simply connected and the dimension of the automorphism group is maximal, and also prove…

The concept of homology, originally developed as a useful tool in algebraic topology, has by now become pervasive in quite different branches of mathematics. The notion particularly appears quite naturally in ergodic theory in the study of…

A discrete group is matricially stable if every function from the group to a complex unitary group that is "almost multiplicative" in the point-operator norm topology is "close" to a genuine unitary representation. It follows from a recent…

S.B. Rao conjectured in 1971 that graphic degree sequences are well quasi ordered by a relation defined in terms of the induced subgraph relation. In 2008, M. Chudnovsky and P. Seymour proved this long standing Rao's Conjecture by giving…