Related papers: Orbit Equivalence and Measured Group Theory

Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on…

Motivated by the work of Birman about the relationship between mapping class groups and braid groups, we discuss the relationship between the orbit braid group and the equivariant mapping class group on the closed surface $M$ with a free…

Stably supported quantales generalize pseudogroups and provide an algebraic context in which to study the correspondences between inverse semigroups and \'etale groupoids. Here we study a further generalization where a non-unital version of…

This paper develops a formal theory of musical scales and their harmonic coverings and introduces orbit covers: coverings obtained by translating a fixed subset across a scale via a group action. Orbit covers generalize familiar…

In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous…

We will show that group exactness is a von Neumann equivalence invariant. This result generalizes the previously known fact stating that group exactness is invariant under measure equivalence and W*-equivalence.

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…

I discuss group averaging as a method for quantising constrained systems whose gauge group is a noncompact Lie group. Focussing on three case studies, I address the convergence of the averaging, possible indefiniteness of the prospective…

In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this…

We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…

Recently a problem concerning the equivalence of joint measurability and coexistence of quantum observables was solved [15]. In this paper we generalize two known joint measurability results from sharp observables to the class of extreme…

This is a review with the ambitious goal of covering the recent progress in: 1) universal relations (in general relativity and alternative theories of gravity), and 2) neutron star models in alternative theories. We also aim to be…

We show that, contrarily to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of "observable". Nonorthogonal repeatability, however, occurs…

In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and…

The interplay between actions of Lie groups and monotone quantum metric tensors on the space of faithful quantum states of a finite-level system observed recently in DOI: 10.1140/epjp/s13360-020-00537-y and DOI: 10.1007/978-3-030-80209-7_17…

Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…

We define the orbit morphism of partial dynamical systems and prove that an orbit morphism being an isomorphism in the category of partial dynamical systems and orbit morphisms is equivalent to the existence of a continuous orbit…

Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and…

We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115, 020403 (2015)]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent…

In this paper we introduce a projective invarinat measure on the special unitary group. It is directly related to transition probabilities. It has some interesting connection with convex geometry. Applications to approximation of quantum…