Related papers: Coamenability and cospectral radius for orbit equi…

Some aspects of phase transitions can be more conveniently studied in the orbit space of the action of the symmetry group. After a brief review of the fundamental ideas of this approach, I shall concentrate on the mathematical aspect and…

Since the work of Ornstein and Weiss in 1987 (J. Analyse Math. 48 (1987)) it has been understood that the natural category for classical ergodic theory would be probability measure preserving actions of discrete amenable groups. A…

We consider random walks on countable groups. A celebrated result of Kesten says that the spectral radius of a symmetric walk (whose support generates the group as a semigroup) is equal to one if and only if the group is amenable. We give…

Recently, Chach\'olski, Neeman, Pitsch, and Scherer studied, in a series of three papers, model approximations for the unbounded category of cochain complexes over a commutative ring. These approximations allow to construct relative…

Let R be a commutative ring containing 1/2. We compute the R-cohomology ring of the configuration space F(m,k) of k ordered points in the m-dimensional real projective space. The method uses the observation that the orbit configuration…

The note identifies which which couniversal spaces have suspension spectra equivalent to commutative orthogonal ring G-spectra for a compact Lie group G. These are precisely those whose cofamily is closed under passage to finite index…

The goal of this note is to announce certain results in orbit equivalence theory, especially concerning the approximation of p.m.p. standard equivalence relations by increasing sequence of sub-relations, with applications to the behavior of…

In this note, we first give a criterion of pseudo-Einstein contact forms and then affirm the CR analogue of Frankel conjecture in a closed, spherical, strictly pseudoconvex CR manifold of nonnegative pseudohermitian curvature on the space…

In the present work, metrics which lead to projected closed orbits are found by comparing the relativistic differential equation of orbits with the corresponding classical differential equation. Physical and geometrical properties of these…

In this paper, we review the approach leading to cosmic polarization rotation observation and present the current status with an outlook. In the study of the relations among equivalence principles, we found that long-range…

We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and…

We establish two conditions equivalent to coamenability for type I locally compact quantum groups. The first condition is concerned with the spectra of certain convolution operators on the space…

We compute the Dolbeault cohomology ring of the configuration spaces of $\mathbb{C}^n$ and construct a spectral sequence that converges to the Dolbeault cohomology ring of the configuration spaces of an arbitrary complex manifold.

We construct models for the classifying spaces of coabelian subgroups of right-angled Coxeter groups as homotopy orbit spaces of real moment-angle complexes, generalizing well-known models for the classifying space of a right-angled Coxeter…

This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix theory, including the randomized Horn's problem, the…

We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some formal resemblance with the quantum…

We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…

We complete the classification of isometric cohomogeneity-one actions on all symmetric spaces of noncompact type up to orbit equivalence.

We give a survey of various recent developments in orbit equivalence and measured group theory. This subject aims at studying infinite countable groups through their measure preserving actions.

We analyze Euclidean spheres in higher dimensions and the corresponding orbit equivalence relations induced by the group of rational rotations from the viewpoint of descriptive set theory. It turns out that such equivalence relations are…