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From the mid-1970s, Eberhard Kirchberg undertook a remarkable extensive study of $C^*$-algebras exactness whose applications spread out to many branches of analysis. In this review we focus on the case of groupoid $C^*$-algebras for which…
We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…
We continue our study of ends non-compact manifolds. The over-arching aim is to provide an appropriate generalization of Siebenmann's famous collaring theorem that applies to manifolds having non-stable fundamental group systems at…
In this paper we construct examples of $CR$ deformations of Lorentzian hypersurfaces which are $CR$ embeddable at all points outside an arbitrarily small compact set whose interior contains a point where $CR$ embeddablity is not possible.
We provide a simple criterion for a non-singular and conservative Bernouilli action to have a weakly mixing Maharam extension. As an application, we show that every countable amenable group admits a stable type III_1 Bernoulli action,…
The purpose of this paper is to study the notion of relative extreme amenability for pairs of topological groups. We give a characterization by a fixed point property on universal spaces. In addition we introduce the concepts of an…
Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split…
This is a survey of our recent results on the amenability problem for Thompson's group $F$. They mostly concern esimating the density of finite subgraphs in Cayley graphs of $F$ for various systems of generators, and also equations in the…
We prove the existence of a weak solution to a non-isothermal compressible model for nematic liquid crystals. An initial-boundary value problem is studied in a bounded domain with large data. The existence of a global weak solution is…
We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.
We provide a class of non-contracting groups containing an infinite family of fractal and weakly regular branch groups, and study certain properties including abelianization, just infiniteness, and word problem. We present an example of a…
We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and…
In this paper we deal with four generalized notions of amenability which are called approximate, approximate weak, approximate cyclic and approximate $n$-weak amenability. The first two were introduced and studied by Ghahramani and Loy in…
It has been a longstanding problem whether every amenable operator algebra is isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a nonseparable counterexample. The existence of a separable counterexample remains an open…
We consider a model for prion proliferation that includes prion polymerization, polymer splitting, and polymer joining. The model consists of an ordinary differential equation for the prion monomers and a hyperbolic nonlinear differential…
Let $N$ be a submodule of a finitely generated module $M$ over a Noetherian ring. A method for the computation of the submodule generated by the envelope of $N$ is given. The relations between weakly prime submodules and their envelopes are…
In the recent paper by A. A. Klyachko, V. Yu. Miroshnichenko, and A. Yu. Olshanskii, it is proven that the center of any finite strongly verbally closed group is its direct factor. One of the results of the current paper is the…
We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure $M$, Polish group $G$ of permutations of $M$, and $n \geq 1$,…
We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular we show that, a large class of commutative hypergroups are weakly amenable with the…
A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable…