Related papers: Generalized Gottschalk's conjecture for sofic grou…

We study the notion of linear sofic approximations for algebras, analogous to the concept of sofic representations for groups. We prove that for a finitely generated amenable $K$-algebra with no zero divisors, all linear sofic…

For linear non-uniform cellular automata (NUCA) over an arbitrary universe, we introduce and investigate their dual linear NUCA. Generalizing results for linear CA, we show that dynamical properties namely pre-injectivity, resp.…

Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do not…

In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the…

We study through symmetry principles the form of the functions in the generalizated scalar-tensor theories under the self-similar hypothesis. The results obtained are absolutely general and valid for all the Bianchi models and the flat FRW…

Let $G$ be a countable monoid and let $A$ be an Artinian group (resp. an Artinian module). Let $\Sigma \subset A^G$ be a closed subshift which is also a subgroup (resp. a submodule) of $A^G$. Suppose that $\Gamma$ is a finitely generated…

In this paper, we show how to use the framework of mod-Gaussian convergence in order to study the fluctuations of certain models of random graphs, of random permutations and of random integer partitions. We prove that, in these three…

We give an alternate proof of a Theorem of Elek and Szabo establishing L\"uck's determinant conjecture for sofic groups. Our proof is based on traces on group C*-algebras. We briefly discuss the relation with Atiyah's problem on the…

We solve the twisted conjugacy problem on Thompson's group F. We also exhibit orbit undecidable subgroups of Aut(F), and give a proof that Aut(F) and Aut_+(F) are orbit decidable provided a certain conjecture on Thompson's group T is true.…

In this note, we give explicit expressions of Gauss sums for general (resp. special) linear groups over finite fields, which involves Gauss sums (resp. Kloosterman sums). The key ingredient is averaging such sums over Borel subgroups. As…

Decomposition complexity for metric spaces was recently introduced by Guentner, Tessera, and Yu as a natural generalization of asymptotic dimension. We prove a vanishing result for the continuously controlled algebraic K-theory of bounded…

For a number field $k$ and an odd prime $p$, let $\tilde{k}$ be the compositum of all the ${\mathbb Z}_p$-extensions of $k$, $\tilde{\Lambda }$ the associated Iwasawa algebra, and $X(\tilde{k})$ the Galois group over $\tilde{k}$ of the…

We establish some structural results for the Witt and Grothendieck-Witt groups of schemes over $\mathbb{Z}[1/2]$, including homotopy invariance for Witt groups and a formula for the Witt and Grothendieck-Witt groups of punctured affine…

We prove Carlos Simpson's "semi-strictification" (or "weak unit") conjecture in the case of infinity-groupoids. More precisely, we introduce two precise versions of the conjecture, the "general" and the "regular" conjecture, involving two…

We show that amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This covers amenability of a wide class groups, the amenability of which…

The known facts about solvability of equations over groups are considered from a more general point of view. A generalized version of the theorem about solvability of unimodular equations over torsion-free groups is proved. In a special…

For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. It contains the algebra WAP(G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and…

The normal covering number $\gamma(G)$ of a finite, non-cyclic group $G$ is the least number of proper subgroups such that each element of $G$ lies in some conjugate of one of these subgroups. We prove that there is a positive constant $c$…

This paper is dedicated to a further study of derived Azumaya algebras. The first result we obtain is a Beauville-Laszlo-style property for such objects (considered up to Morita equivalence), which is consequence of a more general…

The analytic von Neumann regular closure $R(\Gamma)$ of a complex group algebra $\C\Gamma$ was introduced by Linnell and Schick. This ring is the smallest $*$-regular subring in the algebra of affiliated operators $U(\Gamma)$ containing…