Related papers: On Mixing Constructions with Algebraic Spacers

We prove mixing on a general class of rank-one transformations containing all known examples of rank-one mixing, including staircase transformations and Ornstein's constructions, and a variety of new constructions.

We prove that a rank one transformation satisfying a condition called restricted growth is a mixing transformation if and only if the spacer sequence for the transformation is uniformly ergodic. Uniform ergodicity is a generalization of the…

We prove that mixing on rank-one transformations is equivalent to the spacer sequence being slice-ergodic. Slice-ergodicity, introduced in this paper, generalizes the notion of ergodic sequence to the uniform convergence of ergodic averages…

We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a…

We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any $f : \mathbb{N} \to \mathbb{N}$ with $f(n)/n$ increasing and…

Suppose we wish to embed an (associative) $k$-algebra $A$ in a $k$-algebra $R$ generated in some specified way; e.g., by two elements, or by copies of given $k$-algebras $A_1,$ $A_2,$ $A_3.$ Several authors have obtained sufficient…

J.-P. Thouvenot and the author showed via different approaches that the centralizer of a mixing rank-one infinite measure preserving transformation was trivial. In this note the author presents his joining proof. We also consider…

We consider suspension flows built over interval exchange transformations with the help of roof functions having an asymmetric logarithmic singularity. We prove that such flows are strongly mixing for a full measure set of interval exchange…

In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…

Fix a prime number $p$. We report on some recent developments in algebraic geometry (broadly construed) over $p$-adically complete commutative rings. These developments include foundational advances within the subject as well as external…

We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.

We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope…

We introduce a new type of Hessian matrix, that we call Mixed Hessian. The mixed Hessian is used to compute the rank of a multiplication map by a power of a linear form in a standard graded Artinian Gorenstein algebra. In particular we…

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…

In this paper, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our…

We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset $E\subset\Bbb N\cup\{\infty\}$ as the set of essential…

Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among…

In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.

We study arrangements of intervals in $\mathbb{R}^2$ for which many pairs form trapezoids. We show that any set of intervals forming many trapezoids must have underlying algebraic structure, which we characterise. This leads to some…

The article concerns the existence and uniqueness of quantisations of cluster algebras. We prove that cluster algebras with an initial exchange matrix of full rank admit a quantisation in the sense of Berenstein-Zelevinsky and give an…