Related papers: Changing the Heights of Automorphism Towers by For…

We classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space and Urysohn sphere, among other related results.

In this paper, we prove that each automorphism of a surface braid group is induced by a homeomorphism of the underlying surface, provided that this surface is a closed, connected, orientable surface of genus at least 2, and the number of…

Let $T$ be any invertible, ergodic, aperiodic measure-preserving transformation of a Lebesgue probability space $(X, \calB, \mu)$, and \P\, any finite measurable partition of $X$. We show that a (finite) Alpern multitower may always be…

We introduce the notion of a contractible subshift. This is a strengthening of the notion of strong irreducibility, where we require that the gluings are given by a block map. We show that a subshift is a retract of a full shift if and only…

This article proposes an effective criterion for lifting automorphisms along regular coverings of graphs, with the covering transformation group being any finite abelian group.

Initially motivated by Hrushovski's paper on definability patterns, we obtain homeomorphisms between Ellis semigroups related to natural actions of the automorphism groups of first order structures and certain collections of types and…

We establish two consequences of the Kawamata--Morrison--Totaro cone conjecture, and prove them unconditionally in all dimensions. First, for a K-trivial variety, the natural action of its automorphism group on the set of ample divisor…

Macroscopic systems with continuous symmetries subjected to oscillatory fields have phases and transitions that are qualitatively different from their equilibrium ones. Depending on the amplitude and frequency of the fields applied,…

The possibility of materials that are governed by a fixed point related to small world networks is discussed. In particular, large-scale Monte Carlo simulations are performed on Ising ferromagnetic models on two different small-world…

We study random trees which are invariant in law under the operation of contracting each edge independently with probability $p\in(0,1)$. We show that all such trees can be constructed through Poissonian sampling from a certain class of…

We prove an acylindrical accessibility theorem for finitely generated groups acting on $\mathbf R$-trees. Namely, we show that if $G$ is a freely indecomposable non-cyclic $k$-generated group acting minimally and $M$-acylindrically on an…

We construct and study the moduli of hypersurfaces in toric orbifolds. Let $X$ be a projective toric orbifold and $\alpha \in Cl(X)$ an ample class. The moduli space is constructed as a quotient of the linear system $|\alpha|$ by $G =…

Automorphism groups are intrincate conjugacy invariants for subshifts, which can reveal important features of the dynamical structure of a shift action. One important case is the study of automorphism groups when the underlying subshift has…

We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms. Several applications to topology are given: we prove that…

We prove twisted homological stability with polynomial coefficients for automorphism groups of free nilpotent groups of any given class. These groups interpolate between two extremes for which homological stability was known before, the…

Controlling the topology of structures self-assembled from a set of heterogeneous building blocks is highly desirable for many applications, but is poorly understood theoretically. Here we show that the thermodynamic theory of self-assembly…

The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of…

We establish a sharp sufficient condition for groups acting on trees to be highly transitive when the action on the tree is minimal of general type. This gives new examples of highly transitive groups, including icc non-solvable…

This article shows that for unitary dual reductive pairs the first occurrence of theta lift of an irreducible cuspidal automorphic representation is irreducible. It also proves a refined tower property for theta lifts and the involutive…

We prove several results concerning automorphism groups of quasismooth complex weighted projective hypersurfaces; these generalize and strengthen existing results for hypersurfaces in ordinary projective space. First, we prove in most cases…