Related papers: Bratteli-Vershik models for partial actions of $\m…

We give the first example of a connected 4-regular graph whose Laplace operator's spectrum is a Cantor set, as well as several other computations of spectra following a common ``finite approximation'' method. These spectra are simple…

Given a finite alphabet $\Lambda$, and a not necessarily finite type subshift $X\subseteq \Lambda^\infty$, we introduce a partial action of the free group $F(\Lambda)$ on a certain compactification $\Omega_X$ of $X$, which we call the…

We consider a natural basis of the Iwahori fixed vectors in the Whittaker model of an unramified principal series representation of a split semisimple p- adic group, indexed by the Weyl group. We show that the elements of this basis may be…

We survey, and extend, results on the adjoint action of the homeomorphism group $H(X)$ on the space of surjective continuous maps, $C_s(X)$, where $X$ is a Cantor set. We look also at the restriction of the action to various dynamically…

We investigate oriented graphs based on the curve complex $C(S)$ of a closed surface $S$ and induced by functions on the vertex set of $C(S)$. In particular, we introduce the Dehn quasi-homothetic functions, which behave similarly to…

In this article we study conditions to be a continuous or a measurable eigenvalue of finite rank minimal Cantor systems, that is, systems given by an ordered Bratteli diagram with a bounded number of vertices per level. We prove that…

Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a partial skew inverse semigroup ring. We use this to show that for a partial action of a discrete group on a locally compact Hausdorff topological space,…

In this paper we develop an abstract setup for hamiltonian group actions as follows: Starting with a continuous 2-cochain $\omega$ on a Lie algebra $h$ with values in an $h$-module $V$, we associate subalgebras $sp(h,\omega) \supeq…

For typical properly ordered and minimal Bratteli diagrams $(B,\leq_r)$, it is shown that there are finitely many invariant distributions $\mathcal{D}_i$ which are the only obstructions to solving the cohomological equation $f = u-u\circ…

Quasiregular maps are differentiable almost everywhere maps which are analogous to holomorphic maps in the plane for higher real dimensions. Introduced by Gutlyanskii et al, the infinitesimal space is a generalization of the notion of…

Based on the realization of quantum Borcherds-Bozec algebra $\widetilde{\mathbf{U}}$ and quantum generalized Kac-Moody algebra ${}^B\widetilde{\mathbf{U}}$ via semi-derived Ringel-Hall algebra of a quiver with loops, we deduce the braid…

Let $\mathfrak{g}$ be a finite-dimensional semisimple complex Lie algebra and $\theta$ an involutive automorphism of $\mathfrak{g}$. According to G. Letzter, S. Kolb and M. Balagovi\'c the fixed-point subalgebra $\mathfrak{k} =…

Let $V$ be a smooth, projective, rationally connected variety, defined over a number field $k$, and let $Z\subset V$ be a closed subset of codimension at least two. In this paper, for certain choices of $V$, we prove that the set of…

We provide a detailed treatment of Weyl-Titchmarsh theory for half-lattice and full-lattice Cantero-Moral-Velazquez (CMV) operators and discuss their systems of orthonormal Laurent polynomials on the unit circle, spectral functions,…

We introduce a graph-theoretical interpretation of an induced action of Aut$(\Gamma)$ in the discrete de Rham cohomology of a finite graph $\Gamma$. This action produces a splitting of Aut$(\Gamma)$ that depends on the cycles of $\Gamma$.…

We extend the lattice-theoretic approach of Brandhorst--Cattaneo to classify algebraically trivial actions on the known IHS manifolds, up to deformation and birational conjugacy. In particular, we classify even order algebraically trivial…

This article shows that knowledge of the Dirichlet-Neumann map on certain subsets of the boundary for input functions supported roughly on the rest of the boundary can be used to determine a magnetic Schr\"{o}dinger operator. With some…

Rauzy-type dynamics are group actions on a collection of combinatorial objects. The first and best known example concerns an action on permutations, associated to interval exchange transformations (IET) for the Poincar\'e map on compact…

The Virasoro operations in Witten's theory of two-dimensional topological gravity have a homotopy-theoretic interpretation as endomorphisms of an ordinary cohomology theory with coefficients in a localization of I. Schur's ring \Delta of…

This paper is an exposition of heuristics related to Witten's functional integral, relating it to Vassiliev invariants and to the Kontsevich integrals that can be used to produce Vassiliev invariants of knots and links.In particular, we…