Related papers: Group actions and geometric combinatorics in ${\ma…

We show that group actions on many treelike compact spaces are not too complicated dynamically. We first observe that an old argument of Seidler implies that every action of a topological group $G$ on a regular continuum is null and…

Given a self-similar groupoid action $(G,E)$ on the path space of a finite graph, we study the associated Exel-Pardo \'etale groupoid ${\mathcal G}(G,E)$ and its $C^*$-algebra $C^*(G,E)$. We review some facts about groupoid actions, skew…

Liedtke (2008) has introduced group functors $K$ and $\tilde K$, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of central extensions…

It is proved that if S^6 possesses an integrable complex structure, then there exists a 1-dimensional family of pairwise different exotic complex structures on P_3(C). This follows immediately from the main result of the paper: S^6 is not…

We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on a compact manifold. The structure is not assumed to be unimodular, so an invariant measure may not exist. Ergodic…

We introduce the `Fourier transform' F_C on the isotropic cone C associated to an indefinite quadratic form of signature (n_1,n_2) on R^n (n=n_1+n_2: even). This transform is in some sense the unique and natural unitary operator on L^2(C),…

Every affine isometric action $\alpha$ of a group $G$ on a real Hilbert space gives rise to a nonsingular action $\hat{\alpha}$ of $G$ on the associated Gaussian probability space. In the recent paper [AIM19], several results on the…

We obtain new bounds on short Weil sums over small multiplicative subgroups of prime finite fields which remain nontrivial in the range the classical Weil bound is already trivial. The method we use is a blend of techniques coming from…

Here we present four independent advances which facilitate the computation of phonons and their interactions from first-principles. First, we implement a group-theoretical approach to construct the order N Taylor series of a d-dimensional…

By treating the vacuum as a medium, H. Euler and W. Heisenberg estimated the non-linear interactions between photons well before the advent of Quantum Electrodynamics. In a modern language, their result is often presented as the archetype…

We prove that the mapping class group $\Gamma_{g,n}$ for surfaces of negative Euler characteristic has a cofinite universal space $\E$ for proper actions (the resulting quotient is a finite $CW$-complex). The approach is to construct a…

Let X be a normal affine T-variety of complexity at most one over a perfect field k, where T stands for the split algebraic torus. Our main result is a classification of additive group actions on X that are normalized by the T-action. This…

We study superstable groups acting on trees. We prove that an action of an $\omega$-stable group on a simplicial tree is trivial. This shows that an HNN-extension or a nontrivial free product with amalgamation is not $\omega$-stable. It is…

We prove a general result about the decomposition on ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree…

We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of non-compact real reductive Lie groups on topological…

We construct an algebra of generalized functions $^*\mathcal{E}(\mathbb{R}^d)$. We also construct an embedding of the space of Schwartz distributions $\mathcal{D}^\prime(\mathbb{R}^d)$ into $^*\mathcal{E}(\mathbb{R}^d)$ and thus present a…

In this article, we give a general construction of spectral triples from certain Lie group actions on unital C*-algebras. If the group G is compact and the action is ergodic, we actually obtain a real and finitely summable spectral triple…

We study admissible and equivalence point transformations between generalized multidimensional nonlinear Schr\"odinger equations and classify Lie symmetries of such equations. We begin with a wide superclass of Schr\"odinger-type equations,…

A general framework for investigating topological actions of $Z^d$ on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces of $R^d$. Here we completely describe this expansive…

We obtain global analytic hypoellipticity for a class of differential operators that can be expressed as a zero-order perturbation of a sum of squares of vector fields with real-analytic coefficients on compact Lie groups. The key…