Group action ≈ Group action
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On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups Open
Convolutional neural networks have been extremely successful in the image recognition domain because they ensure equivariance to translations. There have been many recent attempts to generalize this framework to other domains, including gr…
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Flowing in Group Field Theory Space: a Review Open
We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension d≥3.…
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Group-symmetric holomorphic functions on a Banach space Open
We study the holomorphic functions on a complex Banach space $E$ that are invariant under the action of a given group of operators on $E$. A great variety of situations occur depending, of course, on the group and the space. Nevertheless, …
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Topological stability and pseudo-orbit tracing property of group actions Open
In this paper we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces and prove that if an action of a finitely generated group is expansive and has the pseudo-orbit tracing property, th…
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Poc Sets, Median Algebras and Group Actions Open
An extended Study of Dunwoody's Construction and Sageev's Theorem
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Cherednik and Hecke Algebras of Varieties with a Finite Group Action Open
This paper is an expanded and updated version of the preprint arXiv:math/0406499. It includes a more detailed description of the basics of the theory of Cherednik and Hecke algebras of varieties started in arXiv:math/0406499, as well as a …
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Orbit equivalence rigidity of equicontinuous systems Open
The paper is focused on the study of continuous orbit equivalence for minimal equicontinuous systems. We establish that every equicontinuous system is topologically conjugate to a profinite action, where the finite-index subgroups are not …
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Additive actions on toric varieties Open
By an additive action on an algebraic variety $X$ of dimension $n$ we mean a regular action $\mathbb{G}_a^n \times X \to X$ with an open orbit of the commutative unipotent group $\mathbb{G}_a^n$. We prove that if a complete toric variety $…
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Theoretical Aspects of Group Equivariant Neural Networks Open
Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and diffe…
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Besicovitch Covering Property on graded groups and applications to measure differentiation Open
We give a complete answer to which homogeneous groups admit homogeneous distances for which the Besicovitch Covering Property (BCP) holds. In particular, we prove that a stratified group admits homogeneous distances for which BCP holds if …
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Semigroup and Category-Theoretic Approaches to Partial Symmetry Open
This thesis is about trying to understand various aspects of partial symmetry using ideas from semigroup and category theory. In Chapter 2 it is shown that the left Rees monoids underlying self-similar group actions are precisely monoid HN…
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Graphs of curves on infinite-type surfaces with mapping class group actions Open
We study when the mapping class group of an infinite-type surface admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on . We introduce a topological invariant for infinite-type surfaces tha…
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Reductive group actions Open
In this paper, we study rationality properties of reductive group actions which are defined over an arbitrary field of characteristic zero. Thereby, we unify Luna's theory of spherical systems and Borel-Tits' theory of reductive groups. In…
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On large deviations for amenable group actions Open
By proving an amenable version of Katok's entropy formula and handling the quasi tiling techniques, we establish large deviations bounds for countable discrete amenable group actions. This generalizes the classical results of Lai-Sang Youn…
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On Følner sets in topological groups Open
We extend Følner’s amenability criterion to the realm of general topological groups. Building on this, we show that a topological group $G$ is amenable if and only if its left-translation action can be approximated in a uniform manner by a…
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Two simultaneous actions of big mapping class groups Open
We study two actions of big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. The first two pa…
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Additivity of higher rho invariants and nonrigidity of topological manifolds Open
Let $X$ be a closed oriented connected topological manifold of dimension $n\geq 5$. The structure group of $X$ is the abelian group of equivalence classes of all pairs $(f, M)$ such that $M$ is a closed oriented manifold and $f\colon M \to…
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Measurable equidecompositions for group actions with an expansion property Open
Given an action of a group \Gamma on a measure space \Omega , we provide a sufficient criterion under which two sets A, B\subset \Omega are \textit{measurably equidecomposable} , i.e., A can be partitioned into finitely many measurable pie…
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A variational principle of topological pressure on subsets for amenable group actions Open
In this paper, we establish a variational principle for topological pressure on compact subsets in the context of amenable group actions. To be precise, for a countable amenable group action on a compact metric space, say , for any potenti…
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Palindromic subshifts and simple periodic groups of intermediate growth Open
We describe a new class of groups of Burnside type, giving a procedure transforming an arbitrary non-free minimal action of the dihedral group on a Cantor set into an orbit-equivalent action of an infinite finitely generated periodic group…
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Doubling constructions: Global functoriality for non-generic cuspidal representations Open
We study the generalized doubling method for pairs of representations of $G\times GL_k$ where $G$ is a symplectic group, split special orthogonal group or split general spin group. We analyze the poles of the local integrals, and prove tha…
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A Local Resolution of the Problem of Time. II. Configurational Relationalism via a generalization of Group Averaging Open
In this article, we consider a second Problem of Time Facet. This started life as Wheeler's Thin Sandwich Problem, within the narrow context of 1) GR-as-Geometrodynamics, in particular its momentum constraint. 2) A Lagrangian variables lev…
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Invariant subsets under compact quantum group actions Open
We investigate compact quantum group actions on unital C^* -algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact …
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Frobenius algebras and homotopy fixed points of group actions on bicategories Open
We explicitly show that symmetric Frobenius structures on a finite-dimensional, semi-simple algebra stand in bijection to homotopy fixed points of the trivial SO(2)-action on the bicategory of finite-dimensional, semi-simple algebras, bimo…
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Some properties of distal actions on locally compact groups Open
We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We obtain a decomposition for contraction group…
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Key Structural Aspects for Adaptive Facades - Activity Progress from the EU-COST Action TU1403 ‘Structural’ Task Group Open
Adaptive facades are getting more and more widespread in modern buildings. These facade systems, among many others, need to fulfil the requirements of several structural considerations, such as structural safety, serviceability, durability…
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Continuous Combinatorics of Abelian Group Actions Open
This paper develops techniques which are used to answer a number of questions in the theory of equivalence relations generated by continuous actions of abelian groups. The methods center around the construction of certain specialized hyper…
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Periodic points for amenable group actions on dendrites Open
We show that if $G$ is a countable amenable group acting on a dendrite $X$, then $G$ has either a fixed point or a 2-periodic point in $X$.
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Giving to versus Taking from In- and Out-Group Members Open
In this experiment, we test whether subjects’ responses to variations in the action set in a dictator game depends on induced group identities. The action set includes choices in which the dictator can either give money to or take money fr…
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Hyperbolic and cubical rigidities of Thompson’s group<i>V</i> Open
In this article, we state and prove a general criterion allowing us to show that some groups are hyperbolically elementary, meaning that every isometric action of one of these groups on a Gromov-hyperbolic space either fixes a point at inf…