Publications related to Non-Supramenable Groups Acting On Locally Compact Spaces

A type I conjecture and boundary representations of hyperbolic groups

We establish new results on the weak containment of quasi-regular and Koopman representations of a second countable locally compact group G

G

associated with nonsingular G

G

-spaces. We deduce that any two boundary representations of a hyperbolic locally ...

WILEY2023

Compact, Spatial-mode-interaction-free, Ultralow-loss, Nonlinear photonic integrated circuits

Tobias Kippenberg, Rui Ning Wang, Xinru Ji, Zheru Qiu, Junqiu Liu, Jijun He

We implement Euler bends to build compact high-Q Si3N4 racetrack microresonators, featuring a small footprint of only 0.21 mm(2) for 19.8 GHz FSR. We demonstrate that these multi-mode microresonators can be operated in the single-mode regime and generate a ...

IEEE2022

A combinatorial proof of a sumset conjecture of Furstenberg

Florian Karl Richter

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if

\log r / \log s

is irrational and

X

and

Y

are

\times r

- and

\times s

-invariant subsets of

[0,1]

, respectively, then $\dim_\text{ ...

2021

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Maria Carola Colombo, Silja Noëmi Aline Haffter

We consider the SQG equation with dissipation given by a fractional Laplacian of order α

2021

On the stress tensor light-ray operator algebra

Grégoire Olivier Mathys, Matthew Thomas Walters, Alexandre Mathieu Frédéric Belin

We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and ...

2021

Geometric ergodicity for some space-time max-stable Markov chains

Erwan Fabrice Koch

Max-stable processes are central models for spatial extremes. In this paper, we focus on some space-time max-stable models introduced in Embrechts et al. (2016). The processes considered induce discrete-time Markov chains taking values in the space of cont ...

ELSEVIER SCIENCE BV2019

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Masato Mimura

The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union ...

2019

Extensive amenability and an application to interval exchanges

Nicolas Monod, Nicolas Matte Bon

Extensive amenability is a property of group actions which has recently been used as a tool to prove amenability of groups. We study this property and prove that it is preserved under a very general construction of semidirect products. As an application, w ...

2018

Hochschild homology and cohomology of down–up algebras

We present a detailed computation of the cyclic and the Hochschild homology and cohomology of generic and 3-Calabi–Yau homogeneous down–up algebras. This family was defined by Benkart and Roby in [3] in their study of differential posets. Our calculations ...

2018

Representing groups against all odds

Maxime Gheysens

We investigate how probability tools can be useful to study representations of non-amenable groups. A suitable notion of "probabilistic subgroup" is proposed for locally compact groups, and is valuable to induction of representations. Nonamenable groups ad ...

EPFL2017

Non-Supramenable Groups Acting On Locally Compact Spaces

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A type I conjecture and boundary representations of hyperbolic groups

Compact, Spatial-mode-interaction-free, Ultralow-loss, Nonlinear photonic integrated circuits

A combinatorial proof of a sumset conjecture of Furstenberg

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

On the stress tensor light-ray operator algebra

Geometric ergodicity for some space-time max-stable Markov chains

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Extensive amenability and an application to interval exchanges

Hochschild homology and cohomology of down–up algebras

Representing groups against all odds

Compact, Spatial-mode-interaction-free, Ultralow-loss, Nonlinear photonic integrated circuits

A type I conjecture and boundary representations of hyperbolic groups

A combinatorial proof of a sumset conjecture of Furstenberg

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Extensive amenability and an application to interval exchanges

On the stress tensor light-ray operator algebra

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Hochschild homology and cohomology of down–up algebras

Geometric ergodicity for some space-time max-stable Markov chains

Representing groups against all odds