Related papers: Future directions in locally compact groups

This paper contains several results about the Chabauty space of a general locally compact abelian group. Notably, we determine its topological dimension, we characterize when it is totally disconnected or connected; we characterize isolated…

In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We develop the theory completely within the von Neumann algebra framework. At various points, we also do…

We describe the global structure of totally disconnected locally compact groups having a linear open compact subgroup. Among the applications, we show that if a non-discrete, compactly generated, topologically simple, totally disconnected…

In this paper we consider the existence of dense embeddings of Limit groups in locally compact groups generalizing earlier work of Breuillard, Gelander, Souto and Storm [GBSS] where surface groups were considered. Our main results are…

Our aim is to find some new links between linear (circular) orderability of groups and topological dynamics. We suggest natural analogs of the concept of algebraic orderability for topological groups involving order-preserving actions on…

This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…

In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…

We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.

We prove continuity results for abstract epimorphisms of locally compact groups onto finitely generated groups.

In this paper, we survey some of the recent advances on embeddings into finitely generated (left-orderable) simple group such that the overgroup preserves algorithmic, geometric, or algebraic information about the embedded group. We discuss…

This habilitation memoir (in French, submitted in May 2014) is made up of five chapters, each being an introduction to work of the author between 2006 and 2014. The core of the memoir consists of the first three chapters, pertaining to…

In the framework of locally compact quantum groups, we study cocycle actions. We develop the cocycle bicrossed product construction, starting from a matched pair of locally compact quantum groups. We define exact sequences and establish a…

The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…

The rapidly expanding corpus of medical research literature presents major challenges in the understanding of previous work, the extraction of maximum information from collected data, and the identification of promising research directions.…

These are the lecture notes of a 2-hour mini-course on Lie groups over local fields presented at the "Workshop on Totally Disconnected Groups, Graphs and Geometry" at the Heinrich-Fabri-Institut Blaubeuren in May 2007. The goal of the notes…

In this short survey article, we try to list maximum number of known results on class preserving automorphisms of finite $p$-groups. We conclude the survey with some interesting (at least for the author) open problems on this topic.

The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…

This thesis is devoted to the study of the interactions existing between the algebraic structure of locally compact groups and the properties of their continuous unitary representations, with a special emphasis on the Type I groups. On the…

The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this…

It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones as topological groups. In this paper the…