Research

This page is about a french-speaking working group around non-sofic groups. Details are given in the french version of this page.

Broadly speaking, my research focuses on group theory. I am particularly interested in combinatorial, geometric, and dynamical properties of countable groups, as well as certain connections with operator algebras and Polish groups. In my recent work, I am particularly interested in (discrete or topological) high transitivity , (dense) embeddings in certain Polish groups, and the properties of the space of subgroups (of a countable group G) and the dynamical system obtained when G acts by conjugation. In the past, I have worked on large-scale geometric properties such as coarse embeddings in Hilbert spaces or weak forms of amenability such as the Haagerup property and inner amenability, as well as on the space of marked finitely generated groups. ...

My scientific publications, including preprints, are exhaustively referenced in HAL. This is the page I update most often when it comes to revisions. I also post the published versions of my articles there whenever possible. You can also find me on ArXiV, ORCID and ResearchGate, but these sources are less up-to-date than HAL.

Space of marked groups and Baumslag-Solitar groupsEspace des groupes marqués et groupes de Baumslag-Solitar Original title : Espace des groupes marqués et groupes de Baumslag-Solitar Defense : 5 décembre 2005, à l’Université de Neuchâtel Comitee : Prof. Alain Valette (advisor, Neuchâtel), Dr. Paul Jolissaint (referee, Neuchâtel), Prof. Goulnara Arjantseva (referee, Genève), Prof. Thomas Delzant (referee, Strasbourg), Prof. Bruno Colbois (Neuchâtel) Direct access : Version pdf DOI : 10.35662/unine-thesis-1845 Keywords Baumslag-Solitar groups, inner amenability, HNN extensions, space of marked groups, groups acting on trees, a-T-menability, presentations. Abstract Baumslag-Solitar groups are very natural groups. As soon as one introduces the concept of an HNN extension, they appear among the simplest examples of such a structure. If $m$ and $n$ are two nonzero integers, the group $BS(m,n)$ is generated by two elements, denoted $a$ and $b$, which satisfy the relation $ab^{m}a^{-1} = b^{n}$. ...