- 2019- PostDoc, KIT, postdoctoral supervisor: Roman Sauer.
- 2015-2019 PostDoc, TU-Dresden, postdoctoral supervisor: Andreas Thom.
- 2014-2015 ATER (attaché temporaire de recherche), ENS-Lyon.
- 2011-2015 PhD under the direction of Damien Gaboriau, ENS-Lyon.
This dissertation is about measured group theory, sofic entropy and operator algebras. More precisely, we will study actions of groups on probability spaces, some fundamental properties of their sofic entropy (for countable groups), their full groups (for Polish groups) and the amenable subalgebras of von Neumann algebras associated with hyperbolic groups and lattices of Lie groups. This dissertation is composed of three parts. The first part is devoted to the study of sofic entropy of profinite actions. Sofic entropy is an invariant for actions of sofic groups defined by L. Bowen that generalize Kolmogorov's entropy. The definition of sofic entropy makes use of a fixed sofic approximation of the group. We will show that the sofic entropy of profinite actions does depend on the chosen sofic approximation for free groups and some lattices of Lie groups. The second part is based on a joint work with François Le Maître. The content of this part is based on a prepublication in which we generalize the notion of full group to probability measure preserving actions of Polish groups, and in particular, of locally compact groups. We define a Polish topology on these full groups and we study their basic topological properties, such as the topological rank and the density of aperiodic elements. The third part is based on a joint work with Rémi Boutonnet. The content of this part is based on two prepublications in which we try to understand when the von Neumann algebra of a maximal amenable subgroup of a countable group is itself maximal amenable. We solve the question for hyperbolic and relatively hyperbolic groups using techniques due to Popa. With different techniques, we will then present a dynamical criterion which allow us to answer the question for some amenable subgroups of lattices of Lie groups of higher rank.
- 2010-2011 Internship with Damien Gaboriau, ENS-Lyon (LLP-Erasmus).
- 2009-2011 Corso di Laurea Specialistica in Matematica (Master),
Università degli Studi di Roma “La Sapienza”.
We extend the theory of cost to measured discrete groupoids. The cost of a groupoid is the infimum of the measure of its generating set. We will compute the cost of free groupoids, free products of groupoids and smooth groupoids. Given any countable group we will consider the family of actions of the group on a standard probability space and the cost of the associated groupoids. These values are included in the interval $[\cost(G),\rank(G)]$, where $\rank(G)$ is the rank of $G$ and $\cost(G)$ is the cost of the group. As in the free case, all the actions of a free group have the same cost. We will obtain that the possible costs of a free product are an interval and using free products we will construct an uncountable family of finitely generated group with the same cost values. We will show also that for direct product this set can be highly disconnected.
My MSc thesis hasn't been properly revisioned and it could contain mistakes, misprints and misquotations. pdf.
- 2006-2009 Corso di Laurea Triennale in Matematica (Bachelor), Università degli Studi di Roma “La Sapienza”.