Related papers: Marked length spectrum rigidity in groups with con…

We show that the (topological) full group of a minimal pseudogroup over the Cantor set satisfies various rigidity phenomena of topological dynamical and combinatorial nature. Our main result applies to its possible homomorphisms into other…

We consider group measure space II$_1$ factors $M=L^{\infty}(X)\rtimes\Gamma$ arising from Bernoulli actions of ICC property (T) groups $\Gamma$ (more generally, of groups $\Gamma$ containing an infinite normal subgroup with relative…

We introduce the notion of measurable bounded cohomology for measured groupoids, extending continuous bounded cohomology of locally compact groups. We show that the measurable bounded cohomology of the semidirect groupoid associated to a…

We prove that rigid representations of the fundamental group of a surface into the group of oreintation-preserving homeomorphisms of the circle are geometric, thereby establishing a converse statement of a theorem by the first author.

We study actions of groups by homeomorphisms on $\mathbf{R}$ (or an interval) that are minimal, have solvable germs at $\pm \infty$ and contain a pair of elements of a certain type. We call such actions coherent. We establish that such an…

An action of a complex reductive group $\mathrm G$ on a smooth projective variety $X$ is regular when all regular unipotent elements in $\mathrm G$ act with finitely many fixed points. Then the complex $\mathrm G$-equivariant cohomology…

We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…

We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly…

Let $G$ be a right-angled Artin group with $|\mathrm{Out}(G)|<+\infty$. We prove that if a countable group $H$ with bounded torsion is measure equivalent to $G$, with an $L^1$-integrable measure equivalence cocycle towards $G$, then $H$ is…

We consider the ortho spectrum of hyperbolic surfaces with totally geodesic boundary. We show that in general the ortho spectrum does not determine the systolic length but that there are only finitely many possibilities. As a corollary we…

A contractive condition is addressed for extended 2-cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. It is…

We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…

Let $\Gamma_1,\dots,\Gamma_n$ be hyperbolic, property (T) groups, for some $n\ge 1$. We prove that if a product $\Gamma_1\times\dots\times\Gamma_n \curvearrowright X_1\times\dots\times X_n$ of measure preserving actions is stably orbit…

Let $G$ be a countable group whose action on a metric space $X$ involves a contracting isometry. This setting naturally encompasses groups acting on Gromov hyperbolic spaces, Teichm{\"u}ller space, Culler-Vogtmann Outer space and CAT(0)…

Two groups are virtually isomorphic if they can be obtained one from the other via a finite number of steps, where each step consists in taking a finite extension or a finite index subgroup (or viceversa). Virtually isomorphic groups are…

We initiate a quantitative study of measure equivalence (and orbit equivalence) between finitely generated groups, which extends the classical setting of $\mathrm L^p$ measure equivalence. In this paper, our main focus will be on amenable…

We define an operation on finite graphs, called co-contraction. By showing that co-contraction of a graph induces an injective map between right-angled Artin groups, we exhibit a family of graphs, without any induced cycle of length at…

This thesis is dedicated to random walks on spaces with non-positive curvature. In particular, we study the case of group actions on CAT(0) spaces that admit contracting elements, that is, whose properties mimic those of loxodromic…

A framework (a straight-line embedding of a graph into a normed space allowing edges to cross) is globally rigid if any other framework with the same edge lengths with respect to the chosen norm is an isometric copy. We investigate global…

It is known that if each point $x$ of a dynamical system is generic for some invariant measure $\mu_x$, then there is a strong connection between certain ergodic and topological properties of that system. In particular, if the acting group…