My main research activity revolves around the study of dynamical features of group actions on homogeneous spaces, directed towards applications ranging from geometry to number theory. Classical examples of geometric nature include the geodesic and the horocycle flow on the unit tangent bundle of hyperbolic surfaces. Typically relevant to arithmetic problems is the classification of measures invariant under the evolution of such systems, and the ensuing description of how trajectories distribute in the ambient space.
I’m also interested in various aspects of the interplay between dynamics and probability theory, notably in the investigation of statistical limit theorems in a number of different contexts, from spatial and temporal limit theorems for time averages along orbits of homogeneous flows, to large deviations properties of random walks on discrete structures.
For a closer look at the type of problems I have worked on so far, you may consult my papers below.
Articles and preprints
|The distribution of dilating sets: a journey from Euclidean to hyperbolic geometry||submitted||2023|
|Large hyperbolic circles (with D. Ravotti)||submitted||2022||arXiv|
|Disjointness of higher rank diagonalisable actions on semisimple and solvable quotients (with M. Luethi)||in progress||2021|
|Large deviations for irreducible random walks on relatively hyperbolic groups||2021||arXiv|
|Large deviations for random walks on free products of finitely generated groups||Electron. J. Probab. 26, 1-22||2021||journal||arXiv|
|Temporal limit theorems for horocycle ergodic integrals||Appendix to: Asymptotics and limit theorems for horocycle ergodic integrals à la Ratner (D. Ravotti)||submitted||2021||arXiv|
Here is the manuscript of my PhD thesis.