Davide Ravotti

I have completed my Ph.D. at the University of Bristol in 2018 under the supervision of Corinna Ulcigrai.

From April to August 2018, I was a Research Associate at the University of Bristol, from September 2018 to February 2019 I was a Postdoctoral Assistant at the University of Zürich, from March 2019 to May 2021 I was a Research Fellow at Monash University, and from June 2021 to February 2024 I was a Postdoctoral Assistant at the University of Vienna.

Since March 2024, I am a Chaire de Professeur Junior CNRS at the Laboratoire Paul Painlevé of the Université de Lille.

Here you can find my full CV.

I study the ergodic and mixing properties of some classes of smooth dynamical systems, in both the finite and infinite measure setting.

I focus on smooth parabolic flows, including locally Hamiltonian flows on surfaces, nilflows, unipotent flows, and their smooth perturbations. I am also interested in their rigidity properties.

Publications and preprints

1. Multiple mixing for parabolic systems, (joint paper with Adam Kanigowski), preprint arXiv:2410.13686, 2024.

2. Horocycle flows on abelian covers of surfaces of negative curvature, (joint paper with Roberto Castorrini), preprint arXiv:2405.08592, 2024.

3. On asymptotic expansions of ergodic integrals for $\Z^d$-extensions of translation flows, (joint paper with Henk Bruin, Charles Fougeron, and Dalia Terhesiu), preprint arXiv:2402.02266, 2024.

4. Quantitative infinite mixing for non-compact skew products, (joint paper with Paolo Giulietti, and Andy Hammerlindl), preprint arXiv:2401.10776, 2024.

5. On rigidity properties of time-changes of unipotent flows, (joint paper with Mauro Artigiani and Livio Flaminio), Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, to appear.

6. Large hyperbolic circles, (joint paper with Emilio Corso), Bollettino dell'Unione Matematica Italiana, to appear.

7. Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows, (joint paper with Livio Flaminio), Nonlinearity, 37, Paper No. 075015, 2024.

8. Asymptotics and limit theorems for horocycle ergodic integrals à la Ratner, (with an appendix by Emilio Corso), Journal de l'École polytechnique - Mathématiques, Vol. 10:305-334, 2023.

9. Quantitative global-local mixing for accessible skew products, (joint paper with Paolo Giulietti, and Andy Hammerlindl), Annales Henri Poincaré, 23:923-971, 2022.

10. Polynomial mixing for time-changes of unipotent flows, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, Vol. XXIII(3):1491-1506, 2022.

11. Mixing for smooth time-changes of general nilflows, (joint paper with Artur Avila, Giovanni Forni, and Corinna Ulcigrai), Advances in Mathematics, 385, Paper No. 107759, 2021.

12. Quantitative equidistribution of horocycle push-forwards of transverse arcs, L'Enseignement Mathématique, 66(1-2):131-146, 2020.

13. Polynomial 3-mixing for smooth time-changes of horocycle flows, (joint paper with Adam Kanigowski), Discrete and Continuous Dynamical Systems, 40(9):5347-5371, 2020.

14. Parabolic perturbations of unipotent flows on compact quotients of SL(3,R), Communications in Mathematical Physics, 371(1):331-351, 2019.

15. Mixing for suspension flows over skew-translations and time-changes of quasi-abelian filiform nilflows, Ergodic Theory and Dynamical Systems, 39(12):3407-3436, 2019.

16. Quantitative mixing for locally Hamiltonian flows with saddle loops on compact surfaces, Annales Henri Poincaré, 18(12):3815-3861, 2017.

17. Measures induced by units, (joint paper with Giovanni Panti), Journal of Symbolic Logic, 78(3):886-910, 2013.

I have been a tutor for the following courses:

• Metric spaces, Banach spaces, Hilbert spaces (Co-lecturer and tutor). Monash University, 2020/21.
• Dynamical Systems and Ergodic Theory. University of Zürich, 2018/19.
• Analysis 1, Foundations and Proof. University of Bristol, 2017/18.
• Introduction to Geometry, Analysis 1, Foundations and Proof. University of Bristol, 2016/17.
• Analysis 1, Linear Algebra and Geometry. University of Bristol, 2015/16.
• Dynamical Systems and Ergodic Theory, Algebra II. University of Bristol, 2014/15.

Here is an example of a class I gave at the ICTP Summer School in Dynamics.

Below you can find the slides for the minicourse I lectured at IMPAN on Ergodic and mixing properties of horocycle flows and their time-changes.

• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4
• Lecture 5