Davide Ravotti

I am a Postdoctoral Researcher at the Faculty of Mathematics of the University of Vienna.

My pronouns are he/him/his.


Faculty of Mathematics
University of Vienna
Oskar Morgenstern-Platz 1
1090 Vienna Austria


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, and from March 2019 to May 2021 I was a Research Fellow at Monash University.

Since June 2021, I am a Postdoctoral Researcher at the University of Vienna, working with Henk Bruin.

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. On rigidity properties of time-changes of unipotent flows, (joint paper with Mauro Artigiani and Livio Flaminio), preprint arXiv:2209.01253, 2022.

  2. Large hyperbolic circles, (joint paper with Emilio Corso), preprint arXiv:2208.07771, 2022.

  3. Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite mixing asymptotics for horocycle flows, (joint paper with Livio Flaminio), preprint arXiv:2207.08263, 2022.

  4. 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.

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

  6. 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.

  7. 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.

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

  9. 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.

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

  11. 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.

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

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


Mar. 2023: Universtité de Bourgogne, Dijon, France.
Mar. 2023: Conference 56th Spring Topology and Dynamical Systems Conference, online seminar.
Feb. 2023: TU Graz, Graz, Austria.
Feb. 2023: University of Pisa, Pisa, Italy.
Jan. 2023: Nicolaus Copernicus University, Torun, Poland.
Nov. 2022: Tsinghua University (online seminar).
Oct. 2022: KTH, online seminar.
Jul. 2022: Conference Summer Topology Conference, Vienna, Austria.
Jun. 2022: Workshop Ruelle Resonances in Parabolic Dynamics, Zürich, Switzerland.
May 2022: Jagiellonian University in Krakow, online seminar.
Apr. 2022: Universtité de Lille, Lille, France.
Apr. 2022: IST Austria, Klosterneuburg, Austria.
Feb. 2022: Workshop Dynamics, Foliations, and Geometry II, Regensburg, Germany.
Jan. 2022: The Budapest-Wien Dynamics Seminar, Wien, Austria.
Oct. 2021: University of Zürich, Zürich, Switzerland.
Mar. 2021: UNSW Pure Math Seminar, online seminar.
Oct. 2020: Vienna Ergodic Seminar, online seminar.
Jul. 2020: Sydney Dynamics Group, online seminar.
Apr. 2020: University of Maryland, online seminar (here is the video of the talk).
Apr. 2020: Monash University, Melbourne, Australia.
Dec. 2019: Conference AustMS, Melbourne, Australia.
Sep. 2019: Conference Smooth and Homogeneous Dynamics, Bangalore, India (here is the video of the talk).
Jul. 2019: Conference Dynamics of Parabolic Flows, Zürich, Switzerland.
Mar. 2019: Monash University, Melbourne, Australia.
Dec. 2018: Scuola Normale Superiore, Pisa, Italy.
Sep. 2018: Conference Dynamics Days Europe, Loughborough, UK.
Jan. 2018: Queen Mary University, London, UK.
Nov. 2017: Scuola Normale Superiore, Pisa, Italy.
Oct. 2017: University of Warwick, Coventry, UK.
Oct. 2017: University of Manchester, Manchester, UK.
Aug. 2017: Conference Dynamics in Number Theory and Geometry, Kingston, Canada.
Jun. 2017: Workshop Modern Trends in the Ergodic Theory of Dynamical Systems, Rome, Italy.
Mar. 2017: University of Bristol, Bristol, UK.
Jan. 2017: Workshop One-day Workshop on Dynamical Systems, ICTP, Trieste, Italy.
Jan. 2017: University of Udine, Udine, Italy.

At the University of Vienna

2023S: Lecturer for the course Ergodic Theory (joint with Henk Bruin). Click here for further information.

2022W: Lecturer for the course Measure and Integration Theory (joint with Henk Bruin). Click here for further information.

2022S: Lecturer for the course Homogeneous Dynamics. Click here for further information.

2021W: Problem classes for the course Basic concepts in Topology.

Previous teaching activities

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.

Student supervision

Gibeom Kim (Bachelor thesis), January 2023.

Minicourse at IMPAN

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

  • Lecture 1
  • Lecture 2
  • Lecture 3
  • Lecture 4
  • Lecture 5
  • Lecture 6