I am a Postdoctoral Researcher at the Faculty of Mathematics of the University of Vienna.
My pronouns are he/him/his.
Contacts
Faculty of Mathematics
University of Vienna
Oskar MorgensternPlatz 1
1090 Vienna Austria
davide.ravotti@gmail.com
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.
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

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

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

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.

Asymptotics and limit theorems for horocycle ergodic integrals à la Ratner, (with an appendix by Emilio Corso), Journal de l'École polytechnique  Mathématiques, Vol. 10:305334, 2023.

Quantitative globallocal mixing for accessible skew products, (joint paper with Paolo Giulietti, and Andy Hammerlindl), Annales Henri Poincaré, 23:923971, 2022.

Polynomial mixing for timechanges of unipotent flows, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, Vol. XXIII(3):14911506, 2022.

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

Quantitative equidistribution of horocycle pushforwards of transverse arcs, L'Enseignement Mathématique, 66(12):131146, 2020.

Polynomial 3mixing for smooth timechanges of horocycle flows, (joint paper with Adam Kanigowski), Discrete and Continuous Dynamical Systems, 40(9):53475371, 2020.

Parabolic perturbations of unipotent flows on compact quotients of SL(3,R), Communications in Mathematical Physics, 371(1):331351, 2019.

Mixing for suspension flows over skewtranslations and timechanges of quasiabelian filiform nilflows, Ergodic Theory and Dynamical Systems, 39(12):34073436, 2019.

Quantitative mixing for locally Hamiltonian flows with saddle loops on compact surfaces, Annales Henri Poincaré, 18(12):38153861, 2017.

Measures induced by units, (joint paper with Giovanni Panti), Journal of Symbolic Logic, 78(3):886910, 2013.
Talks
Sep. 2023: Jagiellonian University, Krakow, Poland.
Sep. 2023: Conference XXII Congresso UMI, Pisa, Italy.
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 BudapestWien 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 Oneday Workshop on Dynamical Systems, ICTP, Trieste, Italy.
Jan. 2017: University of Udine, Udine, Italy.
At the University of Vienna
2023W: Lecturer for the course Measure and Integration Theory. Click here for further information.
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.
Minicourses
May 2023: 6h minicourse Ergodic and mixing properties of horocycle flows and their timechanges, IMPAN, Warsaw, Poland.
Previous teaching activities
I have been a tutor for the following courses:
 Metric spaces, Banach spaces, Hilbert spaces (Colecturer 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.
Student supervision
Gibeom Kim (Bachelor thesis), January 2023.