Davide Ravotti

I am a Research Fellow at the School of Mathematics of Monash University.

Contacts

School of Mathematics
Monash University
9 Rainforest Walk, Clayton Campus
Victoria 3800 Australia

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, and from September 2018 to February 2019 I was a Postdoctoral Assistant at the University of Zürich.

Since March 2019, I am a Research Fellow at Monash University, working with Andy Hammerlindl.

Here you can find my full CV.

I study the ergodic and mixing properties of some classes of smooth dynamical systems.

I am interested in smooth parabolic flows, in particular locally Hamiltonian flows on compact surfaces, time-changes of nilflows, and perturbations of unipotent flows on quotients of semisimple Lie groups, and, more recently, in partially hyperbolic diffeomorphisms.

Publications and preprints

  1. Quantitative equidistribution of horocycle push-forwards of transverse arcs, preprint arXiv:1910.03187, 2019.

  2. Polynomial decay of higher order correlations for discrete-series reparametrizations of horocycle flows, (joint paper with Adam Kanigowski), preprint arXiv:1909.08799, 2019.

  3. Mixing for smooth time-changes of general nilflows, (joint paper with Artur Avila, Giovanni Forni, and Corinna Ulcigrai), preprint arXiv:1905.11628, 2019.

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

  5. 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.

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

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

Talks

Sep. 2019: Conference Smooth and Homogeneous Dynamics, Bangalore, India.
Jul. 2019: Conference Dynamics of Parabolic Flows, Zuerich, 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.

I have been a tutor for the following courses:

  • 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.