Slide Presentations - Surveys/colloquium style: [WARNING: download the pdf and open them with a visualizer to see the presentation! (otherwise you will see a page for every of the -many!- clicks!]
These are the slides of my professorial inaugural lecture:
the talk was aimed at presenting to a general audience some of the highlights of research area and achievements (the actual audience consisted of about 150 people, which were a quite equal mixture of colleagues, undergraduate students and general public).
You can also listen to a audio recording of the lecture.
This is a survey/colloquium style talk on mathematical billiards and area preserving flows on surfaces, with particular focus on billiards in rational polygons
and their unfolding to translation surfaces and locally Hamiltonian flows on surfaces.
It is meant as an introduction to Teichmueller dynamics and it
presents my works on locally Hamiltonian flows on surfaces (Annals of Math 2011, J. Modern Dynamics 2009 and Erg. Theory and Dyn. Systems 2007) and my
joint works with J. Smillie (Proc. Lond. Math. Soc. 2011 and AMS Contemporary Math. 2010)
This is a colloquium style talk which surveys some results on mixing for different type of parabolic flows.
It seems that shearing is a key geometric mechanism in producing mixing in several parabolic flows.
We survey and compare mixing results and mechanisms (and spectrum) for time-changes of horocycle flows (joint work with Forni),
mixing for locally Hamiltonian flows and mixing for time-changes of Heisenberg nilflows (joint work with Avila and Forni).
This talk was given at the
conference in memory of Jean-Christophe Yoccoz
at College de France, in June 2017. It presents some work in progress with Jean-Christophe Yoccoz and Stefano Marmi, but it starts with an accessible introduction to the study of Birkhoff sums over interval exchange transformations, in particular deviations, the Kontsevich-Zorich conjecture and limit shapes of Birkhoff sums.
This is a accessible introductory talk on Sturmian sequences and cutting sequences of linear trajectories in regular polygons.
The first focus on the characterization of Sturmian sequences (that is, sequences that code how an irrational line cross a square grid)
in the spirit of C. Series (Math. Intelligencer) and their relation with continued fractions.
The second part focus on results and ideas of proofs based on my joint works (Proc. Lond. Math. Soc. 2011 and AMS Contemporary Math. 2010)
with J. Smillie (Cornell University).
Slide Presentations - conferences/seminar research talks: [WARNING: download the pdf and open them with a visualizer to see the presentation! (otherwise you will see a page for every of the -many!- clicks!]
This talk starts with an introduction on limit theorems in dynamical systems, then focus on my joint work with Michael Bromberg (currently my postdoc in Bristol) on a generalization of a (temporal) Central Limit Theorem for cocycles over rotations, generalizing earlier work by J.Beck and D.Dolgopyat and O. Sarig
(see preprint). A sketch of the symbolic coding and main ideas in the proof is given.
This is a more specialized talk which focus on my joint paper with Giovanni Forni (Maryland) and Artur Avila (IMPA and CNRS) on mixing time-changes of Heisenberg Nilflows
(see Journal of Differential Geometry, 2011).