Dynamics of the Weil-Petersson geodesic flow and First Palis-Balzan International Symposium on Dynamical Systems

During the last two weeks I attended two very pleasant conferences:

• from June 18 to 22 there was in AIM (Palo Alto, US) a conference on Dynamics of the Weil-Petersson geodesic flow;
• from June 25 to 30 there was in IMPA (Rio, Brazil) a conference entitled First Palis-Balzan International Symposium on Dynamical Systems around the so-called Palis conjecture/program for a global understanding of dynamical systems.

For the first conference, it was my first time participating in a conference in AIM style and I enjoyed it a lot: it gave me the opportunity to learn a lot of the geometry and dynamics of the Weil-Petersson flow (my second favorite geodesic flow on moduli spaces after Teichmuller flow) and/or interesting question on this topic directly from experts like J. Brock, K. Burns, F. Ledrappier, H. Masur, Y. Minsky, M. Mirzakhani, M. Pollicott and S. Wolpert among (several) others.  In particular, it is likely that I will write some posts on this topic in the future.

For the second conference, I was really happy to visit IMPA and to discuss with many friends. Also, I felt extremely honored to deliver a talk in this conference. Indeed, even though my choice of topic was not original for readers of this blog, my talk “Fractal geometry of non-uniformly hyperbolic horseshoes” concerned a work still in progress (with J. Palis and J.-C. Yoccoz) giving a sort of continuation of an article by J. Palis and J.-C. Yoccoz (see here), and my talk was delivered at Auditorium Ricardo Mañé, the same place were J.-C. Yoccoz announced in 2000 the results of his article with J. Palis during the International Conference on Dynamical Systems (in honor of J. Palis’ 60th birthday). Furthermore, I was in the audience for J.-C. Yoccoz’s talk 12 years ago and, as I was in the first year of my PhD, I remember that I could barely follow the first 10 minutes of the talk. In particular, it never came to my mind that I could work in this subject, let alone collaborate with J. Palis and J.-C. Yoccoz on a continuation of their project!

Anyhow, let me close this short post by making the slides of my talk in Palis-Balzan conference here (they are a variant of the slides in this previous post) and by pointing out that all talks in Palis-Balzan conference were recorded by IMPA’s staff and all videos are available here (and, for instance, the link for the video of my talk is here).