During the last 10 days, I was attending J. Palis’ 70th birthday conference held at Atlantico Hotel, Buzios, Brazil. As one could expect from a conference of this size (~220 participants), it was a nice opportunity to talk to coauthors/friends and to learn several interesting tools. Also, since Buzios has plenty of superb beaches (very close to the hotel) and we had 2 hours of lunch time break, the conference atmosphere was an interesting mixture of intense and relaxing moments. Furthermore, I guess that the fact that the young and senior participants were together in the same place provided a great opportunity to the young generations to meet (and talk directly) with the senior generations, so that they could start new collaborations. In particular, I strongly believe that Jacob Palis and the organizers are very proud of this beautiful conference (which was extremely successful in many ways).
Concerning the (intense) conference program (with 5 plenary talks and 2 parallel sessions per day), you can find the details here, but I should advance that I’m planning to write some posts related to some talks (e.g., J.C. Yoccoz, A. Zorich, A. Avila, etc.).
In any case, this post is intended to accomplish two goals: firstly, I’m making the slides of Enrique Pujals’ talk (on Palis’ work) available here (with his permission, of course), and secondly, I’m fulfilling my (public) promise of putting the slides of my talk here. Remark: Please notice that these pdf files contain photos, so that their sizes are relatively big (~46MB and ~34MB resp.)
About Enrique Pujals’ talk, let me mention that it was a very touching moment: during the preparation of his slides, Enrique had the nice idea of inviting some of Jacob’s mathematical sons and nephews to draw some pictures in order to show how Palis influence appears in several contexts; in particular, each slide of Enrique’s talk was a small tribute of some son/nephew of Jacob (whose signature always appears in the corresponding slide). Also, Enrique putted a lot of effort in making the exposition as funny as possible (e.g., when he showed a picture of Gugu’s son illustrating Newhouse phenomena with his hands, Enrique said that Jacob is still recruiting young people to Dynamical Systems). Finally, the talk ended with Enrique embracing Jacob and saying to him that student isn’t a word meant to refer to a past event, but to a present one.
About my talk, I have only to acknowledge the organizers for the imense honor to give the final talk of the conference: in fact, I was extremely touched (and nervous) with this invitation, specially because 10 years ago (during Palis 60th birthday conference), I was a 1st year graduate student trying to choose my primary research area (and of course my choice was particularly influenced by J. Palis). During the talk, I started by telling the audience about my first meeting with Palis. I guess that the first time Palis heard of me was during a visit of Jean-Pierre Serre. In fact, I was so excited to learn that J.P. Serre was at IMPA that I interrupted him in the middle of a calculation (in his office) to ask in Portuguese to take a photo with him. Of course, Serre didn’t understand my request and told to Jacob (IMPA’s director in 1997) about a strange boy who went into his office like a crazy. After this initial bad impression, during Palis 60th birthday conference (in 2000), I talked to him asking for some advice concerning my research career. Instead of giving me a long speech, Palis saw that I was planning to read his joint book with Floris Takens and he told me to take read the book to decide if I liked the subject or not. I acknowledge his advice and asked for an autograph in this book. Again, instead of writing a long dedicatory, he simply put one decisive word of encouragement: Sucess (this appears as the second slide of my talk). After that, I talked about two mathematical results (joint with J.C. Yoccoz, and G. Forni and A. Zorich) and I closed the exposition with a selection of key (serious and funny) moments of the conference. I hope you will enjoy it!