Interview avec Jacob Palis et Welington De Melo 15.12.2014 (anglais)

#### Brésil

# Jacob Palis

## Prix Balzan 2010 pour les mathématiques (pures et appliquées)

### Pour ses contributions fondamentales à la théorie mathématique des systèmes dynamiques.

#### Interview avec Jacob Palis et Welington De Melo

www.balzan.org 15 décembre 2014

**A recent interview with the 2010 Balzan Prizewinner Jacob Palis and Welington Celso De Melo from the Instituto de Matemática Pura e Aplicada (IMPA).**

Palis was the seventh Prizewinner in Balzan’s history in the discipline of Mathematics. He was awarded for his “fundamental contributions to the mathematical theory of dynamical systems”. **Welington Celso De Melo** is a Brazilian mathematician at IMPA, the National Institute of Pure and Applied Mathematics.

We had the opportunity to speak with Professors Palis and de Melo in a recent phone interview.

We discussed the ongoing project that Palis started in 2011 with the monies from the Balzan Prize.

*I got the prize in 2010. My research project is a five-year one that started in 2011 and runs through 2015. We are funding it with half the money coming from the prize that I had the honor to receive from the Balzan Foundation. It supports the scientific work of young researchers and the organization of Symposia. This is a wonderful idea of the Balzan Foundation, since several relevant activities are possible because of this project. We also get some funding from other sources, but the Foundation prize money covers the main part of such activities.*

Jacob Palis is coordinating his Balzan Research Project on Dynamical Systems at the IMPA, Brazil, together with Jean-Christophe Yoccoz, from the College de France.

*This mathematical field can be used to model the evolution of phenomena in nature, like weather predictions and climate, among other applications. As part of the project, two very successful Palis-Balzan Symposia have taken place, the first at IMPA in 2012 and the second at the Institut Henri Poincaré – Paris in 2013. A third and final one will occur again at the Institut Henri Poincaré in June 2015. It’s very symbolic that the Balzan Symposia take place at such an Institute named after one of the greatest mathematicians of all time and the father of the modern theory of dynamics.*

How has your project progressed these years?

*Exceedingly well. It is to be noted that one of the participants of the project, ***Artur Avila**, was awarded the prestigious Fields Medal this year. He is the first mathematician that has obtained his PhD in an Institution in the Southern Hemisphere, namely IMPA, to be awarded with a Fields Medal. He works on many areas of dynamics, going from there to applications in other areas. For instance, he made use of dynamical systems in the Spectral Theory of Schrödinger Equations, which are very important in physics and mathematics. He solved the case of one-dimensional equations and pointed a possible way to deal with the equations in higher dimensions. Despite the fact that he works in many fields of mathematics, he has always been a dynamicist at heart.

Besides granting some post-doctoral fellowships, we also have been providing funding for the exchange of visitors that has led to a number of publications thanks to the Balzan Research Project.

The participation on the two Balzan’s work shop by myself and my former students A. Avila, A. Koksard, P. Guarino, and M. Pacifico was very inspiring. We look forward for the next one, noted Professor de Melo. **What did you think when you heard you that you had won the prize?**

*I was of course happy and surprised. Memories came to my mind, for instance, my 42 PhD students at IMPA. Welington de Melo, also taking part in this interview, was the first one that concluded his degree in 1972. In turn, he was Avila’s PhD advisor, who finished his degree about 30 years after de Melo at the age of 21. In my case, I got my PhD under Stephen Smale, a great mathematician, during the period 1964-1967 at Berkeley. He won the Fields Medal in 1966. It was for me a great incentive to work with him and a number of colleagues in dynamical systems. Smale has visited IMPA in the late fifties invited by Mauricio Peixoto, who was the first to work in dynamics at IMPA.*

Today, thanks to Avila, a lot of young people in Brazil are excited to have some people to follow, and to do great mathematics in Brazil. And the Balzan Foundation is playing a relevant role in the process.

Are there links between the Balzan prizewinners in Mathematics and your institution or your field of study? From Andrej Kolmogorov (1962) to Enrico Bombieri (1980), to Jean-Pierre Serre (1985), Armand Borel (1992), Mikhail Gromov (1999), Pierre Deligne (2004), Jacob Palis (2010) and Dennis Sullivan (2014)?

*Kolomogorov was certainly relevant to Brazilian Mathematics and his influence was very important at IMPA in dynamical systems. For a period, he was the main person worldwide in some areas of dynamics and we have had a lot of contact with some of his students. Gromov is very important to the area of Geometry and has had a strong influence at IMPA. Finally, there is a very solid link between mathematicians at IMPA and Dennis Sullivan, who has visited the Institute many times and worked with its researchers.*

Sullivan has provided very substantial contributions to dynamics, while now he works in topology.

Sullivan was announced as a winner of this year’s Balzan prize in Mathematics. We conclude by saying that Avila began his studies at IMPA when he was 18 years old and early on he was studying the main ideas of Dennis Sullivan in dynamics.

Susannah Gold

New York