# Interview with Jacob Palis in 2014

On 15 December 2014 Jacob Palis was interviewed and asked about the project he had undertaken funded by money that he had received as the winner of the Balzan Prize for Mathematics in 2010. Palis and Jean-Christophe Yoccoz were coordinating the Balzan Research Project on Dynamical Systems at the Instituto de Matemática Pura e Aplicada (IMPA), in Brazil.

**Jacob Palis describes his Balzan Project.**

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 honour to receive from the Balzan Foundation. It supports the scientific work of young researchers and the organisation 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.

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.

The project has proceeded 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.

I was of course happy and surprised when I heard that I had won the prize. 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.

Last Updated February 2023