Interview with Freddy Dumortier

By Bernd Krauskopf
Freddy Dumortier addresses the participants at the conference dinner for his 60th birthday in April 2007; photograph by Bernd Krauskopf

Interview with Freddy Dumortier

by Bernd Krauskopf, University of Bristol, UK

Freddy Dumortier speaks at the dinner of his 60th birthday conference.

Freddy Dumortier is Professor at the Universiteit Hasselt in Belgium. He is well known for his work in bifurcation theory, blow-up techniques and slow-fast systems. His 60th birthday was celebrated in April 2007 in Hasselt and Brussels with the conference Dynamics in Perturbations. Bernd Krauskopf used this opportunity to talk to him at the Belgian Academy of Sciences Building about his views on the field of dynamical systems.

BK: How did you get involved in dynamical systems?

FD: After my Master's research in 1969 on questions of differential topology I was looking for a suitable topic for PhD research. In 1970 I went to a conference in Amsterdam on manifolds to meet and talk to Nico

    The Belgian Academy of Sciences Building
The Belgian Academy of Sciences Building.

Kuipers, whose work I knew through his publications. He advised me to switch my interest to the new and emerging field of dynamical systems and to work with his former student Floris Takens. So I started PhD work on singularities of planar vector fields as Floris's first PhD student.

What was that like?

During my PhD time I was in Brussels, funded by the Fonds voor Wetenschappelijk Onderzoek, and officially supervised by Professor Wuyts. So in effect, I did a long-distance PhD with regular meetings, many of them at the train stations, and through letters when Floris was away for longer periods of time. I really enjoyed the freedom this arrangement gave me and the leadership that Floris provided. It allowed me to find out things all by myself.

What about meeting other researchers?

In summer 1972 I went to a summer school at ICTP in Trieste organised by Jim Eells and Christopher Zeeman. It was a stimulating two months of courses and presentations. There I met a young Brazilian mathematician, Jorge Sotomayor, from the Instituto Nacional de Matemática Pura e Aplicada (IMPA). While we did not work closely together initially, I later published a number of papers with him.

In Brazil in 1974.    

After my promotion in 1973 I spent a whole year at IMPA. In total I must have spent at least three full years of my life there. The atmosphere at IMPA was very open and vibrant with many visitors. Jacob Palis was a main driving force and I took part in his seminar and other seminars. IMPA is also where I met my long-term close collaborator Robert Roussarie for the first time in 1976. He had made use in his work of results in my thesis and we started working together straight away on a question suggested by Jacob Palis. Today Robert and I have more than twenty joint papers and are continuing to work together.

In Brazil in 1974.
Taking notes in Diepenbeek in 1998.
Taking notes in Diepenbeek in 1998.

How do you see yourself as a mathematician?

I am a pure mathematician in the sense that I want to get to the bottom of things by constructing rigorous proofs. I do not feel the urge to delve into an application area, but rather enjoy sorting out the technical issues that are needed to make a proof work. At the same time, I have the hope that my results fall within `Applicable Mathematics'.

Do you have an example of the latter?

With Robert Roussarie and Jorge Sotomayor I worked on the codimension-three unfoldings that arise at degenerate cases of the Bogdanov-Takens bifurcation. In fact, already in 1975 I wrote a letter to Vladimir Arnold asking him to send me the publications of Professor Bogdanov and inquiring whether the generalization to higher codimension had been done. Arnold informed me that, first, Bogdanov is not a professor and, second, the codimension-three problem had been solved. Therefore, I stopped working on this problem. However, it turned out only much later that the codimension-three problem was actually still unresolved, and I picked it up again with Robert and Soto.

    Robert Roussarie, Jorge Sotomayor and Freddy Dumortier at Hasselt University in 1990
Robert Roussarie, Jorge Sotomayor and Freddy Dumortier at Hasselt University in 1990.

After they appeared as Springer Lecture Notes in Mathematics, our results have been applied quite quickly by other colleagues in fields as diverse as laser physics and ecology. I am confident that my more recent work on singular perturbations will also lead to insights and results that are applicable to models arising in different scientific domains.

How do you see the relationship between pure and applied mathematics more widely?

Presenting an unfolding in 1990    

To me both aspects seem essential to mathematics and they should continue to influence each other closely. There really is a need for good research ranging from direct applications, as done by engineers, for example, all the way to work that deals with the foundations of mathematical thinking itself. Policy makers should better be convinced of this point of view as well. However, present funding, certainly in Europe, is primarily directed towards subjects

Presenting an unfolding in 1990.

that have a certain market value, such as cancer or telecommunications research. This is not a bad thing as such, but it creates a need to justify fundamental research, which is no longer seen as useful in its own right. A lot of mathematics is of course quite fundamental. While mathematics is perceived as inexpensive --- and the more so the more theoretical it is --- funders nevertheless expect some sort of return after a few years. This easily creates the message that pure mathematics is not essential. Yet I believe that most countries ought to invest more in fundamental research.

What about funding opportunities for the next generation of mathematicians?

In the last years a lot of new positions for PhD research have been created, but generally the number of permanent faculty to supervise them has stayed the same or has even decreased. Not only does this increase the work load of permanent staff, but it also means that there are insufficient opportunities for young researchers after their PhD. Certainly in Belgium there is a shortage of postdoctoral positions with a perspective of a permanent academic career.

    Freddy with the `Finite bicyclicity shirt' that he received as a thank-you from the students on the 1992 spring course on dynamical systems that he organised in Hasselt
Freddy with the `Finite bicyclicity shirt' that he received as a thank-you from the students on the 1992 spring course on dynamical systems that he organised in Hasselt.

How do you see the role of dynamical systems research in society.

I think that society is only beginning to see how important mathematics is in our daily lives. In particular, statistics is now seen as crucial for any sort of major decision, and sometimes this is taken to absurd extremes. Nevertheless --- and this is positive --- the feeling is that statistics is a must, and this attracts people to become statisticians. The field of dynamical systems, on the other hand, is much less visible in society. I think that we are simply not selling ourselves well enough.

With King Albert II at Hasselt University in 2003     Opening speech of Equadiff2003 in Hasselt
With King Albert II at Hasselt University in 2003. Opening speech of Equadiff2003 in Hasselt.

What do you think needs to be done?

We should really promote more widely the usefulness of mathematics. Indeed, mathematics is applied in very useful things every day and on a large scale, from aeroplanes to mobile phones, but this is often not so well known. I do not have a simple solution, but believe that we should all do more lobbying and public awareness work. For example, I was involved in media activities around the World Mathematics Year 2000. I also try to use all opportunities to get in touch with the press. Some journalists know that they can call me when they have a mathematical question. Personal contacts count and they take a long time to establish. Of course, professional societies such as SIAM are already playing an important role in popularizing mathematics, but we could always do more.


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