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Paul R. Halmos - Lester R. Ford Award

Martin Bellet - 10/10/2014

A Question of Elegance

A version of " Christiane's Hair " set

Last August, Jacques Lévy-Véhel, an Inria research team director (Regularity team), and his friend and colleague, Franklin Mendivil, received the Paul R. Halmos - Lester R. Ford. Jacques Lévy-Véhel took our questions about this award.

You received the Paul R. Halmos - Lester R. Ford Award. Can you tell us more about this honour?

Each year, the award recognizes the best articles published in The American Mathematical Monthly . It is bestowed by the Mathematical Association of America (MAA) and gives its recipients international visibility. The journal is intended for the entire mathematical community rather than those working in specialised fields. The subjects must therefore be understood at least by masters students in mathematics. In contrast, the selection is rather high, with approximately 8% of articles submitted accepted for publication. From among these fifty-odd articles, the best three or four are chosen by the MAA for the Halmos-Ford Award.

What is the subject of your contribution?

Our article concerns certain geometric objects built from Cantor sets*. While very simple to build, they have counterintuitive and bizarre properties! In this article, we had the idea of no longer taking away 1/3 of the interval unit as usual, but to let the number vary from 0 to 1, then to stack the results to obtain a two-dimensional figure (see accompanying illustration). With this research, we were able to confirm that the properties of the planar representation were even more surprising than the original set.

How do you explain your receiving the award?

While the article makes no revolutionary contribution, it concerns concepts that all mathematicians have probably dealt with at one time or another. We took an elegant approach using simple tools. The notion is essential in our community: reaching a goal with a solution that is too complex is not always satisfying. I think this in part explains the award.

The unusual title of the article, " Christiane's hair " , may also have played a role!

Why did you choose to write an article on this subject?

The choice was made after a discussion with Franklin Mendivil with whom I've worked for many years on modelling irregular phenomena. We discovered that both of us were interested in stacking of Cantor sets early in our careers. We then wanted to apply the current methods that we're working on. In the process, we discovered we could approach the subject in a simpler manner, which is how we decided to submit the article to The American Mathematical Monthly.

*The Cantor set is located in the interval between 0 and 1. It is built by removing the central third of this interval and then repeating the operation on the two remaining segments indefinitely until “point dust” remains. It was created by the German mathematician Georg Cantor in the late 19th century.

Keywords: Mathematical Association of America Cantor set Award Publication Inria Saclay Ile-de-France