Award - PhD
Clément Maria wins the Gilles Kahn Prize 2015 for his work as a member of the Geometrica research team
Clément Maria - ESA 2012
The Gilles Kahn Prize 2015, awarded by the French Computer Science Society (SIF) and sponsored by the Academy of Sciences, has been won by Clément Maria for his doctoral thesis entitled, ‘Algorithms and Data Structures in Algorithmic Topology’, supervised by Jean-Daniel Boissonnat of the Geometrica project team, and based on research carried out at the Inria Sophia Antipolis – Méditerranée Research Centre.
Clément, tell us about your career so far?
I developed a taste for algorithmics when preparing for university. So it wasn’t surprising that I chose to study Computer Science and Mathematics when I became a student at ENS Rennes in 2008. For my Masters, I went to study the various aspects of algorithmics at the University of Aarhus in Denmark, before moving to Paris to join the MPRI Masters in Computer Science programme. I was also able to gain a number of research placements at Inria and the Federal Institute of Technology (ETH) in Zurich.
This experience, particularly abroad, gave me a much wider view of the various fields of research in computer science. This was how I developed an interest in algorithmic geometry and topology, eventually joining Jean-Daniel Boissonnat in the Geometrica team at the Inria Sophia Antipolis - Méditerranée Research Centre to study for my PhD.
You have just won the Academy of Sciences Gilles Kahn Prize for your PhD work with the Geometrica team. Tell us a little about the work that you did during your three years studying for a PhD?
For my PhD, I wanted to investigate the algorithmic aspects of Topological Data Analysis (TDA). TDA is an unconventional approach to the analysis of data, in which statistical data is considered as a cloud of geometric points defining a shape. The challenge is to describe the appearance of the shape drawn in this way, in particular features such as voids and cavities, or even wrapping or twisting. Despite its newness, this approach has already been picked up by applied scientists, and it has been used successfully in fields as diverse as dynamic systems and artificial intelligence. Before I started my PhD, the concept of shape inference from a cloud of points had already been formalised mathematically in persistent homology theory.However, the technique had not been scaled to a practically useful level, in which the geometric shapes represented by the data are usually complex and multi-dimensional. The aim of my work was to use original and efficient algorithmic methods to solve the problem of topological data analysis from a computer science point of view.
My research therefore focused on introducing new algorithms and data structures to estimate a shape from sampled data points, to calculate its persistent homology, and then to refine this topological analysis in a number of directions. As the practical aspect of the problem was important, we also developed open-source software to make these techniques widely available, and the software that I developed is now available as part of the Gudhi software library.
The beauty of the problem is that it impinges on number of different mathematical fields, including multi-dimensional geometry, algebraic topology and quiver theory. Our computer science solutions involve all these, as well as the various fields of algorithmics.
And now, how do you see your career progressing?
The application of computer science techniques to topological analysis falls within the field of algorithmic topology. I am currently a postdoc at the University of Queensland, in Brisbane, Australia, in a team led by Benjamin Burton. I am studying another aspect of algorithmic topology, low-dimensional topology and knot theory. There are still many fascinating questions to be answered in algorithmic topology, and I intend to carry on researching in this field.
The Geometrica project team, jointly located in the Saclay and Sophia Research Centres, was succeeded by the Datashape team at the end of 2015.