Jean-Daniel Boissonnat : Geometry in high dimensional spaces

What are your research topics?

The aim of my area of research, computational geometry, is to develop data structures and algorithms in the field of geometry. Among the numerous areas of application, my research team Geometrica and I have specifically worked on mesh generation and processing for visualisation or numerical simulations, surface reconstruction and robot motion planning. On a more fundamental level, we have worked on geometric data structures, randomized algorithms and robustness issues in geometric computing. The results of our research are distributed via the CGAL open source library, which is the leading library in our field and is also marketed by GeometryFactory, a start-up established in 2003.

What does your GUDHI project, as accepted by the ERC, have to offer?

GUDHI means Geometry Understanding in Higher Dimensions. The aim of the project is to extend the techniques we have developed in dimensions higher than 3  and to develop a geometric and topological approach for data analysis. Although the data are not necessarily of a geometric nature,  we view them as points in a metric space, which is most frequently high dimensional. The generally accepted hypothesis is that, although it is embedded in spaces of high dimensions, data lives usually close to a much smaller structure, the geometric and topological properties of which it is important to compute, in order to gain a better understanding of the system that produced the data. At a time when the quantity of available data is increasing exponentially, this new approach could have a significant impact. The aim of the GUDHI project is to progress from mathematical and algorithmic foundations to applications validated experimentally. A major part of the project relates to the development of an open software platform, which will act as a medium for research and the distribution of results. Collaborations with astrophysicists and biologists are already planned.

In practice, what will the grant be used for?

The project will be launched on 1st February 2014 and will last for five years. The grant will provide a significant boost for our research and will enable a top-flight team to be assembled by recruiting researchers, post-docs, PhD students and engineers. Like Geometrica, the team will be based at Saclay and Sophia Antipolis. The project should be of benefit to the entire algorithmic geometry and topology community by making software and data available.