When I am asked to summarize my research activity in a short and simple sentence, I answer that I am applying Computer Science to Mathematics. Indeed, even if certain questions such as computing GCDs of integers have been studied for centuries, it remains a challenge today to solve them efficiently on computers, in particular on parallel architectures.
Another example, which is in fact my favorite problem, is the solving of systems of polynomial equations. This fundamental question, well studied in Algebra textbooks, still offers many algorithmic and implementation challenges in order to address users' needs.
My research activity has four directions. First, I study theoretical aspects of systems of polynomial equations and try to answer the question ``what is the best form for the set of solutions?'' Then, I study algorithmic answers to the question ``how to compute this form of the set of solutions at the lowest cost?'' Next, I study implementation techniques for my algorithms to make the best use of today's computers. When the prototype solver is ready, I apply it to unsolved problems. This last step terminates with the distribution of a new solver, before entering a new cycle theory, algorithms, implementation, applications motivated by new challenging problems or architectures.
These four research directions are supported by three research grants
More details can be found in my CV in PDF format