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.

- Study theoretical aspects of systems of polynomial equations and try to answer the question ``what is the best form for the set of solutions?''
- Study algorithmic answers to the question ``how to compute this form of the set of solutions at the lowest cost?''
- Study implementation techniques for my algorithms to make the best use of today's computers.
- Apply these algorithms and software to unsolved problems.

These four research directions are supported by two research grants.

**Hardware Acceleration Technologies Enabling Polynomial System Solving,**- which is a Discovery grant funded by
**NSERC of Canada**.-
**Comprehensive Optimization of Parametric Kernels for Graphics Processing Units,**- which is a Collaborative Research and Development (CRD) Grant project funded by
**CAS Research, IBM Canada Lab.**and**NSERC of Canada**.

A short overview of my research group in 8 **slides.**

More details can be found in my
**CV in PDF format**.