Geometry is involved in many domains (manufacturing, simulation, communication, virtual world, …), raising many challenging questions related to the representations of shapes, to the analysis of their properties, and to the computation with these models. The stakes are multiple: the accuracy in numerical engineering, simulation, and optimization, the quality in the design and manufacturing processes, as well as the capacity of modeling and of analyzing physical problems.
AROMATH is a project in Computational Algebraic Geometry, investigating algebraic approaches to address these geometric problems. It aims at developing new methods for high quality and efficient modeling and processing in geometry, based on algebraic representations and tools.
We explore two main research directions:
- High order geometric modeling: we aim at exploiting algebraic representations, for the accurate description of shapes, and for developing efficient geometric modeling techniques,
- Robust algebraic-geometric computation: we aim at developing efficient algorithms, stable against numerical perturbation, for solving the algebraic problems occurring in geometry.