This section describes my research works: my vitae, a list of publications and the list of my talks can be found here.
My current main research topic is the resolution of inverse magnetization problems in rocks. Some rocks carry ferro-magnetic materials that behave like microscopic magnets; at the moment when the rock is formed, these magnets align like a compass in the direction of the ambient magnetic field. When the rock further becomes cold and solid, these ferro-magnetic materials stay fixed in that position. For geologists, measuring the characteristics of the magnetization carried by a given rock is a mean of understanding what the magnetic field used to be at a given place and time. However, this magnetization cannot be measured directly: but one may measure the magnetic field that is generated by the magnetization itself. The overall problem that I am addressing consists in finding ways to retrieve the characteristics of the magnetization, based on measurements of the field it produces.
More generally, I am interested with problems at the boundary between mathematical analysis and computer science, such that, typically, approximation problems. Within my PhD thesis, and later on, I worked on problems related to the evaluation of real valued function, either in arbitrary or fixed precision. In particular, I studied the question of how to approximate functions as well as possible by polynomials whose coefficients are floating-point numbers with a given precision. This led me to study objects of algorithmic number theory, such as euclidean lattices. I promote rigorous computing: algorithms that manipulate, in principle, real numbers and functions, shall not only return a numerical value (as accurate as it could be) but must have a clear and proven semantic (such as, e.g. a rigorous bound of all committed errors).
I develop with Christoph Lauter a software called Sollya. It is a toolbox containing efficient and safe implementations of numerical algorithms (such as infinite norm, searching zeros of a function, evaluation of a function with interval arithmetic, Remez' algorithm, plot of a function, etc.). Moreover, Sollya can compute with arbitrary high precision.