Presentation of Professor Pierre Mathonet (Department of Mathematics)

His background, his research...

Professional Background

‘I finished my undergraduate studies in Mathematics in 1994 and began research work under the supervision of Marc De Wilde, in the field of differential geometry. I defended my doctoral thesis in 1998, obtained a First Assistant’s post in 2000 and gained promotion to Tutor level in 2005. I carried out postdoctoral research work at the University of Luxembourg between September 2009 and August 2011.’

Research activities

‘The general theme of my work in differential geometry is the classification of natural operators. Without going into details, which are necessarily technical, we could say that differential geometry studies the manifolds, which are sets endowed with local coordinates (such as the circle, the sphere, the torus, the Möbius strip, etc.), and the objects that can be associated with them (space functions, vector fields, tensor fields, connections, differential operators, etc.). Natural operators are thus operators between these spaces linked to manifolds, which behave correctly with respect to the changes of coordinates.

By way of simple examples, let us mention the de Rham differential or tensor contractions, which are natural in general, raising and lowering the indexes which are natural operations in Riemannian geometry, or the Hamiltonian operator, which is natural in symplectic geometry.

I have been more particularly interested in the classification of natural operators between certain spaces of differential operators, or between tensors and differential operators. I have tackled these problems in classical differential geometry, and since recently in super-geometry, in working jointly with Fabian Radoux (FNRS-ULg).

I have also taken an interest in other subjects, beyond geometry, through meeting up with various people and working on joint projects.

Thus I have since 1995 been working with Jean-Luc Marichal, who hired me as a postdoctoral researcher at the University of Luxembourg between 2009 and 2011.  We are working on more applied subjects, such as the axiomatic characterisation of certain aggregation functions (generalisations of the well known arithmetic mean), the geometrical definition of influence and interaction indexes in the theory of cooperative games, and more recently the theory of coherent systems and several functional equations.

I have also had the pleasure of working within the Faculty of Sciences with Roland Billen, within the context of geographic information systems (GIS), as well as with Thierry Bastin, this time on the classification of quantum entanglement.’

Useful links :

- Talk given at the Faculty Council, December 16, 2011

- Contact details, ULg courses and a list of publications

Presentation of new professors at the Faculty

[top]