Batiment 36

root systems

Research

G2

My initial research field is representation theory, mainly the qualitative aspect of branching problems in representation theory. For this I use tools from algebraic geometry and algebraic combinatorics (Littelmann path theory). In this area, I first defended a thesis in 1995 under the supervision of Michel Brion. Later, I collaborated with Nicolas Ressayre and Boris Pasquier.

More recently, I have worked on the classification of certain Fano varieties: first, the toric Fano varieties whose fan is built from a root system (in collaboration with Alvaro Rittatore). This paper entitled Gorenstein Fano Generic Torus Orbits closure in G/P was published in the journal Journal of Algebraic Combinatorics. In this work we provide the list of complete homogeneous spaces G/P such that the closure of the generic orbit of the maximal torus T ⊂ G is a Gorenstein-Fano variety.
I then studied with Thibaut Delcroix the low-dimensional spherical Fano varieties. In a work now on ArXiv and submitted in 2023 (Spherical actions on locally factorial Fano varieties of dimension ≤ 4 and rank ≤ 2), we provide the list of spherical Fano varieties of dimension at most 4 and rank at most 2. This list can be found here.

From September 2024 to January 2025, I was on secondment to CNRS and stayed several weeks in Montevideo as part of the new Franco-Uruguayan IRL laboratoire de la Plata to collaborate with Ivan Pan and Alvaro Rittatore. We finalized a work on the automorphism group of a simple derivation of affine space. This paper entitled On polynomial automorphisms commuting with a simple derivation is now published in the Journal of Pure and Applied Algebra.


In the first version of Gorenstein Fano Generic Torus Orbits closure in G/P , the classification in the exceptional cases was done with a small script using the SageMath software as well as Gap3. Even if it is now unnecessary, I leave this script available for the curious.