The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
The Lamé family of connections on the projective line
This paper deals with rank two connections on the projective line having four simple poles with prescribed local exponents 1/4 and . This Lamé family of connections has been extensively studied in the literature. The differential Galois group of a Lamé connection is never maximal : it is either dihedral (finite or infinite) or reducible. We provide an explicit moduli space of those connections having a free underlying vector bundle and compute the algebraic locus of those reducible connections....
Théories de Galois différentielles et transcendance
On décrit des preuves galoisiennes des versions logarithmique et exponentielle de la conjecture de Schanuel, pour les variétés abéliennes sur un corps de fonctions.