**My research field is the qualitative theory of differential equations. Mainly
geometrical aspects of the phase-portrait of complex differential equations. The term "singular foliations"
found below refers to the phase-portrait.
When considering phase-portraits which are compact, complex algebraic varieties, we have to work with singularities
of the differential equations and also with
holomorphic functions which are not defined everywhere (otherwise the maximum principle implies that they are
constants). They are called rational functions
and when they have inverse (also not everywhere defined) such transformations are called birational functions.
The group of birational functions is very rich: in the projective plane or space it is called the Cremona group (a reference to Luigi Cremona).
Part of my results listed below deals with the effect of the Cremona group on foliations, how it changes
the singularities
or how it changes or preserves some global informations of the foliation.
The origin of the idea that qualitative methods must be employed in the study of the differential equations goes back to Henri Poincaré.
The study of the geometry of complex differential equations goes back to Paul Painlevé.
**