  This text, which appeared in volume 2313 of the Springer Lecture Notes in
Math. dedicated to Catriona Byrne, presents problems in two different areas of
algebraic geometry. The first concerns the role of ``infinitely singular'' or
``non Abhyankar'' valuations in the study of local uniformization of valuations
with a view to resolution of singularities in positive characteristic. The
second one concerns the relationship of the geometry of the discriminant of
real miniversal unfoldings in the sense of Thom with the movements of Morse
functions on a cobordism which differential geometers use.
