Possible PhD project subjects include:

1. Enumerative geometry of the gradient.
2. Study of the local image of analytic map germs.
3. Real polynomial functions: bifurcation locus, deformations, curvature, Lipschitz geometry.
4. Applications of singularities to optimization.

Applicants should send to Professor M. Tibar (by email at the address mihai-marius.tibar@univ-lille.fr ) the following items:

• A motivation letter of 1-2 pages.
• A CV, and the grades of the last 2 years.
• Two recommendation letters from professors of the last 1 or 2 years.

Possibility of co-directed PhD projects, and of co-tutelle with the University of Lille.