Singularities is a broad and fast developing research field at the confluence of many mathematical disciplines, both pure and applied. This is a project which grows from new ideas based on synergistic solid collaborations in the last decade. Our project addresses fundamental problems, as well as applications, along three main axes.

Algebraic complexity of optimization problems via Morsification, with several sub-projects and perspectives of applications.

Bifurcation of polynomial maps, combining methods from topology and complex analysis, with several sub-projects.

Images of analytic map germs, singular fibrations, and arc subspaces, project of fundamental research with foreseen developments and applications.