The scope of this project is to perform an analytical study of the geometric properties of the interafaces arising in the scalar Ginzburg-Landau-Allen-Cahn equation, with particular attention to possible 1D symmetries.

Also, we would like to analyze the cases in which the operator is singular, degenrate, subelliptic or fractional and to obtain results for PDEs in manifold and in inverse overdetermined problems, since all these models share some important features with classical semilinear PDEs and possess a wide range of potential applications.

To achieve our goals, we would like to build a small, mobile and specialized team of young researchers with outstanding professional skills, specialized in the above subjects, which
has a long history together, new upcoming projects and a network to spread out to.