The project is devoted to the study of families of algebraic varieties, with applications to both classical complex algebraic geometry and arithmetic geometry in mind. The two complementary directions concern deformation theory and the topology of degenerations. The more specific goals belong into four groups:

1. Topological aspects of logarithmic geometry
2. Deformation theory in positive characteristic
3. Deformation theory of zero-dimensional schemes
4. Serre–Tate theory for Calabi–Yau varieties and liftings of Frobenius.