Some unsolvable conjectures in finite p-groups

We survey some unsolvable conjectures in finite p-groups and their research progress.     

Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus

We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we investigate how this estimation can be sharpened under the assumption that the abelian surface does not contain low genus curves. This approach naturally leads us to consider Weil restrictions of elliptic curves and abelian surfaces which do not admit a principal polarization.     

A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.