My master thesis was in cryptography: we dealt with the problem of revocation
of users over a broadcast channel. We used combinatorial and probabilistic
methods based on cover free families to construct good revocation schemes.
Since I started my Phd, my research activity is mainly centered on Algebraic
number theory and Galois theory.
In particular I am studying the structure and
the classification of infinite extensions of global fields with special
prescribed conditions on the local degrees. These conditions are related to the Northcott property (of the finiteness of elements of bounded absolute
Weil height) which is an important tool in the theory of heights of
algebraic sets and has strong connections with problems in algebraic dynamics and to the study of preperiodic points for polynomial maps.
I am also interested in the theory of
elliptic curves, modular forms and L-functions and applications to Criptography.