Number Theory @ Pisa

My main interest is Iwasawa theory which studies modules (like class groups and Selmer groups) associated to algebraic number fields and abelian varieties in all characteristics, in an attempt to link algebraic invariants (like orders of class groups and ranks of elliptic curves) to analytic ones (i.e. special values of L-functions). Recently I have been working on a research program on Drinfeld modular forms to establish an analog of Hida theory for function fields.

I work in the area of Algebraic Number Theory and my research is mainly focused on the study of properties of local and global fields related to ramification. Recently, I have also studied problems connected with the determination of the Galois module structureof rings of integers of number fields. My research has a theoretical approach, but I like effective results.

My research interests lie in the area known as Diophantine geometry. I work mostly with elliptic curves and abelian varieties, as well as low-genus curves, and try to connect their arithmetic to their geometric properties. I am also interested in many problems with a computational flavour (explicit determination of rational points, rigorous determination of endomorphism rings...)

My current research concerns various subjects mainly related with Diophantine approximation to values of some special functions, including the Riemann zeta-function, the Euler dilogarithmic or polylogarithmic functions, etc. I employ some algebraic and analytic tools including the permutation group method, introduced by G. Rhin and myself about 20 years ago, and the saddle-point method in several complex variables for the asymptotic study of multiple integrals depending on a real parameter.