I am currently working on arithmetic statistics. My main interest is the problem of counting the number of varieties in a family which contain a rational point. This question lies in both algebraic number and in number theory. Key words : Loughran-Rome-Smeets-Sofos conjecture, rational points, sieve methods, analytic number theory.
After my first year of master, I published a short article in La Gaceta de la RSME : An application of the large sieve in number theory (translated from french to spanish by Javier Fresan)
See also :
Asbjørn Nordentoft's webpage (also interested in arithmetic statistics)
Théo Untrau's webpage (interested in exponential sums)