# Research

I work mainly on elliptic curves over number fields. In particular I am interested in the arithmetic of **Q**-curves, namely elliptic curves over number fields that are geometrically isogenous to all of their Galois conjugates. I am also interested in the arithmetic of finite fields, and in particular in the properties of compositional monoids generated by a finite set of polynomials. Recently, I became interested in arithmetic dynamics and arboreal Galois representations.

7) (with Peter Bruin) Strongly modular models of **Q**-curves, submitted. Arxiv.

6) (with Giacomo Micheli
and Reto Schnyder) Irreducible compositions of degree two polynomials over finite fields have regular structure,
submitted. Arxiv.

5) The set of stable primes for polynomial sequences with large Galois group, to appear in
*Proceedings of the AMS*. Arxiv.

4) (with Peter Bruin) On *L*-functions of quadratic **Q**-curves, *Mathematics of Computation*, electronically published on 13 June 2017. Arxiv.

3) (with Giacomo Micheli and Reto Schnyder) On sets of irreducible polynomials closed by composition, in Arithmetic of Finite Fields, volume 10064 of *Lecture Notes in Computer Science*, 77–83. Springer, Cham, 2017. Arxiv.

2) (with Giacomo Micheli) On the existence of infinite, non-trivial *F*-sets, *Journal of
Number Theory*, 1–12, 168, 2016. Arxiv.

1) (with Giacomo Micheli) On Mertens-Cesàro Theorem for Number Fields, *Bulletin of the Australian Mathematical Society*, 93(2), 199–210, 2016. Arxiv.