# 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, to appear on *Quarterly Journal of Mathematics*. 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*, 87, no. 309, 459–499, 2018. 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.