My research is in group theory, and in the interplay between group theory and number theory.
I work on the generation of finite groups and on finite permutation groups. I investigate questions related to Hilbert's irreducibility theorem and to specializations in number theory. I recently started to think about some aspects of combinatorial and geometric group theory.
Here is my arXiv profile.
10. Conjugacy classes of derangements in finite groups of Lie type
with Sean Eberhard, submitted arXiv
9. Probability of generation by random permutations of given cycle type
with Sean Eberhard arXiv
8. On the probability of generating invariably a finite simple group
with Eilidh McKemmie arXiv, journal
J. Pure Appl. Algebra, 227(6) (2023), 107284.
7. Hilbert's irreducibility theorem via random walks
with Lior Bary-Soroker arXiv, journal
Int. Math. Res. Not., to appear.
6. Large minimal invariable generating sets in the finite symmetric groups
Israel J. Math., to appear.
5. On the number of conjugacy classes of a primitive permutation group
Proc. Roy. Soc. Edinburgh Sect. A 153(1) (2023), 115-136.
4. Random generation with cycle type restrictions
with Sean Eberhard arXiv, journal
Algebr. Comb. 4(1) (2021), 1-25.
3. Connected components in the invariably generating graph of a finite group
Bull. Aust. Math. Soc. 104(3) (2021), 453-463.
2. Minimal invariable generating sets
with Andrea Lucchini arXiv, journal
J. Pure Appl. Algebra 224(1) (2020), 218-238.
1. The invariably generating graph of the alternating and symmetric groups
J. Group Theory 23(6) (2020), 1081-1102.
Lior Bary-Soroker, Sean Eberhard, Nick Gill, Andrea Lucchini, Eilidh McKemmie.