Research interests:

My research is in group theory, and in the interplay between group theory and number theory.

I like asymptotic questions in finite group theory. For example, questions involving large finite simple groups, or permutation groups of large degree. I also like monodromy groups, and problems related to Hilbert's irreducibility theorem and specializations in number theory.

Here is my arXiv profile.

Papers:

• On a conjecture of Peter Neumann on fixed points in permutation groups (with Robert Guralnick and Martin Liebeck)     arXiv

​• Irreducibility of the characteristic polynomials of random tridiagonal matrices (with Lior Bary-Soroker and Sasha Sodin), J. Number Theory 280 (2026), 973--998.     arXiv, journal      

​​​​• Derangements in non-Frobenius groups, Proc. Lond. Math. Soc. 131 (2025) no 4, e70091.     arXiv, journal

​​• On the irreducibility of f(2^n, 3^m, X) and other such polynomials (with Lior Bary-Soroker and Vlad Matei), Math. Z. 310 (2025), 12 pp.     arXiv, journal

​• Probabilistic generation of finite almost simple groups (with Jason Fulman and Robert Guralnick), Adv. Math. 452 (2024), 109796, 33 pp.     arXiv, journal

• Conjugacy classes of derangements in finite groups of Lie type (with Sean Eberhard), Trans. Amer. Math. Soc. 12 (2025), 536--575.     arXiv, journal    

• On the probability of generating invariably a finite simple group (with Eilidh McKemmie), J. Pure Appl. Algebra 227(6) (2023), 107284, 37 pp.     arXiv, journal

• Hilbert's irreducibility theorem via random walks (with Lior Bary-Soroker), Int. Math. Res. Not. 2023(14) (2023), 12512--12537.     arXiv, journal

• Large minimal invariable generating sets in the finite symmetric groups (with Nick Gill), Israel J. Math. 255 (2023), 581--598.     arXiv, journal

• On the number of conjugacy classes of a primitive permutation group (with Nick Gill), Proc. Roy. Soc. Edinburgh Sect. A 153(1) (2023), 115-136.     arXiv, journal

• Random generation with cycle type restrictions (with Sean Eberhard), Algebr. Comb. 4(1) (2021), 1-25.     arXiv, journal

• Connected components in the invariably generating graph of a finite group, Bull. Aust. Math. Soc. 104(3) (2021), 453-463.     arXiv, journal

• Minimal invariable generating sets (with Andrea Lucchini), J. Pure Appl. Algebra 224(1) (2020), 218-238.     arXiv, journal

• The invariably generating graph of the alternating and symmetric groups, J. Group Theory 23(6) (2020), 1081-1102.     arXiv, journal

Not intended for publication:

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Probability of generation by random permutations of given cycle type (with Sean Eberhard).     arXiv