Research interests:

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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.

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Preprints:

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10. Conjugacy classes of derangements in finite groups of Lie type

      with Sean Eberhard, submitted     arXiv

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9. Probability of generation by random permutations of given cycle type

    with Sean Eberhard     arXiv 

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Papers:

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8. On the probability of generating invariably a finite simple group

    with Eilidh McKemmie     arXiv, journal

    J. Pure Appl. Algebra, 227(6) (2023), 107284.

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7. Hilbert's irreducibility theorem via random walks

    with Lior Bary-Soroker     arXiv, journal

    Int. Math. Res. Not., to appear.

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6. Large minimal invariable generating sets in the finite symmetric groups

    with Nick Gill     arXiv, journal

    Israel J. Math., to appear.

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5. On the number of conjugacy classes of a primitive permutation group

    with Nick Gill     arXiv, journal                                        

    Proc. Roy. Soc. Edinburgh Sect. A 153(1) (2023), 115-136.

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4. Random generation with cycle type restrictions

    with Sean Eberhard     arXiv, journal

    Algebr. Comb. 4(1) (2021), 1-25.

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3. Connected components in the invariably generating graph of a finite group

    Bull. Aust. Math. Soc. 104(3) (2021), 453-463.

    arXiv, journal

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2. Minimal invariable generating sets

    with Andrea Lucchini     arXiv, journal

    J. Pure Appl. Algebra 224(1) (2020), 218-238.

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1. The invariably generating graph of the alternating and symmetric groups

    J. Group Theory 23(6) (2020), 1081-1102.

    arXiv, journal

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Coauthors:

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Lior Bary-Soroker, Sean Eberhard, Nick Gill, Andrea Lucchini, Eilidh McKemmie.

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