Daniele Garzoni

Research interests:

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.

Preprints:

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

    with Sean Eberhard     arXiv 

Papers:

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

    with Eilidh McKemmie     arXiv

    J. Pure Appl. Algebra, to appear.

7. Hilbert's irreducibility theorem via random walks

    with Lior Bary-Soroker     arXiv

    Int. Math. Res. Not., to appear.

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

    with Nick Gill     arXiv

    Israel J. Math., to appear.

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

    with Nick Gill     arXiv, journal                                        

    Proc. Roy. Soc. Edinburgh Sect. A (2021), 1-22.

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.

    arXiv, journal

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.

    arXiv, journal

Coauthors:

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