Daniele Garzoni
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, random polynomials, and specializations in number theory.
Here is my arXiv profile.
Papers:
13. Irreducibility of the characteristic polynomials of random tridiagonal matrices
with Lior Bary-Soroker and Sasha Sodin
arXiv
12. Derangements in non-Frobenius groups
11. On the irreducibility of f(2^n, 3^m, X) and other such polynomials
with Lior Bary-Soroker and Vlad Matei arXiv
Math. Z., to appear
10. Probabilistic generation of finite almost simple groups
with Jason Fulman and Robert Guralnick arXiv, journal
Adv. Math., 452 (2024), 109796, 33 pp.
9. Conjugacy classes of derangements in finite groups of Lie type
with Sean Eberhard arXiv, journal
Trans. Amer. Math. Soc. 12 (2025), 536--575.
8. On the probability of generating invariably a finite simple group
with Eilidh McKemmie arXiv, journal
J. Pure Appl. Algebra, 227(6) (2023), 107284, 37 pp.
7. Hilbert's irreducibility theorem via random walks
with Lior Bary-Soroker arXiv, journal
Int. Math. Res. Not. 2023(14) (2023), 12512--12537.
6. Large minimal invariable generating sets in the finite symmetric groups
Israel J. Math. 255 (2023), 581--598.
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.
Not intended for publication:
Probability of generation by random permutations of given cycle type
with Sean Eberhard arXiv