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:
• Irreducibility of the characteristic polynomials of random tridiagonal matrices
with Lior Bary-Soroker and Sasha Sodin arXiv, journal
J. Number Theory 280 (2026), 973--998.
• Derangements in non-Frobenius groups
Proc. Lond. Math. Soc. 131 (2025) no 4, e70091.
• On the irreducibility of f(2^n, 3^m, X) and other such polynomials
with Lior Bary-Soroker and Vlad Matei arXiv, journal
Math. Z. 310 (2025), 12 pp.
• Probabilistic generation of finite almost simple groups
with Jason Fulman and Robert Guralnick arXiv, journal
Adv. Math. 452 (2024), 109796, 33 pp.
• Conjugacy classes of derangements in finite groups of Lie type
with Sean Eberhard arXiv, journal
Trans. Amer. Math. Soc. 12 (2025), 536--575.
• 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.
• Hilbert's irreducibility theorem via random walks
with Lior Bary-Soroker arXiv, journal
Int. Math. Res. Not. 2023(14) (2023), 12512--12537.
• Large minimal invariable generating sets in the finite symmetric groups
Israel J. Math. 255 (2023), 581--598.
• On the number of conjugacy classes of a primitive permutation group
Proc. Roy. Soc. Edinburgh Sect. A 153(1) (2023), 115-136.
• Random generation with cycle type restrictions
with Sean Eberhard arXiv, journal
Algebr. Comb. 4(1) (2021), 1-25.
• Connected components in the invariably generating graph of a finite group
Bull. Aust. Math. Soc. 104(3) (2021), 453-463.
• Minimal invariable generating sets
with Andrea Lucchini arXiv, journal
J. Pure Appl. Algebra 224(1) (2020), 218-238.
• 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