Daniele Garzoni
Research interests:
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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.
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Papers:
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12. Derangements in non-Frobenius groups
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11. On the irreducibility of f(2^n, 3^m, X) and other such polynomials
with Lior Bary-Soroker and Vlad Matei arXiv
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10. Probabilistic generation of finite almost simple groups
with Jason Fulman and Robert Guralnick arXiv
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9. Conjugacy classes of derangements in finite groups of Lie type
with Sean Eberhard arXiv
Trans. Amer. Math. Soc., to appear.
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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. 2023(14) (2023), 12512--12537.
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6. Large minimal invariable generating sets in the finite symmetric groups
Israel J. Math. 255 (2023), 581--598.
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5. On the number of conjugacy classes of a primitive permutation group
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.
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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.
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Not intended for publication:
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Probability of generation by random permutations of given cycle type
with Sean Eberhard arXiv
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