**Carlo Pagano **

Max Planck Institute for Mathematics, Bonn.

NEW WEBPAGE

I am a postdoc at Glasgow University and a visitor at the Max Planck Institute for Mathematics in Bonn, where I was a post-doc from September 2018 to August 2020. Before that I completed my Ph.D. in 2018 under the supervision of Hendrik Lenstra in Leiden, Netherlands.

My interests lie in number theory.

**Publications and preprints: **
**17.** The size of arboreal images, I: exponential lower bounds for PCF and unicritical polynomials
(arXiv).

**16.** On Malle's conjecture for nilpotent groups, I
(with P. Koymans arXiv).

**15.** A sharp upper bound for the 2-torsion of class groups of multiquadratic fields
(with P. Koymans arXiv).

**14.** Higher Redei reciprocity and integral points on conics
(with P. Koymans arXiv).

**13.** Effective convergence of coranks of random Redei matrices
(with P. Koymans arXiv).

**12.** Constraining images of quadratic arboreal representations
(with A. Ferraguti arXiv)

*International Mathematics Research Notices*, (2020).

**11.** On the 4-rank of class groups of Dirichlet biquadratic fields
(with E. Fouvry and P. Koymans arXiv).

*Journal of the Institute of Mathematics of Jussieau *, (2020)

**10.** Diameters of random Cayley graphs of finite nilpotent groups
(with D. El-Baz arXiv).

* Journal of Group Theory, * (2021)

**9.** Higher genus theory
(with P. Koymans arXiv)

*International Mathematics Research Notices*, (2020).

**8.** On the negative Pell equation
(with S. Chan, P. Koymans and D. Milovic arXiv).

**7.** The inverse problem for Arboreal Galois representations of index two
(with A. Ferraguti and D. Casazza, arXiv).

**6.** On the distribution of Cl(*K*)[*l*^{∞}] for degree *l* cyclic fields
(with P. Koymans, arXiv).

*J. Eur. Math. Soc. (JEMS) (to appear).*

**5.** Jump sets in local fields
(arXiv).

**4.** Unit equations and Fermat surfaces in positive characteristic
(with P. Koymans)

*Acta Arithmetica*, **193** (2020), 133-156.

**3.** 4-ranks and the general model for ray class groups of imaginary quadratic number fields
(with E.Sofos, arXiv).

**2.** Calculating the power residue symbols and Ibeta (with K. de Boer)

*Proceedings of the International Symposium on Symbolic and Algebraic Computation*, (2017).

**1.** On the equation x+y=1 in finitely generated groups in positive characteristic (with P. Koymans)

*The Quarterly Journal of Mathematics*, **68** (2017), 923-934.

**CV**

**Notes: **