Research
My main areas of research are Algebraic and Computational Number Theory, and Diophantine Geometry. I am particularly interested in studying arithmetic and diophatine properties of elliptic curves with complex multiplication.
Some key words: Artin's primitive root conjecture, entanglement in families of division fields of abelian varieties, Galois representations, greatest common divisors, heights, natural densities, Mazur's program B, singular moduli.
From April 2021 to December 2024 I am part of the Projet ANR JINVARIANT. I am also part of the board of the Algant Alumni Network (AAN).
Publications
PREPRINTS
Algebraic relations over finite fields that preserve the endomorphism rings of CM j-invariants, with G. Dill, https://arxiv.org/abs/2308.10976.
Ordinary isogeny graphs over F_p: the inverse volcano problem, with H. Bambury and F. Pazuki, https://arxiv.org/abs/2210.01086.
Around the support problem for Hilbert Class Polynomials, with G. Dill, https://arxiv.org/abs/2204.13461.
PUBLISHED AND ACCEPTED ARTICLES
Cyclic reduction densities for elliptic curves, with P. Stevenhagen, Research in Number Theory 9, 61 (2023). Arxiv link: https://arxiv.org/abs/2001.00028
Effective bounds on differences of singular moduli that are S-units, Mathematical Proceedings of the Cambridge Philosophical Society, 174(2), 415-450. Arxiv link: https://arxiv.org/abs/2102.06396
How big is the image of the Galois representations attached to CM elliptic curves?, with R. Pengo, Proceedings of the 18th Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, AMS Contemporary Mathematics (2022). Arxiv link: https://arxiv.org/abs/2201.04046.
Entanglement in the family of division fields of Elliptic Curves with complex multiplication, with R. Pengo, Pacific Journal of Mathematics, Vol. 317, No. 1, 21-66 (2022). Arxiv link: https://arxiv.org/abs/2006.00883
On singular moduli that are S-units, Manuscripta Mathematica, 166(1), pp. 73-90 (2021). Arxiv link: https://arxiv.org/abs/1904.08958.
EXPOSITORY
Singular units do not exist, in Proceedings of the Roman Number Theory Association, Volume 5, number 1 (2020).
Invited talks
UPCOMING TALKS
27 February 2024: Seminario di Teoria dei Numeri, Università di Pisa.
PAST TALKS
29 September 2023: 7th Number Theory Meeting, Politecnico di Torino.
26 September 2023: Journée Clermont-Lyon, Université Lyon 1.
13 July 2023: Number Theory Seminar, Universität Bayreuth.
23 June 2023: Séminaire de Théorie des Nombres, Université Clermont Auvergne.
4 May 2023: Roman Number Theory Symposium, Roman number theory association, Roma.
4 April 2023: Workshop "Density problems in arithmetic", CIRM (Marseille).
30 March 2023: Journée Descartes, Université Aix-Marseille.
3 November 2022: Number Theory lunch seminar, Max-Planck-Institut für Matematik.
2 November 2022: Arithmetic and Algebraic Geometry seminar, University of Amsterdam.
19 October 2022: Number Theory week by GANDA, University of Witswatersrand.
29 July 2022: Park City Mathematics Institute, Park City, Utah.
24 March 2022: Séminaire de Théorie des Nombres, Institut Fourier, Grenoble.
22 March 2022: Séminaire de Théorie des Nombres, Université Clermont Auvergne.
21 February 2022: Number theory seminar, University of Copenhagen.
14 December 2021: JENTE seminar, online event.
24 November 2021: Number Theory lunch seminar, Max-Planck-Institut für Matematik.
15 September 2021: Leiden-Luxembourg Number Theory PhD Day, Université du Luxemburg.
3 June 2021: AGC^2T, online event.
23 September 2020: Séminaire des Théorie des Nombres, Université de Bordeaux.
17 April 2020: Number Theory Seminar, University of Copenhagen.
30 January 2020: Number Theory Seminar, University of Basel.
22-26 May 2019: 2019 AAN Symposium, Centro de Ciencias de Benasque Pedro Pascual.
3 April 2019: Une petite journée diophantienne, Université de Bordeaux.
8 November 2018: PhD seminar "Bernoullis Tafelrunde", University of Basel.
2 May 2018: Number Theory seminar, University of Luxembourg.