Francesco Maria Saettone    


PhD student, Ben-Gurion University of the Negev (expected PhD 2024)
(advisor: Daniel Disegni).

Email: saettone [at] post.bgu.ac.il


Research



I am interested in the arithmetic of algebraic varieties and some related analytic objects. In particular, my research focuses on Shimura curves, automorphic forms, and Chabauty-Kim theory.

My thesis is an ongoing preliminary version of [7] and [8] below.


Work in Progress

[8] Equidistribution for CM points on Shimura curves and ternary quadratic forms

[6] Polylogarithmic motivic Chabauty-Kim for P^1 \ {0, 1, ∞}: the geometric step via resultants, (with David Jarossay, David Lilienfeldt, Ariel Weiss, Sa'ar Zehavi)



Papers and preprints
(Please note that the version here proposed may somehow differ from the journal version.)

[7] Equidistribution of CM points on Shimura curves modulo a ramified prime. [Arxiv Preprint]
Preprint.

[5] On the fundamental groups of the surface parametrizing cuboids, (with David Jarossay, Yotam Svoray) [preprint]
Preprint.

[4] Heights and transcendence of p-adic continued fractions, (with Ignazio Longhi, Nadir Murru)[Arxiv]
To appear on "Annali di Matematica Pura e Applicata".

[3] A profinite theory of distribution: towards the Bateman-Horn conjecture, (with Ignazio Longhi, Luca Demangos) [preliminary draft]
Preprint.

[2] Coset topologies on Z and arithmetic applications, (with Ignazio Longhi, Yunzhu Mu)[Arxiv]
Expo. Math. 41, No. 1, 71-114 (2023).

[1] A novel RSA-like cryptosystem based on a generalization of the Redei rational functions, (with Nadir Murru) [pdf]
Kaczorowski, Jerzy (ed.) et al., Number-theoretic methods in cryptology. First international conference, NuTMiC 2017, Warsaw, Poland, September 11-13, 2017. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 10737, 91-103 (2018).




Seminars

p-adic heights and p-adic L-functions(2023-2024)