Number Theory

Number Theory Seminar

Schedule 2025/26

Abstracts 2025/26

Sara Checcoli, A little bit of little points generated by torsion

The height is a non-negative real-valued function that measures the arithmetic complexity of an algebraic number. While numbers of minimal height are well understood, many questions remain about numbers of small but non-zero height. One such question is whether a given algebraic extension K of the rationals contains only finitely many elements of bounded height, in which case, following Bombieri and Zannier, K is said to have the Northcott property (N). While this holds for number fields, the situation is more subtle for infinite extensions of the rationals. For example, the maximal abelian extension of the rationals does not have (N), but it follows from a result of Bombieri and Zannier that its subextensions with Galois group of bounded exponent do. In this talk, after giving an overview on the subject, I will present joint work with Gabriel Dill establishing, in particular, a similar result for fields generated by torsion points of abelian varieties over number fields.

Pengcheng Zhang, Meromorphic modular forms and symmetric powers of elliptic curves

We will discuss the link between meromorphic modular forms and symmetric powers of elliptic curves through the p-adic behaviors of the former. In particular, we will discuss the heuristical connection as well as justify the heuristics through numerical observations.

Julien Soumier, From Post-Quantum Cryptography to Isomorphisms of Abelian Varieties

In this talk, we present an algorithm for computing isomorphisms between products of supersingular elliptic curves with known endomorphism rings. This work is motivated by the growing interest in the computation of abelian varieties for post-quantum cryptography. We will begin by reviewing the mathematical objects involved and explaining why they have become relevant for cryptographic purposes. Then we will present our approach that leverages the Deuring correspondence, enabling us to reformulate computational isogeny problems into algebraic problems in quaternion algebras. If time permits, we will conclude by a brief overview of the perspectives it offers.

Past Seminar Editions

• Number Theory Seminar 2024/25
• Number Theory Seminar 2023/24
• Number Theory Seminar 2022/23
• Number Theory Seminar 2021/22
• Number Theory Seminar 2020/21