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# La semaine de l’IMB

La semaine de l’IMB recense l’ensemble des événements de la semaine en cours

• Le 22 septembre 2020 à 10:00
• Séminaire de Théorie Algorithmique des Nombres
Online
Nicolas Mascot (Trinity College Dublin)
Modular Galois representations p-adically using Makdisi's moduli-friendly forms

We will present a p-adic method to compute Galois representations attached to modular forms. This method compares very favourably to the better-known complex-analytic approach. The main ingredient is the use of “moduli-friendly” forms introduced by Makdisi, which allow us to evaluate modular forms at p-adic points of modular curves, and thus to compute in the Jacobian of modular curves without writing down any equations nor q-expansions.

• Le 24 septembre 2020 à 15:30
• Le Colloquium
Salle de Conférences
Sébastien Gouezel (Nantes)
Reporté à une date ultérieure

• Le 25 septembre 2020 à 14:00
• Séminaire de Théorie des Nombres
Salle de Conférences
Francesco Campagna (Copenhague)
Singular moduli and $S$-units
A remarkable property of singular invariants of CM elliptic curves (singular moduli) is that they are algebraic integers. Hence it makes sense to ask, for a fixed set of rational primes S, how many singular moduli are S-units. When the set S is empty, Yu. Bilu, P. Habegger and L. Kühne have answered this question by proving that singular units do not exist. What happens now if we allow S to be a non-empty set of primes? We will discuss this problem and give partial answers.

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