# 2024/2025

- 2024-10-0111:00Salle 2Aurel Page (CANARI)Equidistribution of supersingular elliptic curves with extra structureSeveral algorithmic problems on supersingular elliptic curves are currently under close scrutiny. When analysing algorithms or reductions in this context, one often runs into the following type of question: given a supersingular elliptic curve $E$ and an object $x$ attached to $E$, if we consider a random large degree isogeny $f : E \to E'$ and carry the object $x$ along $f$, how is the resulting $f(x)$ distributed among the possible objects attached to $E'$? We propose a general framework to formulate this type of question precisely, and prove a general equidistribution theorem under a condition that is easy to check in practice. The proof goes from elliptic curves to quaternionic automorphic forms via an augmented Deuring correspondence, and then to classical modular forms via the Jacquet–Langlands correspondence. This is joint work with Benjamin Wesolowski.
- 2024-09-2411:00Salle 2Reza Dasbasteh (Universidad de Navarra)Additive Twisted Codes: New Distance Bounds and Infinite Families of Quantum CodesIn this talk, we present a new construction of quantum codes that enables the integration of a broader class of classical codes into the mathematical framework of quantum stabilizer codes. Next, we discuss new connections between twisted codes and linear cyclic codes and provide novel bounds for the minimum distance of twisted codes. We demonstrate that classical tools, such as the Hartmann-Tzeng minimum distance bound, are applicable to twisted codes. This has led to the discovery of five new infinite families and many other examples of record-breaking, and sometimes optimal, binary quantum codes. Additionally, we explore the role of the $\gamma$ value on the parameters of twisted codes and present new findings regarding the construction of twisted codes with different $\gamma$ values but identical parameters.