Local talks on Antoine Leudière

Elliptic curves, Drinfeld modules, and computations

Thu, 13 Mar 2025 00:00:00 +0000

We will talk about Drinfeld modules, and how they compare to elliptic curves for algorithms and computations.

Drinfeld modules can be seen as function field analogues of elliptic curves. They were introduced in the 1970’s by Vladimir Drinfeld, to create an explicit class field theory of function fields. They were instrumental to prove the Langlands program for GL2 of a function field, or the function field analogue of the Riemann hypothesis.

Contributing to SageMath: a guide for mathematicians

Wed, 29 Jan 2025 00:00:00 +0000

In this talk, we outline the process of contributing to SageMath. By that, we mean all kinds of code modifications, ranging from bug fixing and documentation enhancing, to adding complete new modules. The ultimate goal is for these modifications to be included in the standard distribution of SageMath.

The contributing process in fact reduces to a number of individual steps, some code-related, and some community-related. We will go through each step individually, presenting the key issues, and how to solve them.

Drinfeld modules in SageMath

Fri, 07 Apr 2023 00:00:00 +0000

Drinfeld modules are mathematical objects that were introduced in the 1970s to answer profound questions in algebra, particularly in the context of the class field theory for function fields. Over time, the theory of Drinfeld modules has become well-established and is now recognized as an essential tool in various significant areas of Mathematics, such as the Langlands program. Notably, Laurent Lafforgue, who used Drinfeld modules to solve open problems from the Langlands program for function fields, was awarded with the Fields Medal in 2002.