The theme of the conference will be explicit and computational methods in number theory and arithmetic geometry in a broad sense. The format will include scientific talks as well as time for informal collaboration and for coding projects related to (for example) PARI/GP, SageMath, Magma, OSCAR or the L-Functions and Modular Forms Database. On the one hand, various topics where explicit computations have been the key for proving important results will be presented. These will be found in the context of modular forms, the study of rational points, as well as results towards the Birch and Swinnerton-Dyer conjecture. On the other hand, we will also focus on recently stated conjectures, for example the paramodular conjecture by Brumer and Kramer, and challenge participants to exhibit new examples to support such conjectures (in the case of the paramodular conjecture only one non trivial example is currently known). We expect that the colloquium will lead to the emergence of new ideas and methods at the interface of these different fields, to new results as well as to new projects and collaborations.

This conference will be organized with the support of the National Research Agency in the framework of the project « MELODIA ».