56:53
publiée le 18 avril 2025
Extremal eigenvectors, the spectral action, and the zeta spectral triple
De Alain Connes
![[1237] Moments de fonctions et $L$ stabilité homologique](/media/cache/video_light/uploads/video/Bourbaki.png)
On binary quartic Thue equations and related topics
De Gary Walsh
Apparaît dans la collection : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire
In a recent paper, Istvan Gaal and Laszlo Remete studied the integer solutions to binary quartic Thue equations of the form $x^4-dy^4 = \pm 1$, and used their results to determine pure quartic number fields which contain a power integral basis. In our talk, we propose a new way to approach this diophantine problem, and we also show how an effective version of the abc conjecture would allow for even further improvements. This is joint work with M.A. Bennett. We also discuss a relation between this quartic diophantine equation to recent joint work with P.-Z. Yuan.
