Week 04.05.2026 – 10.05.2026

In this talk I will discuss recent progress in uncovering the presence of quantum group symmetries in both 2d and 3d gravity models. This structure is then utilized to better understand various aspects of gravitational models, such as the isometry structure within boundary correlation functions, and edge states at the black hole horizon. Largely based on 2507.13873 and 2505.00501.

We describe two local-global questions generalizing some classical ones considered by Hasse and Cassels, respectively. Along with explaining the relationship between these two problems, we depict some modified Tate-Shafarevich groups whose vanishings imply an affirmative answer to both of them. We also give an overview of the most recent results achieved for the two problems.