Week 30.05.2022 – 05.06.2022

This workshop will include a broad range of topics related to black holes and horizons, such as low-dimensional gravity, de Sitter gravity, supersymmetric microstate counting, AdS/CFT, and IR aspects of gravity.

The Horrocks bundle (not to be confused with the Horrocks-Mumford bundle) is an indecomposable holomorphic rank 3 bundle over CP^5 with c_2=3. It can be interpreted as a solution of the Yang-Mills equations on the quaternionic projective plane HP^2, via a Penrose transform and twistor equation. In joint work with Udhav Fowdar, this realization leads to the existence of nowhere-vanishing spinors on HP^2 invariant by SU(3). I shall use this example to introduce instantons associated with G-structures in higher dimensions, cohomogeneity-one actions by SU(3), and Spin(7) structures on 8-manifolds.

We discuss period-index bounds for the unramified Brauer group of function fields of hyperelliptic curves over number fields. We describe a link to the question of Hasse principle for smooth intersection of quadrics.