Andrea Fontanella is visiting DAMTP at the University of Cambridge today (Tuesday 17th October) to give a talk in the Mathematical Physics Seminar series. The title of his talk is “Towards bulk extension of near-horizon geometries“. A link to the seminar page is here, and the talk is based the paper “Moduli Spaces of Transverse Deformations of Near-Horizon Geometries” co-authored with Jan Gutowski which can be found here. In the talk, he will consider the long-term inverse problem of determining all black hole solutions associated to a prescribed near-horizon geometry. The approach is based on expanding the near-horizon fields at first order in the radial coordinate, the so-called moduli, and it is shown that the moduli must satisfy a system of elliptic PDEs, which implies that the space of moduli is finite dimensional. A picture of the front of the Mathematical Sciences Building at DAMTP is shown below.