# Igor Khavkine: Conformal Killing Initial Data

**Time: **
Tue 2019-09-24 11.00 - 12.00

**Location: **
Seminar Hall Kuskvillan, Institut Mittag-Leffler

**Participating: **
Igor Khavkine, Czech Academy of Sciences

### Abstract

We find necessary and sufficient conditions ensuring that the vacuum development of an initial data set of the Einstein's field equations admits a conformal Killing vector. We refer to these conditions as conformal Killing initial data (CKID) and they extend the well-known Killing initial data that have been known for a long time. The procedure used to find the CKID is a classical argument based on the computation of a suitable propagation identity. The propagation identity is valid in any pseudo-Riemannian signature. In Lorentzian signature it involves hyperbolic operators, while in Riemannian it involves elliptic ones, which may be of independent interest. (Based on arXiv:1905.01231 , with A. García-Parrado.)