Mathematics of General Relativity

Penrose's Cosmic Censorship Conjecture (CCC) proposes that the singularities (black holes) of the equations of General Relativity (GR) are hidden within event horizons. Any precise formulation is a claim about the partial differential equations (PDEs) of GR (the Einstein Equations). These are amongst the most problematic equations of mathematical physics. Establishing properties of CCC kind in full generality is beyond the reach of current techniques in mathematical analysis, but it does appear possible to make progress with very restricted cases. This requires the development of novel techniques in PDE theory, and presents one of the most important challenges in modern analysis. This proposal is to bring a world leader in the area to the UK, and enable him to collaborate with young researchers in Cambridge. Anadditional feature of the proposal is a concerted attempt to promote an area in which the UK is regarded as relatively weak.